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ADHOC NOW 2008 Utility-Based Uplink Power Control in CDMA Wireless Networks with Real-Time Services

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Eirini Eleni Tsiropoulou

University of New Mexico

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Lecture Notes in Computer Science 5198

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Jon M. Kleinberg

Cornell University, Ithaca, NY, USA

Alfred Kobsa

University of California, Irvine, CA, USA

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ETH Zurich, Switzerland

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Stanford University, CA, USA

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Weizmann Institute of Science, Rehovot, Israel

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University of Bern, Switzerland

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Indian Institute of Technology, Madras, India

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Gerhard Weikum

Max-Planck Institute of Computer Science, Saarbruecken, Germany

David Coudert David Simplot-Ryl

Ivan Stojmenovic (Eds.)

Ad-hoc, Mobile

and Wireless Networks

7th International Conference, ADHOC-NOW 2008

Sophia-Antipolis, France, September 10-12, 2008

Proceedings

Volume Editors

David Coudert

Centre de Recherche, INRIA Sophia Antipolis

Mascotte, INRIA, I3S, CNRS UMR 6070, Univ. Nice Sophia

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E-mail: David.Simplot@liﬂ.fr

Ivan Stojmenovic

SITE, University of Ottawa

Ontario K1N 6N5, Canada

and

EECE,University of Birmingham, UK

E-mail: stojmenovic@storm.ca

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Preface

The 7th International Conference on Adhoc, Mobile and Wireless Networks

(AdHoc-NOW 2008) was held at INRIA Sophia Antipolis - M´editerran´ee, on

the French Riviera, during September 10–12, 2008. The six previous conferences

in the series were held in Morelia (2007), Ottawa (2006), Cancun (2005), Vancou-

ver (2004), Montreal (2003) and Toronto (2002). The purpose of this conference

is to provide a forum for researchers from academia/industry and practitioners

to meet and exchange ideas regarding recent developments in the areas of ad-hoc

wireless networks.

AdHoc-NOW 2008 received 110 submissions submitted by authors form the

following 33 countries: Algeria, Australia, Austria, Belgium, Brazil, Canada,

China, the Czech Republic, Denmark, Finland, France, Germany, Greece, India,

Iran, Israel, Italy, Japan, Luxembourg, Macedonia, Norway, Pakistan, Poland,

Slovakia, South Africa, South Korea, Sri Lanka, Sudan, Switzerland, Taiwan,

Tunisia, the UK and the USA. Each paper was assigned to three members of

the Technical Program Committee (TPC). Based on the reviews, we decided

to accept 39 submissions as regular papers, 24 of them with 25 minutes’ oral

presentation time, and 15 as poster presentations. All of the accepted papers

appear in this volume.

We thank the three invited speakers at this conference, Srdjan Krco (Eric-

sson, Ireland), Xuemin (Sherman) Shen (University of Waterloo, Canada), and

Stephan Olariu (Old Dominion University, USA) for accepting our invitation to

share their insights on new developments in their research areas.

We would like to express our sincere gratitude to all the members of the

local organizing committee who invested their time and energy to organize this

conference. In particular, we thank F. Huc, C. Jullien, P. Lachaume, X. Li,

C. Molle, and H. Rivano.

Finally, we acknowledge the various sources of ﬁnancial support for AdHoc-

NOW 2008, namely the GDR ASR ResCom, European project IST AEOLUS

IP-015964, INRIA Sophia Antipolis - M´editerran´ee, I3S, Orange Labs, R´egion

Provence Alpes Cˆotes d’Azur, and the Universit´edeNiceSophia.

September 2008 David Coudert

David Simplot-Ryl

Ivan Stojmenovic

Organization

Steering Committee

Evangelos Kranakis (Carleton Univ.)

Michel Barbeau (Carleton Univ.)

S.S. Ravi (SUNY Albany)

Ioanis Nikolaidis (Univ. Alberta)

Violet R. Syrotiuk (Arizona State Univ.)

Thomas Kunz (Carleton Univ.)

General Chair

David Coudert (INRIA)

Program Co-chairs

David Simplot-Ryl (INRIA)

Ivan Stojmenovic (Univ. Birmingham)

Poster and Demonstration Chairs

Srdjan Krco (Ericsson)

Michel Syska (Univ. Nice Sophia)

Publicity Chair

Herv´eRivano(CNRS)

Submission Chair

Xu Li (Carleton Univ.)

Local Arrangements

Corinne Jullien (CNRS)

Florian Huc (CNRS)

Patricia Lachaume (INRIA)

Christelle Molle (DGA-CNRS)

VIII Organization

Technical Program Committee

E. Altman (INRIA)

D. Barthel (Orange Labs)

J. Cao (Hong Kong Polytechnic Univ.)

N. Abu-Ghazaleh (SUNY Binghamton)

E. Chavez (Univ. Michoacana)

C. Constantinou (Univ. Birmingham)

C. Tung Chou (Univ. New South Wales)

M. Denko (Univ. Guelph)

M. Dohler (CTTC)

E. Fleury (ENS Lyon)

H. Frey (Univ. Southern Denmark)

H. Karl (Univ. Paderborn)

E. Kranakis (Carleton Univ.)

D. Krizanc (Wesleyan Univ.)

T. Kunz (Carleton Univ.)

X.-Y.Li(IIT)

W. Liang (Australian National Univ.)

H. Liu (Univ. Ottawa)

C. Mascolo (Univ. College of London)

L. Narayanan (Concordia Univ.)

I. Nikolaidis (Univ. Alberta)

J. Opatrny (Concordia Univ.)

M. Papatriantaﬁlou (Chalmers Univ.)

P. Penna (Univ. Salerno)

P.M. Ruiz (Univ. Murcia)

Q.-A.Zeng(Univ.Cincinnati)

External Referees1

Andrea Clementi

Pierluigi Crescenzi

Mieso Denko

Ranran Ding

Ralph El-Khoury

Juan J. Galvez

Georgios Georgiadis

Vineet Josh

Ralf Klasing

Xu Li

Weifa Liang

Ke Liu

Hao Luan

Xufei Mao

Juan Antonio Martinez

Benoˆıt Miscopein

Lata Narayanan

Giovanni Neglia

Napole˜ao Nepomuceno

Ioanis Nikolaidis

Bence Pasztor

Paolo Penna

Giuseppe Persiano

Herv´eRivano

Francisco J. Ros

Juan Antonio Sanchez

Divya Sardana

Jean Schwoerer

Qingyan Xie

Ping Xu

Xiao-Hua Xu

Cheng Zhu

Sponsors

GDR ASR ResCom

European project IST AEOLUS IP-015964

INRIA Sophia Antipolis - M´editerran´ee

I3S

Orange Labs

R´egion Provence Alpes Cˆotes d’Azur

Universit´e de Nice Sophia

1This list has been automatically compiled from the conference’s database. We

apologize for any omissions or inaccuracies.

Table o f Cont ents

Local Maximal Matching and Local 2-Approximation for Vertex Cover

in UDGs (Extended Abstract) ..................................... 1

Andreas Wiese and Evangelos Kranakis

Opportunistic Clock Synchronization in a Beacon Enabled Wireless

Sensor Network .................................................. 15

Nicola Altan and Erwin P. Rathgeb

Mitigating Reply Implosions in Query-Based Service Discovery

Protocols for Mobile Wireless Ad Hoc Networks...................... 29

Antˆonio Tadeu A. Gomes, Artur Ziviani, Luciana S. Lima,

Markus Endler, and Guillaume Chelius

Adaptive MANET Routing: A Case Study .......................... 43

Liang Qin and Thomas Kunz

Self-interference in Multi-hop Wireless Chains: Geometric Analysis and

Performance Study ............................................... 58

Saquib Razak and Nael B. Abu-Ghazaleh

Energy-Eﬃcient Multi-path Routing in Wireless Sensor Networks ...... 72

Philipp Hurni and Torsten Braun

Approximating Minimum-Power k-Connectivity ...................... 86

Zeev Nutov

A Secure Cross-Layer Protocol for Multi-hop Wireless Body Area

Networks ....................................................... 94

Dave Singel´ee, Benoˆıt Latr´e, Bart Braem, Michael Peeters,

Marijke De Soete, Peter De Cleyn, Bart Preneel,

Ingrid Moerman, and Chris Blondia

Communication in Random Geometric Radio Networks with Positively

Correlated Random Faults ........................................ 108

Evangelos Kranakis, Michel Paquette, and Andrzej Pelc

The Mathematics of Routing in Massively Dense Ad-Hoc Networks ..... 122

Eitan Altman, Pierre Bernhard, and Alonso Silva

Localized Spanner Construction for Ad Hoc Networks with Variable

Transmission Range .............................................. 135

David Peleg and Liam Roditty

X Table of Contents

Geographic Routing with Early Obstacles Detection and Avoidance in

Dense Wireless Sensor Networks ................................... 148

Luminita Moraru, Pierre Leone, Sotiris Nikoletseas, and Jose Rolim

DIN: An Ad-Hoc Algorithm to Estimate Distances in Wireless Sensor

Networks ....................................................... 162

Freddy L´opez Villafuerte and Jochen Schiller

Cheating on the CW and RTS/CTS Mechanisms in Single-Hop IEEE

802.11e Networks ................................................ 176

Szymon Szott, Marek Natkaniec, and Andrzej R. Pach

Adapting BitTorrent to Wireless Ad Hoc Networks ................... 189

Mohamed Karim Sbai, Chadi Barakat, Jaeyoung Choi,

Anwar Al Hamra, and Thierry Turletti

Optimal Gathering Algorithms in Multi-Hop Radio Tree-Networks ith

Interferences .................................................... 204

Jean-Claude Bermond and Min-Li Yu

Distributed Qualitative Localization for Wireless Sensor Networks ...... 218

Karel Heurtefeux and Fabrice Valois

A Lower Bound on the Capacity of Wireless Ad Hoc Networks with

Cooperating Nodes ............................................... 230

Anthony S. Acampora and Louisa Pui Sum Ip

Attacks on CKK Family of RFID Authentication Protocols ........... 241

Zbigniew Gol

ebiewski, Krzysztof Majcher, and Filip Zag´orski

On Backoﬀ in Fading Wireless Channels ............................ 251

SeonYeong Han and Nael B. Abu-Ghazaleh

TSLA: A QoS-Aware On-Demand Routing Protocol for Mobile Ad Hoc

Networks ....................................................... 265

C. Mbarushimana and A. Shahrabi

Query Dissemination with Predictable Reachability and Energy Usage

in Sensor Networks ............................................... 279

Zinaida Benenson, Markus Bestehorn, Erik Buchmann,

Felix C. Freiling, and Marek Jawurek

A Prediction Based Cross-Layer MAC/PHY Interface for CDMA Ad

Hoc Networks ................................................... 293

Pegdwind´e Justin Kouraogo, Fran¸cois Gagnon, and Zbigniew Dziong

Utility-Based Uplink Power Control in CDMA Wireless Networks with

Real-Time Services ............................................... 307

Timotheos Kastrinogiannis, Eirini-Eleni Tsiropoulou, and

Symeon Papavassiliou

Tab le of Co n t e nt s XI

Adaptive Priority Based Distributed Dynamic Channel Assignment for

Multi-radio Wireless Mesh Networks................................ 321

Tope R. Kareem, Karel Matthee, H. Anthony Chan, and

Ntsibane Ntlatlapa

Ranking and Sorting in Unreliable Single Hop Radio Network ......... 333

Marcin Kik

Distributed Monitoring in Ad Hoc Networks: Conformance and Security

Checking........................................................ 345

Wissam Mallouli, Bachar Wehbi, and Ana Cavalli

Improved Distributed Dynamic Power Control for Wireless Mesh

Networks ....................................................... 357

Thomas Olwal, Felix Aron, Barend J. van Wyk, Yskandar Hamam,

Ntsibane Ntlatlapa, and Marcel Odhiambo

Identifying the Boundary of a Wireless Sensor Network with a Mobile

Sink ............................................................ 369

Majid I. Khan, Wilfried N. Gansterer, and G¨

unter Haring

Analysis of IEEE 802.11e Line Topology Scenarios in the Presence of

Hidden Nodes ................................................... 380

Katarzyna Kosek, Marek Natkaniec, and Andrzej R. Pach

Interference and Congestion Aware Reservations in Wireless Multi-hop

Networks ....................................................... 391

St´ephane Rousseau, Laure Lebrun, Herv´eA

ıache, and Vania Conan

Low-Cost and Accurate Intra-ﬂow Contention-Based Admission Control

for IEEE 802.11 Ad Hoc Networks ................................. 401

Abdelouahid Derhab

An Energy-Eﬃcient Query Aggregation Scheme for Wireless Sensor

Networks ....................................................... 413

Jun-Zhao Sun

Novel Algorithms for the Network Lifetime Problem in Wireless

Settings ........................................................ 425

Michael Elkin, Yuval Lando, Zeev Nutov, Michael Segal, and

Hanan Shpungin

Message Quality for Ambient System Security ....................... 439

Ciar´an Bryce

Request Satisfaction Problem in Synchronous Radio Networks ......... 451

Benoˆıt Darties, Sylvain Durand, and J´erˆome Palaysi

XII Table of Contents

A Novel Mobility Model from a Heterogeneous Military MANET

Trace ........................................................... 463

Xiaofeng Lu, Yung-chih Chen, Ian Leung, Zhang Xiong, and

Pietro Li`o

Measuring Energy-Time Eﬃciency of Protocol Performance in Mobile

Ad Hoc Networks ................................................ 475

Ida Pu, Yuji Shen, and Jinguk Kim

A Framework for Joint Cross-Layer and Node Location Optimization

in Mobile Sensor Networks ........................................ 487

Vladimir Marbukh and Kamran Sayraﬁan-Pour

Author Index .................................................. 497

Local Maximal Matching and Local

2-Approximation for Vertex Cover in UDGs

(Extended Abstract)

Andreas Wiese1,, and Evangelos Kranakis2,

1Technische Universität Berlin, Institut für Mathematik, Germany

2School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa,

Ontario, Canada K1S 5B6

Abstract. We present 1−approximation algorithms for the maximum

matching problem in location aware unit disc graphs and in growth-

bounded graphs. The algorithm for unit disk graph is local in the sense

that whether or not an edge is in the matching depends only on other

vertices which are at most a constant number of hops away from it. The

algorithm for growth-bounded graphs needs at most O(log log∗n+



O(1) ·log∗ncommunication rounds during its execution. Using these

matching algorithms we can compute vertex covers of the respective

graph classes whose size are at most twice the optimal.

1 Introduction

Unit Disk Graphs (UDGs) is a widely used concept for modeling ad hoc and

wireless networks. In these graphs, the connectivity of two nodes is established if

and only if their Euclidean distance of these two nodes is at most one. Therefore,

UDGs model the setting of identical wireless devices on a plane without obstacles

that could obscure the wireless signals. There are also other models for wireless

networks, e.g., Quasi-Unit-Disk-Graphs (Q-UDGs) which were ﬁrst introduced

by Barriere et al. [2]. In Q-UDGs there is a certain radius such that two nodes

which are closer to each other than are always connected whereas nodes with

a larger distance than one unit are always disconnected. This and other models

for wireless networks are captured by growth-bounded graphs. These are graphs

in which for any vertex vthe size of an independent set of the vertices which are

at most rhops away from vis at most f(r)(for a certain growth-function f).

In the setting of wireless and ad-hoc-networks there is usually no global com-

munication backbone available. So for organizing the network traﬃc and solving

Research conducted while the authors were visiting the School of Computing Sci-

ence at Simon Fraser University, Vancouver.

 Research supported by a scholarship from DAAD (German Academic Exchange

Service).

 Research supported in part by NSERC (Natural Science and Engineering Research

Council of Canada). Research supported in part by MITACS (Mathematics of

Information Technology and Complex Systems).

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 1–14, 2008.

Springer-Verlag Berlin Heidelb erg 2008

2 A.WieseandE.Kranakis

problems like matching or vertex cover we need to ﬁnd a method that does not

rely on global information of the network. So we are interested in local algo-

rithms. These are algorithms for which the result of a computation for a vertex

or an edge depends only on the vertices and edges which are at most a certain

distance away from them (the locality distance). With this constraint we ensure

that we do not need knowledge of the entire network but only information about

the network in a certain neighborhood of a vertex or an edge. It is also of in-

terest in dynamically changing networks since if only small changes occur local

algorithms need to recompute only small parts of the solution.

In our UDG graph model we assume that every node is aware of its geographic

position in the plane. Allowing this positional knowledge we will see that the

locality distance of our algorithms can be bounded by a constant. Note that this

constant does not depend on the overall size of the network or the maximal vertex

degree. Since positioning systems like GPS become more and more common, this

setting seems to be relevant.

For organizing communication in wireless networks matching is a useful con-

cept. In one communication round a node can usually receive data from only

sender (due to interference) and each sender can send only one package at a

time (usually to one receiver). Thus the sender/receiver pairs form a matching

in the underlying network graph. Research has been done on ﬁnding matchings

with certain properties [3] in order to deal with interference and noise issues.

Also, in the computation of schedules for allocating bandwidth the matching

problem can arise [12].

1.1 Related Work

The matching problem is in Pfor general graphs [5]. The ﬁrst algorithm due

to Edmonds requires a runtime of On3. For the restricted case of bipartite

graphs there are improvements known, e.g., the Hopcroft-Karp algorithm [7].

The vertex cover problem is NP-hard in general graphs [6], but there are sev-

eral polynomial time approximation algorithms which guarantee an approxima-

tion factor of 2, e.g., in [1]. However, it is NP-hard to approximate the problem

with a factor better than 10√5−21≈1,3607[4]. Thus there can be no poly-

nomial time approximation scheme (PTAS), unless P=NP.Whenwerestrict

the setting to unit disk graphs, vertex cover remains NP-hard. The same holds

for growth-bounded graphs since this class includes unit graphs. However, for unit

disk graphs PTASs are known. For the case where the embedding of the graph is

known, Hunt III et al. [8] presented the ﬁrst approximation scheme. The algorithm

for independent set presented in [10] together with the technique in [14] yields a

global PTAS for vertex cover that does not rely on the embedding of the graph.

There is also a local PTAS known for the setting of location aware UDGs [14].

1.2 Our Results

We present the ﬁrst local approximation algorithms for matching in location

aware Unit Disk Graphs. It achieves an approximation ratio of 1−for arbitrarily

Local Maximal Matching and Local 2-Approximation 3

small . In this setting we can show that the locality distance of our algorithm

(i.e. the radius of the area that needs to be explored in order to compute the

status of one edge) is bounded by a constant. In particular, this constant does

not depend on the size of the entire network or the maximal degree of a vertex.

For growth-bounded graphs we also give a 1−approximation algorithm. For

this setting we lift the assumption of positional information in the nodes and

require only a unique ID in each vertex. The locality distance for this algorithm is

in Ologlog∗n+1



O(1) log∗n. All matchings computed by these algorithms

are maximal.

Each matching algorithm yields a local approximation algorithm for the vertex

cover problem. The locality properties of these algorithms are identical to the

respective matching algorithms. The size of the computed vertex covers are at

most twice the size of an optimal vertex cover. As mentioned above, for location

aware unit disk graphs there is a local PTAS known [14]. However, the locality

distance of this PTAS when executed with approximation factor 2is a lot larger

than the locality of Algorithm 3.

1.3 Organization of the Paper

In Section 2 we present our local 1−approximation algorithm for matching

in location aware unit disk graphs. In Section 3 we show how the ideas of this

algorithm can be used in order to derive a local 1−approximation algorithm

for the same problem in growth-bounded graphs. Our local approximation algo-

rithms for vertex cover with approximation factor 2are presented in Section 4.

Finally in Section 5 we summarize our results and address open problems.

2 Maximum Matching in Location Aware UDGs

In this section we present a local 1−approximation algorithm for the maximum

matching problem in location aware unit disk graphs. First we give some basic

deﬁnitions. Then we deﬁne a tiling of the plane that we are going to use in our

algorithm. Finally we present the algorithm and prove its correctness.

2.1 Deﬁnitions

The graph G=(V, E)considered in this section is a unit disk graph. For two

vertices uand vlet d(u, v)be the hop-distance between uand v, that is the

number of edges on a shortest path between these two vertices. Note that the hop-

distance between two vertices does not necessarily equal the geometric distance

between them. Denote by Nr(v)={u∈V|d(u, v)≤r}the r-th neighborhood

of a vertex v. In Section 3 we will consider growth-bounded graphs.

Deﬁnition 1. An undirected graph G=(V, E)is called a f-growth-bounded

graph if there exists a polynomial bounding function f(r)such that for every

v∈Vand r≥0, the size of the largest independent set in the r-neighborhood

Nr(v)is at most f(r).

4 A.WieseandE.Kranakis

Similarly we deﬁne families of graphs to be growth-bounded.

Deﬁnition 2. Let Gbe a family of graphs. We call Gpolynomially growth-

bounded, if there exists a polynomial bounding function f(r)such that for every

graph G∈G, every vertex vin Gand every r≥0, the size of the largest

independent set in the r-neighborhood Nr(v)in Gis at most f(r).

In the sequel when refering to growth-bounded we will mean polynomially growth

bounded. In addition, we will implicitly assume that the family and its bounding

function f(r)are known and ﬁxed for the given class Gof graphs.

Let M⊆Ebe a set of edges. We call Mamatching,ifnotwoedgesinM

share an end-vertex. We call Mamaximum matching, if for all matchings M

it holds that |M|≤|M|.Amaximal matching is a matching which cannot be

extended by adding another edge.

Let Mbe a matching. We call a path pan M-alternating path,ifitcontains

alternating matching- and non-matching edges. We call a vertex van isolated

vertex, is it is not adjacent to an edge from M.WecallanM-alternating path

pan M-augmenting path, if it starts from and ends on isolated vertices. Note:

An M-augmenting path has an odd number of edges.

Lemma 1. AmatchingMis a maximum matching, if and only if there is no

M-augmenting path.

2.2 Tiling of the Plane

Let 1−be the desired approximation ratio for the matching algorithm. We

deﬁne kto be the smallest integer such that ≥2

k+1 . We tile the plane with

an inﬁnitely repeated pattern of rectangles as seen in Figure 1. Each rectangle

is assigned class number 1, 2 or 3. The height of each rectangle is 2k+2,the

width of each rectangle is 4k+4.

2 1

3 2

23 1

Fig. 1. The tiling of the plane

Local Maximal Matching and Local 2-Approximation 5

2.3 The Algorithm

Now we present the algorithm. It has three phases:

1. For each rectangle Rwe compute a matching that includes only edges that

have both end-vertices in R.

2. For each class 1 rectangle Rwe check if there are augmenting paths in the

subgraph induced by the vertices which are at most khops away from R.If

there are such paths, we augmented the matching until no such paths are

left.

3. For each class 2 rectangle Rwe check if there are augmenting paths in the

subgraph induced by the vertices in Rand the vertices in class 3 rectangles

which are at most khops away from R. As in the step before, we augment

the matching along all these paths.

Now we present the algorithm in detail. For all rectangles Rwe do the following:

Denote by VRthe vertices in R. For the subgraph induced by VRwe compute a

maximum matching using a standard matching algorithm. Since all VRfor the

diﬀerent rectangles Rare disjoint the order in which we do this does not matter.

Now we come to phase 2: For each class 1 rectangle Rwe take the set of vertices

which are in Ror at most khops away from a vertex in R. Denote this set by V

In the subgraph induced by V

Rwe augment the matching along all augmenting

paths. Since the height of the rectangles is 2k+2and their width is 4k+4,

the order in which the class 1 rectangles are being processed does not matter.

Finally we start phase 3: For each class 2 rectangle Rwe compute all vertices

which are at most khops away from R. Denote this set by V

R. For the subgraph

induced by V

Rwe we augment the matching along all augmenting paths. Denote

by Mthe resulting matching. We refer to the above as Algorithm 1.

In the following theorem we prove that Algorithm 1 is a local algorithm that

computes a valid matching with a competitive ratio of 1−.

Theorem 1. Algorithm 1 has the following properties:

1. The computed matching Mis a maximal matching for G.

2. Let MOP T be an optimal matching for G. It holds that |M|≥(1−)·|MOPT |.

3. Whether or not an edge e=(u, v )is a matching edge depends only on the

vertices which are at most O1/2hops away from uor v, i.e. Algorithm 1

is local.

4. The processing time for an edge e=(u, v)is bounded by a cubic polyno-

mial in the number of vertices which are at most O1/2hops away from

uor v.

2.4 Proof of Correctness

We will prove the four parts of this theorem in four steps.

Validity and Maximality. We prove that Mis a valid matching for Gand

that it is maximal.

6 A.WieseandE.Kranakis

Algorithm 1. Algorithm for ﬁnding a matching in a unit disk graph G=

(V,E)

// Phase 1;

foreach rectangle Rdo

// denote by VRthe vertices in R;

determine a maximum matching MRfor the subgraph induced by VR;

end

Deﬁne M:= R∈TMR;

// Phase 2;

foreach rectangle Rwith class(R)=1do

Denote by VRall vertices in R;

Explore all vertices which are at most khops away from vertices in VR;

// Denote these vertices by V

Augment Malong augmenting paths in the subgraph induced by V

end

// Phase 3;

foreach rectangle Rwith class(R)=2do

Denote by VRall vertices in R;

Explore all vertices which are at most khops away from vertices in VR;

// Denote these vertices by V

Augment Malong augmenting paths in the subgraph induced by V

end

Proof. (of part 1 of Theorem 1): The matchings constructed in phase 1 are clearly

valid. Since in phase 2 and 3, Mis only augmented along augmenting paths, the

resulting matching is valid as well.

Now we want to prove that Mis maximal. We call an edge that would extend

Man extending edge. Since we augment the matching along augmenting paths a

vertex which is adjacent to a matching edge once will be adjacent to a matching

edge in the ﬁnal matching as well. We see that after phase 1 all extending

edges must have their adjacent vertices in diﬀerent rectangles since we compute

maximum matchings for each rectangle. From the construction of the tiling we

see that these rectangles must have diﬀerent class number (since the length of

an edge is at most 1). After phase 2 there are no extending edges between class 1

and 2 rectangles left since the matching would be augmented along such “paths”.

With the same reasoning we see that after phase 3 there are no extending edges

between class 2 and 3 rectangles left. So for the ﬁnal matching there are no

extending edges in the graph. This implies that the matching Mis maximal.

Approximation Ratio. Let MOP T be an optimal matching for G.Weprove

that |M|≥(1 −)·|MOPT |.

Proof. (of part 2 of Theorem 1): Denote by Mithe matching computed by the

algorithm after phase ifor i∈{1,2,3}.LetPibe the set of augmenting paths

for Miwith i∈{1,2,3}. From the construction of M1it follows that all paths

in P1must have their start - and endvertices in two diﬀerent rectangles. From

the algorithm we see that all paths in P2either

Local Maximal Matching and Local 2-Approximation 7

–do not have their start- and endvertex in a rectangle of class 1 or

–are longer than k,

since all other augmenting paths in P1are eliminated in phase 2. Similarly, in

P3all augmenting paths which are left are longer than kedges.

Consider M:= M3MOP T =(M3−MOP T )∪(MOPT −M3)and G:=

(V,M). All nodes in Ghave a degree of at most two (since M3and MOPT are

both matchings). Its connected components are

–isolated vertices

–cycles of even length

–paths of three possible types

•Paths starting and ending with an edge from M. This cannot happen

since this would be an augmenting path for MOP T and MOP T is optimal.

•Paths starting with an edge from Mand ending with an edge from

MOP T . These paths have the same number of edges from Mas from

MOP T .

•Paths starting and ending with an edge from MOP T . These are augment-

ing paths for M. Denote all these paths by P

Every augmentation would increase the number of edges in Mby one, so |M|+

|P

3|=|MOP T |.SinceP

3⊆P3all paths in P

3have more than kedges. So every

path in P

3contains at least k+1

2edges of MOP T . Since the paths are disjoint, it

follows that |P

3|≤|MOP T |/k+1

2.Wethenhave

|M|=|MOP T |−|P

≥|MOP T |−2|MOP T |

k+1

≥(1 −)|MOP T |

Locality. We prove that whether or not an edge e=(u, v)belongs to Mdepends

only on the vertices which are at most O1/2hops away from uor v.Firstwe

need to give a technical lemma.

Lemma 2. Let Rbe a rectangle and G[R]the graph Grestricted to R.Foreach

connected com ponent Cin G[R]it holds that diam(C)≤22k2+58k+39.Let

Rbe a rectangle and G[R]the graph Grestricted to the vertices which are at

most khops away from R(including the vertices in Ritself). Then for each

connected com ponent Cin G[R]it holds that diam(C)≤30k2+70k+31.

Proof. First we derive an upper bound for the maximum size of an independent

set in G[R]. The area of Rplus a surrounding belt of width 1/2around it is (2k+

3) ·(4k+5) =8k2+22k+15

.Sotherecanbeatmost8k2+22k+15

π/4centers

of non-overlapping discs of radius 1/2in R. We compute that 8k2+22k+15

π/4≤

32k2

π+88k

π+60

π≤11k2+29k+20. It follows that the cardinality of a

8 A.WieseandE.Kranakis

maximum independent set in G[R]is at most 11k2+29k+20. Now consider a

connected component Cin G[R]and two vertices u, v ∈Csuch that d(u, v)=

diam(C).Denotebypthe shortest path between uand vin C.Ifwetakeevery

alternating vertex in pwe get an independent set in R. As the size of such a set

is bounded by 11k2+29k+20, the length of pis bounded by 22k2+58k+39

and therefore diam(C)≤22k2+58k+39.

Applying the same reasoning to Rwe derive an upper bound of 15k2+35k+16

for an independent set in G[R](since (2k+3+k)·(4k+4+k)

π/4=15k2+27k+12

π/4≤

60k2

π+108k

π+48

π=15k2+35k+16) and therefore we get diam(C)≤

30k2+70k+31for any connected component Cin G[R].

(of part 3 of Theorem 1): Denote by aithe maximum number of hops which

we need to explore around uand vin order to compute whether e∈Mafter

phase i(for i∈{1,2,3}).

In order to determine the status of an edge eafter phase 1, we need to explore

only the connected component of ein its rectangle if uand vare in the same

rectangles or nothing if uand vare in diﬀerent rectangles. From Lemma 2 it

follows that a1≤22k2+58k+39. For computing the status of eafter phase 2

we need to explore the connected component V

Rwith u∈V

Rand v∈V

R(if it

exists) and what edges in V

Rwere assigned to Mafter phase 1. It follows that

a2≤a1+30k2+70k+31(see Lemma 2). Analogously for computing the status

of eafter phase 3 we need to explore the connected component V

Rsuch that

u∈V

Rand v∈V

R(if such a component exists) and what edges in V

Rwere

assigned to Mafter phase 2. This implies that a3≤a2+30k2+70k+31.So

altogether we get that a3≤22k2+58k+39+30k2+70k+31+30k2+70k+31 =

82k2+198k+ 101 ∈Ok2.

By deﬁnition kis the smallest integer such that ≥2

k+1 . This implies that

k≥2

−1and thus k∈O(1/). It follows that a3∈O1/2.

Processing time. We want to show that the processing time of Algorithm 1

for a single edge eis in O¯n(e)3where ¯n(e)is the number of vertices within the

locality distance of e(i.e. the number of vertices which we really need to explore

in order to compute the status of e).

Proof. (of part 4 of Theorem 1): In phase 1 we need to compute a maximum

matching for edges in a single rectangle. This can be done in O¯n(e)3using any

algorithm for computing a maximum matching (e.g. Edmonds algorithm [5]). In

phase 2 we need to ﬁnd augmenting paths in the subgraph induced by V

Rfor

several class 1 rectangles R. Since in the locality distance of ethere can be only a

constant number of class 1 rectangles this requires O¯n(e)3time (note that the

number of such class 1 rectangles does not depend on the desired approximation

ratio). Applying the same reasoning in phase 3 we need a processing time of

O¯n(e)3. This leads to an overall processing time of O¯n(e)3.

Local Maximal Matching and Local 2-Approximation 9

3 Maximum Matching without Location Awareness

In this section we present a local algorithm which computes a 1−approximation

for the maximum matching problem in growth-bounded graphs. In contrast to

the algorithm presented in Section 2 we assume a graph model in which the

embedding of the graph is unknown. We will specify this in the following section.

3.1 Graph Model

Let G=(V, E)be a growth-bounded graph. We assume that every node has

a unique identiﬁer (ID). Apart from that there is no information available to

distinguish the nodes from each other.

3.2 The Algorithm

Let 1−be the desired approximation ratio. The algorithm uses the same

methodology as Algorithm 1 for ensuring the approximation ratio: We will com-

pute a maximal matching Msuch that the length of each of the augmenting

paths that could turn Minto a maximum matching is at least a certain con-

stant k. At the beginning of the algorithm we choose kaccording to .

The role of the rectangle classes in the algorithm above will be taken by a

maximal independent set which is also a dominating set. In order to organize

the computation distributively we use the same methods which were originally

presented in [10].

Similarly as in Algorithm 1 we deﬁne kto be the smallest even integer such

that ≥2

k+1 . We compute a maximal independent set Iin G.Thiscanbe

done locally using the distributed algorithm [5]. Then we deﬁne the clustergraph

G=(

V, ¯

E)with radius 2k+2by ¯

V:= Iand

(u, v)∈¯

E⇔dG(u, v)≤2k+2

Since Gis a growth-bounded graph, the maximum degree ¯

Gof ¯

Gis bounded by

a constant. This allows us to use the algorithm in [11] for coloring the vertices of

Gwith at most O2

Gcolors. We initialize our matching Mwith M:= ∅.Then

we iterate over the diﬀerent colors of ¯

G. For each color cwe do the following: For

each vertex vcwhich was colored with color cwe compute the subgraph induced

by Nk+1 (vc).DenotebyGc(vc)such a subgraph around a vertex vc.Fromthe

deﬁnition of ¯

Gwe see that the subgraphs are all disjoint. In each subgraph

Gc(vc)we augment our matching Malong augmenting paths until we cannot

ﬁnd any more augmenting paths. This can be done using a standard matching

algorithm, e.g., the algorithm by Edmonds [5]. Since the subgraphs are disjoint

this can be done distributively. After having iterated over all colors, we output

M. We refer to this as Algorithm 2.

Theorem 2. Algorithm 1 has the following properties:

1. The computed matching Mis a maximal matching for G.

2. Let MOP T be an optimal matching for G. It holds that |M|≥(1−)·|MOPT |.

10 A. Wiese and E. Kranakis

Algorithm 2. Algorithm for ﬁnding a matching in a unit disk graph G=

(V,E)

// Let 1−be the desired approximation ratio;

Deﬁne kto be the smallest integer such that k+1

k+3 ≥1−;

Compute a maximal independent set Ifor G;

Construct cluster graph ¯

Gwith radius 2k+2;

Color ¯

Gwith γ=O2

Gcolors;

M:= ∅;

for i:= 1 to γdo

foreach vertex vcwith color cdo do

compute subgraph Nk+1 (vc);

augment Malong augmenting in Nk+1 (vc);

end

3. The algorithm requires at most Ologlog∗n+1



O(1) ·log∗ncommuni-

cation rounds.

3.3 Proof of Correctness

We will prove the four parts of this theorem in four steps.

Validity and Maximality. We want to prove that Mis a matching and that

it is maximal.

Proof. (of part 1 of Theorem 2): For the correctness of the subroutines for com-

puting the maximal independent set and the vertex coloring we refer to their

respective articles [9,11]. In each iteration the matching is augmented along aug-

menting paths. This clearly constructs a valid matching. Now we want to prove

that Mis maximal. Assume on the contrary that there is an edge e=(u, v)

with e/∈Mbut such that M∪{e}is a valid matching. Since Iis a maximal

independent set it is also a dominating set. So there is a vertex u∈Iwhich is

adjacent to u.Letcbe the color of u. There is an iteration in which uwas con-

sidered. Since we always augment our matching along augmenting paths, both

uand vwere unmatched in this iteration (in Gc(u)). Since eis in Gc(u)and

we augment Malong all augmenting paths in Gc(u),theedgeeis added to M.

In all future iterations uand vwill always be matched (adjacent to a matching

edge). This is contradiction.

Approximation Ratio. We want to prove that for a maximum matching

MOPT for Git holds that |M|≥(1 −)·|MOPT |.

Proof. (of part 2 of Theorem 2): Like in the proof of Theorem 1 we show that

there are no augmenting paths for Mwhose length is shorter or equal to k.

Denote by Ii⊆Iall vertices in Iwhich were colored with color i.Denoteby

Local Maximal Matching and Local 2-Approximation 11

Piall vertices which are either in Iior adjacent to a vertex in Iiand denote

by Mithe computed matching after the ith iteration. In the ith iteration of

the algorithm we check for augmenting paths in the subgraphs Gc(v)(for each

v∈Ii). Thus after the ith iteration there are no more augmenting paths which

start with an isolated vertex in Piand whose length is at most k.

Now consider M

i:= MiMOP T .TheedgesinM

iform either circles of even

length or augmenting paths. When we compare M

iwith M

jfor j>iwe see that in

Mjthe paths from Miare either unchanged, eliminated (because we augmented

the matching along them), or two paths are connected (becauseweaugmented

along a path that connected these two paths). In both cases it still holds that all

augmenting paths starting with an isolated vertex in Piare longer than kedges.

Since Iis a dominating set for Git holds that Pi=V.Thusafterall

iterations there are no augmenting paths left which have at most kedges. So

with the same argumentation as in part 2 of Theorem 1 we can show that

|M|≥(1 −)·|MOPT |.

Locality. We show that we need at most Ologlog∗n+1



O(1) ·log∗ncom-

munication rounds.

Proof. (of part 3 of Theorem 2): Computing the maximal independent set Ican

be done in O(loglog∗n)communication rounds [9]. The coloring of the cluster

graph takes O(k·log∗n)rounds [11]. The computation of the matchings needs

Ok·2

Gcommunication rounds since we have O2

Gdiﬀerent colors and we

explore the vertices which are at most k+1hops away from each vertex v∈I.

The maximum degree of the cluster graph ¯

Gis bounded by O(f(2k+2)) where

f(n)is the growth-bounding-function of G. By deﬁnition kis the smallest integer

such that ≥2

k+1 . This implies that k≥2

−1and thus k∈O(1/).

Altogether this implies that Algorithm 2 needs at most OTMIS +1

(log∗n+

f2

+22communication rounds where TMIS are the communication rounds

needed for computing a maximal independent set. Using the algorithm in [9] for

this task we need Ologlog∗n+1



O(1) ·log∗ncommunication rounds in total.

4 Vertex Cover

In this section we present local approximation algorithms for the minimum vertex

cover problem. We use the local matching algorithms presented in Sections 2

and 3 respectively as subroutines. First we compute a maximum matching. Then

we assign all vertices which are adjacent to matched edges to the vertex cover.

Using a well-known reasoning we prove that this gives a factor 2 approximation

for vertex cover.

4.1 The Algorithm

Let G=(V,E)be a unit disk graph. First we use Algorithm 1 or Algorithm 2 in

order to compute a maximal matching M. We modify the algorithm as follows:

12 A. Wiese and E. Kranakis

Since we are not interested in a good approximation for the matching problem we

choose k:= 1. In order to improve the runtime of the algorithm, we consider only

augmenting paths of length 1in each phase (this is eﬀectively a greedy-algorithm

for the matching problem). Then we deﬁne our vertex cover VCas follows: VC :=

{u, v|(u, v)∈M}.

Using Algorithms 1 and 2 we cannot only compute maximal matchings, but

also maximal matchings which are not much smaller that maximum matchings.

However, for this algorithm, we could not prove a better performance ratio if

we computed a matching with a certain performance guarantee. So in order to

achieve a small locality distance we just compute a maximal matching.

Algorithm 3. Algorithm for ﬁnding a vertex cover in a unit disk graph

G=(V,E)

Deﬁne k:= 1;

Compute a maximum matching Musing Algorithm 1 or Algorithm 2 and only

augmenting along paths of length 1;

Deﬁne VC := {u, v|(u, v)∈M};

Output VC;

Depending an which algorithm we use for computing the matching we get a

diﬀerent algorithm for vertex cover. Theorem 3 represents the algorithm that we

get by using Algorithm 1, Theorem 3 the algorithm which is the result of using

Algorithm 2 as a subroutine.

Theorem 3. There is an algorithm for location aware unit disk graphs which

computes a set VC with the following properties:

1. The computed set VC is a vertex cover for G.

2. Let VC

OPT be an optimal vertex cover for G. It holds that |VC|≤2·

|VC

OP T |.

3. If a vertex vis in VC depends only on the vertices which are at most 381

hops away from v, i.e. Algorithm 3 is local.

4. The processing time for a vertex vis bounded by a linear polynomial in the

number of edges whose adjacent vertices are both at most 381hops away

from v.

There is an algorithm for growth-bounded graphs with unique vertex-IDs which

computes a set VC with the following properties:

1. The computed set VC is a vertex cover for G.

2. Let VC

OPT be an optimal vertex cover for G. It holds that |VC|≤2·

|VC

OP T |.

3. The algorithm requires at most Ologlog∗n+1



O(1) log∗n

commu nication rou nds .

Local Maximal Matching and Local 2-Approximation 13

4.2 Proof of Correctness

Here we only prove Theorem 3. The proof of Theorem 3 can be done similarly.

Proof. (of Theorem 3): From Theorem 1 we know that Mis a maximal matching.

Thus V\M=VC is a vertex cover. The cardinality of any matching in a graph

forms a lower bound for the cardinality of a minimum vertex cover. This holds

since every vertex of an optimal vertex cover can cover at most one edge of the

matching. As we assign two vertices to VC for each edge in Mwe conclude

that |VC|≤2·|M|≤2·|VC

OP T |. The other properties of the algorithm follow

immediately from the respective properties of the matching subroutine.

5Conclusion

We presented local 1−approximation algorithms for matching in the setting of

location aware unit disk graphs and growth-bounded graphs without positional

information. They are the ﬁrst local approximation algorithms for matching in

their respective settings. Since a local algorithm cannot perform optimally in

all graph instances our approximation factors are the best possible. It remains

open to ﬁnd local algorithms which achieve the same approximation ratios but

which need lower locality distances. For real applications low localities are always

desirable since they reduce the size of the area that needs to be explored when

computing the status of an edge. For Algorithm 2 the locality distance needed for

computing a maximal independent set plays an important role. A local algorithm

for this task with a lower locality would immediately lead to a lower locality

distance of our algorithm. Also of interest would be lower bounds for the best

possible approximation ratio of local algorithms for matching in these settings

(depending on their locality distance).

In Section 4 we used the two matching algorithms for getting factor 2approx-

imation algorithms for vertex cover in the respective settings. Our algorithms

achieve the best known locality distances for this approximation factor. For the

setting of growth-bounded graphs without positional information, our algorithm

is even the ﬁrst non-trivial local algorithm for vertex cover. It remains open

to fully analyze the price for good approximation ratios in terms of required

locality distance. The ﬁrst lower bounds on this are [13]. All improvements for

the matching algorithms regarding locality distance would immediately lead to

better locality distances for the vertex cover algorithms.

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Opportunistic Clock Synchronization in a

Beacon Enabled Wireless Sensor Network

Nicola Altan and Erwin P. Rathgeb

University of Duisburg-Essen

{nicola.altan,erwin.rathgeb}@uni-due.de

Abstract. Wireless sensor networks (WSN) consisting of a large number

of tiny inexpensive sensor nodes are a viable solution for many problems

in the ﬁeld of building automation. In order to meet the energy con-

straints, the nodes have to operate according to an extremely low duty

cycle schedule. In such a scenario the reduction of the synchronization

error, at least among directly communicating nodes, is a crucial function-

ality of the MAC layer. We propose a time synchronization mechanism

based on the usage of a Kalman Filter (KF) on a smoothed sequence

of measured beacon intervals. A side eﬀect of this method is the intro-

duction of a global clock synchronization. The implementation of the

proposed solution is feasible on sensor devices with minimum processor,

memory and energy capacity.

1 Introduction

Recent advances in electronics and radio communications have enabled the de-

velopment of low-cost, low-power sensor nodes which are small in size and com-

municate through short range radio devices.

Building automation is, apart from the military applications, one of the most

promising ﬁelds for the deployment of wireless sensor network (WSN) technolo-

gies. In this case, the WSNs will typically be deployed in an already existing

building such that mains operation is much too costly because a large number of

power outlets would have to be retroﬁtted for that purpose. Therefore, the nodes

have to be autonomous, i.e. battery powered operation is necessary despite the

fact that the network is operated in an indoor environment.

Simple economical considerations suggest that that the sensor nodes have to

be as inexpensive as possible and they have to work unattended for several years

such that the replacement of the nodes can be included into the scheduling for

routine maintenance.

Considering the strict constraints with respect to the total energy budget and

the expected life time imposed by the building automation scenario, the network

nodes have to adopt an extremely low duty cycle scheduling. Therefore, the

implementation of an at least local clock synchronization protocol is mandatory

to enable the communication between the nodes over an extended period of time.

The contribution of this paper is to propose an eﬃcient synchronization algo-

rithm which relies only on the measurements of the beacon interval and hence

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 15–28, 2008.

Springer-Verlag Berlin Heidelberg 2008

16 N. Altan and E.P. Rathgeb

makes an opportunistic usage of the MAC management frames. It is applicable

over a wide range of sensor network scenarios including in particular the case of

very low duty cycles.

2 Requirements and Assumptions

With respect to scalability, network sizes from just a few nodes in residential

buildings up to 1000 nodes in large complexes are realistic for building automa-

tion scenarios. We assume the number of nodes to be proportional to the number

of rooms for the respective building.

Simple business plan considerations mandate the use of oﬀ-the-shelf sensor

hardware and an unattended node life time of up to 10 years. In order to meet

the total energy budget under these assumptions, the nodes have to operate with

an extremely low duty cycle (no higher than 10−4).

The medium access control protocol (MAC) we assume as basis for the WSN

operation combines contention based reservation and contention free access peri-

ods into a single frame, which begins with the generation of a beacon signal. The

reception of these beacons is the mandatory precondition for the communication

with the respective sender.

The self-conﬁguration process performed to bootstrap the network implicitly

deﬁnes which nodes are able to receive the beacon signal a speciﬁc node gener-

ates, and hence the direction of the communication between neighbor nodes [1].

The assumption of a beacon based MAC protocol and of a tree-like rout-

ing structure with unidirectional links apply to a large class of WSNs. There-

fore, the proposed synchronization method is generally applicable to many WSN

scenarios - irrespective of the use of the speciﬁc MAC layer and bootstrap

algorithm.

The interval between two consecutive beacons emitted by the same node is

ﬁxed and its nominal value Tbeacon =6min. is known.

Each node is equipped with a free running clock, which is characterized by

a precision clock.Atypicalclockerrorof20ppm, e.g., results in a diﬀerence

between nominal and real beacon interval of 7.2ms in the considered network.

Environmental changes may impose additional clock errors.

In order to accommodate the synchronization errors, each node activates the

receiver prior to the expected beacon emission time to provide a guard period1.

3 Related Work

There exist multiple proposals for solving the clock synchronization problem in

the literature. Most of the approaches adopt the basic principle also used in the

network time protocol (NTP) [2]: the nodes exchange data packets including

1Since hardware and energy constraints impose an upper limit on the duration of

an activity period, the minimization of the guard period is of crucial importance in

order to achieve a high utilization of the channel.

Opportunistic Clock Synchronization 17

time stamps and then adjust their own clock in order to minimize the diﬀerence

from the reference clock. All solutions based on this approach have two main

drawbacks which make these unsuitable for the considered network. The syn-

chronization protocol itself requires the transmission of data packets and hence

causes additional energy costs which may be non-negligible if the system requires

a tight synchronization. Moreover, all these solutions rely on the bidirectional

exchange of synchronization packets and, therefore, they can not be used in a

network where most of the communication links are unidirectional.

The synchronization problem in WSN has been speciﬁcally addressed in some

recent publications ( [3,4, 5,6,7]). Each of these proposals seems to be optimized

for a speciﬁc kind of WSN – and with respect to speciﬁc conditions.

Romer and Elson outline in [5] many of the challenges and issues with respect

to synchronization in a WSN. In particular, the authors highlight the necessity

of exploiting the a-priori knowledge about the involved systems. The same paper

highlights the importance of creating an operational clock on top of the local

free running clock instead of trying to modify the clock parameters.

The Reference Broadcast Synchronization (RBS) [7] performs well for multi-

hop synchronization. It requires that nodes which receive the same synchroniza-

tion packet are able to communicate. Even though this is likely in the network

we consider, the additional traﬃc represents a source of energy expenses.

The approach proposed by Hu and Servetto [6] shows many interesting prop-

erties which meet the requirements of the WSN we consider. In particular it does

not rely on the exchange of additional traﬃc, it uses the broadcast characteristics

of the physical medium and it relies on local estimations for the emission time

of synchronization pulses. In this case, the synchronization takes the form of an

estimation problem. The authors show the optimality of the proposed approach

if the number of nodes approaches inﬁnity. An application to a network with a

ﬁnite number of nodes is described in [8]. The algorithm used seems to be insta-

ble in networks of ﬁnite size and requires the introduction of a feedback from the

reference node in order not to diverge. A critical aspect of the whole construc-

tion is the assumption of the wide sense stationarity of the process describing

the measurements. In a real scenario, modiﬁcations of the environmental param-

eters have inﬂuence on the parameters of the stochastic process which describes

the measurements. The process itself will, therefore, be no more stationary. A

continuous adjustment of the parameters of the used estimator may solve the

problem but it would make the algorithm particularly ineﬃcient (and maybe

infeasible) on the low-resource nodes we consider, e.g., because an update of the

used estimator requires the computation of a matrix inversion.

4 Problem Description

We consider a sensor network consisting of a ﬁnite number of nodes M.Each

node is equipped with a free running clock source according to the recommen-

dations in [5]. Instead of adjusting the parameters of the local clock, we build

an operational clock on top of the free running local clock, like in [6].

18 N. Altan and E.P. Rathgeb

A simpliﬁed clock error model indicates that at time t, measured according

to a hypothetic absolute time reference, the clock of the node iindicates the

time ci,t =(1+δi)·(t−t0)+∆i,0+Ψ(t), where ∆i,0is the initial clock oﬀset

at the time t0,δi∈[−clock,

clock] is a constant frequency oﬀset and Ψ(t)is

an additional error which takes into account the dependency of the clock on the

environmental conditions.

We want to minimize the length of the guard period by forcing all the nodes to

have the same beacon interval. From this perspective, the global clock synchro-

nization is a side eﬀect of our procedure. Once a node is chosen as reference, all

other nodes have to adjust the own beacon interval to the one of the reference.

Each node generates periodically (every Tbeacon) a beacon signal, which indi-

cates the beginning of a MAC frame. The beacon interval is measured using the

internal clock and hence it diﬀers from the nominal value.

A node is able to measure the beacon generation interval for each one of its

neighbor nodes, with a precision of one symbol duration. The error due to signal

propagation is much lower than the measurement error.

We assume that the sink is providing the gateway to a public network (e.g.

GSM or UMTS) for remote storage and processing of the measurement data

by the WSN operator. It is connected to the regular power supply and is also

more powerful. Since it is equipped with a better clock, we want that all nodes

generate the beacon signal at the same rate the sink does.

5 Proposed WSN Synchronization Algorithm

We consider the synchronization problem to be an estimation problem. A node

ntries to estimate the beacon interval of the reference node using the measure-

ments of the beacon interval of all observed neighbor nodes (In

i,k denotes the

measurement of the k-th beacon interval of the node i,takenbythenoden).

The reference node generates its beacon signal exactly each Tk=Tseconds.

The measurements done by the node nare aﬀected by additive errors ξn

i,k.

At the time k, the node ncomputes the estimation of the reference interval

kby using the previous observations and uses this value as length of the next

beacon interval.

If we consider the network between the reference node and the node nas a

blackbox (Fig. 1), we can write the following relation (1) between the reference

interval and the measurement taken by the node n(in order to improve the

readability of the formulas, we omit the indexes nand ifrom the notation).

Reference

Node

i,k

Node n th

TkTn

Fig. 1. Schematic representation of the blackbox approach

Opportunistic Clock Synchronization 19

First we assume the node nhaving only one neighbor, then we introduce a

simple extension in order to deal with a multiplicity of uplink nodes.

Tk+1 =Tk

Ik=Tk+ξk

(1)

The error ξkis the diﬀerence between the measured beacon interval and the

beacon interval of the reference node. If the quantity ξkhas the characteristics

of white Gaussian noise (AWGN), it can be removed easily with a Kalman Filter

(KF). In general, however, ξkis not AWGN.

A similar problem had been addressed in [9] for estimating the generation

rate of ATM cells on the basis of the observation of their arrival time. However,

it has to be noted that the origin of the measurement errors, and hence the

characteristics of the error process, diﬀers in the two cases. In the cited paper,

ATM cells arrive with variable delays, which depend mainly on the queuing

process in the intermediate nodes, while, in our case, the measurement error ξk

is mainly due to the the adjustment process of the beacon generation time in

all nodes between nand the reference and might experience sudden variations.

In spite of these diﬀerences we argue that the preﬁltering approach is useful in

order to smooth the measurement error and make the problem tractable.

If ξkis AWGN the following approach is equivalent to the one proposed in [6].

As ﬁrst step we smooth ξkby computing the moving average of the mea-

surements taken during the last Nintervals (2). The resulting signal, which has

low-pass characteristics, is then modelled with an autoregressive process of the

ﬁrst order (AR(1)),which is one of the simplest low-pass models.

Ik=1

N−1



i=0

Ik−i=Tk+1

N−1



i=0

ξk−i=Tk+¯

ξk(2)

Nowwecanrewriteeq.1usingeq.2.

Tk+1 =Tk

Ik=Tk+¯

ξk

(3)

We postulate that ¯

ξkcan be modelled as AR(1) system as follows:

ξk=a¯

ξk−1+rw

k;wk∈N(0,1) i.i.d (4)

We can compute the equations of the Kalman Filter (KF) for the given model

with the colored noise according to eq. 4

initialization (k=0) ⎧

⎪

⎨

⎪

⎩

T0=mT0−σ2

T0(mT0−¯

I0)

σ2

T0+r

P0=σ2

T0−1+r−1−1(5)

20 N. Altan and E.P. Rathgeb

k≥1⎧

⎪

⎨

⎪

⎩

Gk=HP

k−1

H2Pk−1+r

Pk=(1−HG

k)Pk−1

Tk=ˆ

Tk−1+Gk¯

Ik−a¯

Ik−1−Hˆ

Tk−1(6)

Where mT0and σ2

T0are the expectation and the variance of T0, respectively,

H≡1−a,ˆ

Tkis the estimation of Tk,Pkis the variance of the estimation error

Tk−Tkand Gkis the gain of the KF.

To compute the KF we have to determine the parameters for the initial con-

dition (mT0and σ2

T0) and the parameters of the autoregressive model (a,r).

The following description suggests how the former can be derived from the a

priori knowledge about the clock, the latter can be estimated by using a small

number of measurements collected before starting the synchronization procedure.

Initial conditions - Following the same reasoning as in [9] and assuming that

for each node nthe frequency fnof the oscillator is uniformly distributed in the

interval [(1 −clock )fnom ,(1 + clock)fnom ] and considering that clock 1we

obtain σ2

T0≈2/3(Tbeacon clock)2and mT0≈Tbeacon.

AR(1) parameters - The stored measurements are used in order to com-

pute an estimation of the autocovariance coeﬃcients c0and c1. By applying the

covariance method we obtain a=c1/c0and r2=(1−a2)c0.

If a node observes the beacon signals generated by diﬀerent neighbors, it uses

the mean value of the measurements collected during the last beacon interval.

This approach ﬁts with our idea of considering the network as a blackbox. In fact,

in absence of a-priori knowledge about the quality of the diﬀerent measurements,

this is the estimator which minimizes the square estimation error.

The continuous adjustment of the beacon generation interval modiﬁes the

model parameters an observer perceives. The system has to adapt itself to these

changes and in particular it may be necessary to reinitialize the KF, as noted

in [9], where the author suggested a continuous observation of the buﬀer state in

an ATM switch in order to determine when the network conditions change and

KF reinitialization was needed. In our model we try to follow the modiﬁcation of

the system parameters by continuously adjusting the parameters of the AR(1)

model. At the same time we observe the mean absolute synchronization error

(absolute value of the diﬀerence between the arrival time of a beacon and the

corresponding expected value) and we reset the KF if this value starts growing.

An alternative approach based on using a second KF for the estimation of the

model parameters seems to converge slower.

6 Simulation

The behavior of the proposed synchronization algorithm and its sensitivity to

the parameter variations have been studied using simulation. A model of the

Opportunistic Clock Synchronization 21

proposed algorithm has been implemented using the Omnet++ [10] simulation

library, along with diﬀerent models of the free running clock. Each node measures

the time intervals using the own clock which is characterized by a precision in

the order of the duration of a symbol (10−5sfor the analyzed network).

6.1 Clock Models

If the frequency oﬀset is not constant, the time perceived by the ith node can be

expressed by the following equation

ci,t =t

(1 + δi(x))dx +∆i,0+Ψ(t)(7)

where tis the time measured by a hypothetical reference clock, ∆i,0is the

diﬀerence between the local and the global clock at time t0and δi(t)isthe

ﬁrst derivative of the diﬀerence between the frequency of the local and the ideal

oscillator. Ψ(t) takes in account all other error components.

In order to identify the behavior of the proposed algorithm in response to

diﬀerent error conditions, we implemented the following four clock models:

Frequency oﬀset (Freq Oﬀ )- The model considers only a constant frequency

oﬀset which is speciﬁc for each node: δi(t)=δi∈[−clock,

clock]wherethe

clock tolerance clock depends on the manufacturing process (=40ppm for

the simulation study). The additional error component Ψ(t) consists only of the

quantization error and is upperbounded by the symbol duration (10−5s).

Aging - Since the expected lifetime of the considered network spans over many

years, we modelled the eﬀect on the clock stability due to the aging process of

the electronic components assuming the frequency oﬀset to be a linear function

ofthetime(δi(t)=δi,0+ρi·t). For a commercial quartz ρmay range between

±5and±10 ppm/year [11]. (ρi∈[−10−4ppm/s, 10−4ppm/s] for this study).

Environmental changes (EnvChange )- Environmental parameters and in

particular the temperature inﬂuence the frequency of a quartz driven oscillator.

The nodes of an indoor network may experience signiﬁcant temperatue variations

over a relatively short time interval, especially during the cold season if the nodes

are placed close to a radiator typical for e.g. a heat meter application. We try

to reproduce this eﬀect by means of a simple Markov model with two states

(H,L). The transitions between the two states happen with rate λHL and λLH ,

respectively. The frequency oﬀset is constant as long as a node does not change

the state δi(t)=δibase +δistate ,whereδistate is speciﬁc for each state. It has to

be noted that, from the point of view of the synchronization mechanism, this

behavior is worse than the real case because it introduces a discontinuity in the

frequency oﬀset ( λ−1

HL ∈[500s, 1000s], λ−1

LH ∈[1000s, 2000s], δiH∈[−40ppm, 0],

δiH∈[0,40ppm], δibase ∈[−40ppm, 40ppm] are the parameters used for the

simulation runs).

22 N. Altan and E.P. Rathgeb

Fig. 2. Network structure used for the simulation study

Jitter - In order to stress the synchronization algorithm we consider the pres-

ence of a random clock jitter superimposed to a constant frequency oﬀset. The

additional jitter error component (Ψ(t)) is modelled as a Poisson process with

intensity λjitter and normal distributed amplitude Aj∈N(0,σ

Aj) (for the fol-

lowing simulation runs λ−1∈[500s, 2000s]andσAj=0.01s).

All four clock error models have been used in our simulation study to assess

the behavior of the proposed algorithm. The error model assuming random clock

jitter systematically provided the worst case results. Therefore, we will mainly

focus on this error model in the remainder of the paper and only refer to the

others if speciﬁc eﬀects have to be described.

6.2 Metrics Used for the Evaluation

As stated before, the aim of the study was ﬁnding a way to reduce the guard

period and hence to increment eﬃciency of the MAC Layer protocol. In order

to get a metric for the quality of the local synchronization, we observe the abso-

lute synchronization error (ASE) for each node (absolute value of the diﬀerence

between the expected and the real beacon arrival time). As consequence of the

local error reduction, the length of the beacon intervals (BI) selected by each

node converge to a common value, achieving a global synchronization. The stan-

dard deviation of the beacon intervals (SDBI) measured at a given time is an

indicator of the quality of the synchronization achieved. The measurements were

smoothed using a moving average computed over the last ten samples.

6.3 Simulation Setup and Methodology

Taking in account the typical routing structure generated by our bootstrap al-

gorithm, we decided to consider a network with only unidirectional links where

the time information propagates from the concentrator to the periphery.

Opportunistic Clock Synchronization 23

(a) ASE metric (b) SDBI metric

Fig. 3. Behavior for jitter error model (beacon interval 360s)

The Mnodes were organized in a grid consisting of mlevels (the level number

is the distance from the reference node) with nnodes each (Fig. 2). Each node

at level ireceived the beacon generated by all the neighbors at level i−1. There

was no communication path between nodes belonging to the same level.

An experiment consisted of at least ﬁfty runs, each one with diﬀerent seeds

for the random number generators. The nodes drew the parameters for the given

clock error model randomly at the beginning of each run. A run spanned 10 days

of simulated time.

6.4 Results

Preliminary results showed that the synchronization error increases for increasing

mand decreasing n(assuming the total number of nodes Mto be constant).

Therefore, we ﬁrst concentrated on the worst case where the network structure

degenerates to a line (m=M,n=1).

Behavior Observed Using the Jitter Clock Error Model. The two graphs

in Fig. 3 have been generated by computing the mean of the values collected

during a simulation study consisting of 50 runs for each value of the network

length m=M. It can be easily seen that the proposed approach is eﬀective

in reducing the eﬀect of jitter, in particular the mean absolute synchronization

error between neighboring nodes quickly reaches its minimum and saturates

after few tens of beacon intervals (Fig. 3(a)) even for relatively large networks.

While the convergence time (time required to reduce the error to 10% above

the ﬁnal value) of the ASE metric is almost independent of the network length

m, the convergence time of the beacon interval estimation depends on m.For

a network with 100 aligned nodes the convergence requires no more than 900

beacon intervals (Fig. 3(b)).

The Impact of Preﬁltering. As stated before, the collected data is smoothed

using a moving average ﬁlter of length N. If using few preﬁltering points, the

quality of the synchronization increases signiﬁcantly with Nand then saturates

24 N. Altan and E.P. Rathgeb

(a) ASE metric (b) SDBI metric

Fig. 4. Inﬂuence of preﬁltering in presence of jitter

(Fig. 4) if jitter modelled as a Gaussian process is assumed. Howewer, if the

measurement errors do not reﬂect a normal distribution an increase of Nmay

cause a degradation of the estimation by reducing the systems ability to follow

the changes of the model parameters (Fig. 5).

If the clock error consists merely of frequency oﬀset, the estimation error is

almost independent from the length of the smoothing preﬁlter.

The estimation error increases with the maximum distance mfrom the ref-

erence node at a rate which seems to be lower than √mfor larger values of m

(Fig. 6). Similar curves have been observed for the synchronization error between

adjacent nodes.

Dependence on the Number of Nodes Per Level. As stated before, a

network structure consisting only of aligned nodes is a worst case which is not

really representative for the typical network topology. The behavior for a more

typical network structure has been analyzed locating the nodes in a grid structure

consisting of 50 levels (rows, m= 50) and increasing the nodes per level n

(columns, n=2,5,10). As shown in Fig. 7 a reduction of the convergence time

along with a slight reduction of the synchronization error can be observed in

such a structure. However, the basic behavior is the same as in the worst case

network.

(a) Aging (b) Environmental changes

Fig. 5. Inﬂuence of preﬁltering for diﬀerent clock error models

Opportunistic Clock Synchronization 25

Fig. 6. Dependence of the SDBI metric on the network length m

(a) ASE metric (b) SDBI metric

Fig. 7. Behavior in presence of jitter for increasing number of nodes per level

Improvement Due to the Synchronization Algorithm. Table 1 summa-

rizes the results for a network consisting of hundred aligned nodes.

The runs without synchronization algorithm have been done assuming that –

upon reception of a beacon signal generated by a parent – a node simply updates

the estimation of the arrival time of the next signal and leaves its own beacon in-

terval unchanged. The length of the smoothing ﬁlter used by the synchronization

algorithm has been set to N=8 points.

The synchronization algorithm causes a signiﬁcant improvement of the ob-

served metrics for all error models. As stated before the jitter error model

represents a worst case for the synchronization algorithm. For the also critical

EnvChange error model the synchronization algorithm is able to reduce the ab-

solute synchronization error to 1% of the original one. However, the estimation

of the beacon interval is only reduced to 1

3. This is, however, not a shortcomming

of the algorithm but is a consequence of the stochastic properties of the error

process.

Comparison with the Algorithm of Servetto and Hu. As stated before

the work of Servetto and Hu [8] has many similarities with our approach. It is

therefore used for comparing our observations with their results. The graph in

26 N. Altan and E.P. Rathgeb

Table 1 . Comparison of the observations done using diﬀerent clock error models, in a

network with 100 aligned nodes (N=8)

No Sync Sync

Clock error

model

ASE-mean

(sec.)

BI-stdev

(sec.)

ASE-mean

(sec.)

Fre q O ﬀ 9.5e-3 8.2e-3 5.7e-5 8.5e-4

Aging 2.3e-2 2.0e-2 4.4e-4 1.5e-3

EnvChange 4.9e-3 4.2e-3 4.7e-5 1.6e-3

Jitter 1.0e-2 8.2e-3 3.0e-3 1.5e-3

Fig. 8. SDBI metric in a grid network with 20x15 nodes, σjitter =0.1Tbeacon

in Fig. 8 has been obtained averaging the observations done in an experiment

consisting of 50 runs in a network with 300 nodes, which have been organized

in a mesh structure with 15 columns and 20 rows. The standard deviation of

the jitter amplitude has been set to 10% of the beacon interval like in [8]. The

results have been normalized to the duration of a beacon interval in order to

permit a direct comparison with the results in the cited paper.

The observed error parameter is – after convergence – less than 10 percent

of the value reported in the reference paper. This indicates that our proposed

algorithm performs better than the other one. However, diﬀerences in the clock

error model do not allow to exactly quantify the improvement.

Contrary to the algorithm proposed in [8], the solution we propose does also

not require any additional traﬃc in order to make the synchronization stable.

On the Implementation on Low-Resource Devices. An implementation

of the proposed algorithm on a sensor node requires the availability of enough

memory to store the data for the computation of the smoothing ﬁlter and of

the coeﬃcients of the AR(1) model. The number of data items which have to

be stored is proportional to N+P+1,wereNisthenumberofpointsofthe

preﬁlter and Pis the number of points considered for the computation of the

autocorrelation values.

Opportunistic Clock Synchronization 27

(a) FreqOﬀ (b) Jitter

Fig. 9. Inﬂuence of EMA preﬁltering on SDBI metric

In case of severe memory constraints it is possible to reduce the memory usage

by substituting the moving average with the exponential moving average (EMA),

which requires only the storage of the last value of the computed quantity. In this

case the smoothing ﬁlter takes the form ¯

Ik=α·Ik+(1−α)·¯

Ik−1where 0 <α<1

(similar equations may be written for all parameters which are computed by

averaging some quantity). The length of the impulsive response of this ﬁlter is

inﬁnite. In order to permit a comparison with the previous results, the X-axis

of the graphs in Fig. 9 reports the number of previous samples contributing to

90% of the ﬁlter output (N90% =log(1−α)(0.9·α)).

The diﬀerent behavior of the EMA inﬂuences the quality of the synchro-

nization. Fig. 9 shows an example of the eﬀects which may be observed. If the

clock error is mainly due to jitter, the behavior of the synchronization algorithm

(Fig. 9(b) does not diﬀer much from the previous observations (Fig. 4(b)). In

presence of non-Gaussian errors, the EMS approach causes a noticeable degra-

dation of the performance(Fig. 9(a)). The beacon interval estimation error also

becomes sensitive to the parameters of the smoothing ﬁlter. An intuitive ex-

planation is that now a larger number of previous samples contributes to the

computation of a new value and, therefore, the system adapts itself slower to

the modiﬁcations of the error process.

7 Conclusion and Outlook

This work proposes a local synchronization mechanism for a general class of

WSNs using a beacon enabled MAC and having unidirectional communication

links. It relies on the a priori knowledge of the MAC layer behavior and, in

particular, it makes an opportunistic usage of the beacon frames, which are

necessary for the functioning of the MAC layer.

The synchronization problem has been reformulated as an estimation prob-

lem, which has been solved using a Kalman Filter (KF). In order to allow the

operation of the KF on data aﬀected by errors which are not AWGN, a smooth-

ing preﬁlter has been introduced. The proposed method, which relies only on

28 N. Altan and E.P. Rathgeb

local computation is eﬀective in reducing the impact of diﬀerent clock errors

and behaves better than the similar solution proposed in [8]. The algorithm may

also be implemented in devices with severe RAM limitations by modifying the

smoothing ﬁlter.

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nization. Technical report, UCLA (2002)

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sensor networks. In: WSNA 2003: Proceedings of the 2nd ACM international

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New York (2003)

[7] Karp, R., Elson, J., Estrin, D., Shenker, S.: Optimal and global time synchroniza-

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in large-scale sensor networks. ACM/Kluwer Journal on Mobile Networks and

Applications (2004)

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Mitigating Reply Implosions in

Query-Based Service Discovery Protocols for

Mobile Wireless Ad Hoc Networks

Antˆonio Tadeu A. Gomes1,ArturZiviani

1, Luciana S. Lima1,2,

Markus Endler2, and Guillaume Chelius3

1National Laboratory for Scientiﬁc Computing (LNCC)

Av. Get´ulio Vargas 333, 25651-075, Petr´opolis-RJ, Brazil

{atagomes,ziviani,lslima}@lncc.br

2Pontiﬁcal Catholic University of Rio de Janeiro (PUC-Rio)

Rua Marquˆes de S˜ao Vicente 225, 22453-900, Rio de Janeiro-RJ, Brazil

{lslima,markus}@inf.puc-rio.br

3INRIA ARES team – CITI Lab – INSA-Lyon

Villeurbanne, France

guillaume.chelius@inria.fr

Abstract. Providing service discovery in an eﬃcient and scalable way

in ad hoc networks is a challenging problem, in particular for multihop

scenarios, due to the large number of potential participant nodes and

the scarce resources in these networks. In this paper, we propose and

evaluate an approach to mitigate the reply implosion problem in query-

based service discovery protocols for multihop mobile ad hoc networks.

Our simulation results show the scalability and eﬃciency of the proposed

solution. We demonstrate that the proposed scheme considerably reduces

the number of transmissions without compromising the eﬃciency of the

service discovery in scenarios of pedestrian mobility.

1 Introduction

Eﬃcient discovery of services, or resources, in arbitrary and ever-changing, dy-

namic network topologies is a key requirement of several distributed applications,

such as grids with mobile nodes, P2P computing, or sensor networks. Neverthe-

less, research related to service discovery protocols (SDPs) in mobile ad hoc

networks (MANETs) is relatively new—as compared with wired and infrastruc-

ture wireless networks [1]—and particularly challenging in multihop scenarios, as

they are formed opportunistically and can change rapidly according to node mo-

bility. Some approaches to service discovery in multihop MANETs incorporate

the discovery functionality into the ad hoc routing protocols at the network and

This work was supported by the Brazilian Funding Agencies FAPERJ, CNPq, and

CAPES, and by the Brazilian Ministry of Science and Technology (MCT).

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 29–42, 2008.

Springer-Verlag Berlin Heidelberg 2008

30 A.T.A. Gomes et al.

link levels [2], but the inherent instability of such networks makes routing con-

sistency hard to achieve, leading to ineﬃciency in service selection. Application-

level SDPs—i.e. independent of the underlying ad hoc routing protocols—have

also been proposed for such networks [3]. As usual, these protocols adopt one

of the two basic approaches to exchange service information [4]: service queries

and service announcements.1Both approaches raise issues when considered from

the viewpoint of multihop MANETs. One the one hand, announcement-based

protocols are clearly inadequate for computational resources (e.g. CPU load

and available memory), such as the ones provided in mobile grids [5], because

resource announcements would need to be constantly updated/refreshed with

the current status of resource availability due to the dynamic nature of these

resources, as their availability can considerably vary in short periods. On the

other hand, query-based protocols can cause a serious waste of resources if

consumer nodes naively ﬂood much service requests over the network (a.k.a.

the broadcast storm problem) and provider nodes naively reply to these re-

quests (a.k.a. the reply implosion problem). As we are interested in dealing with

dynamic resources, we focus on enabling more eﬃcient query-based SDPs for

multihop MANETs.

In this paper, we present a mechanism to relieve the reply implosion problem

in query-based SDPs. The proposed Suppression by Vicinity (SbV) mechanism

works in a peer-to-peer fashion, regardless of the underlying routing protocol and

network-level addressing adopted in the MANET. The SbV mechanism assumes

a service-usage model in which one or more service-providing nodes can reply

to the same request and a consumer node can select one or more instances of

the required service. Hence, diﬀerent query-based SDPs can employ the SbV

mechanism, with only minor adaptations.

To experiment with the SbV mechanism, we have incorporated it into the

P2PDP protocol [6], a purely query-based SDP tailored for discovery of compu-

tational services in (single-hop) ad hoc mobile grids. The P2PDP protocol allows

the simultaneous selection of multiple nodes as the most suitable providers—

based on the availability of the speciﬁc resources being requested—of a par-

ticular computational service. We demonstrate through simulations that the use

of the SbV mechanism improves the scalability of query-based SDPs in multihop

MANETs. Our simulation results also show that the SbV mechanism reduces the

overall network load generated by such protocols in a distributed way through

the MANET. Moreover, these results indicate that the SbV mechanism does

not compromise the eﬃciency of service discovery in the P2PDP protocol under

scenarios of slow mobility, i.e. pedestrian walking speed.

The remainder of the paper is structured as follows. In Section 2 we survey

some related work on service discovery protocols. We describe the SbV mecha-

nism in detail in Section 3. In Section 4 we present our implementation of the

SbV mechanism in the P2PDP protocol. In Section 5 we evaluate the perfor-

mance of the proposed mechanism based on some simulation results. Finally,

Section 6 presents some concluding remarks.

1Some application-level SDPs support both approaches.

Mitigating Reply Implosions in Query-Based Service Discovery Protocols 31

2 Related Work

The past few years have witnessed many new research eﬀorts in the area of service

discovery for multihop MANETs. Some researchers have focused on extensions

to legacy protocols. Examples are Nordbotten et al. [7] and their work on service

discovery in scatternets (multihop Bluetooth ad hoc networks), and Varshavsky

et al. [2] and their cross-layer approach to integrating service discovery func-

tionalities within previous routing protocols for MANETs. Such approaches are

either platform-speciﬁc or inherit some ineﬃciency from the underlying proto-

cols. Others propose improvements to the broadcasting of service requests in

multihop MANETs, such as Konark [8] and GSD [3]. The Konark architecture

introduces the concept of ‘service gossiping’, in which a node can selectively

forward both service requests and replies based on cached announcements from

other nodes. The eﬃciency of the Konark approach, however, is highly dependent

on caching of advertised service information, thus being inadequate for grid-like

computational services. The GSD architecture controls request broadcasts based

on the semantic grouping of services as ontology classes, but its eﬃciency is also

dependent on the advertisement and caching of such classes.

Overall, the aforementioned approaches to service discovery in multihop

MANETs focus mainly on reducing the amount of packet transmissions related

to service requests in such networks. Nevertheless, to the best of our knowledge,

there is no other approach that explicitly tackles the speciﬁc problem of reply

implosions in purely query-based SDPs for multihop MANETs.

3 Suppression by Vicinity (SbV)

3.1 Message Fields and Data Structures

We make two main assumptions about the implementation of our SbV mecha-

nism in query-based SDPs.

First, service requests and replies need to convey information that allows the

nodes in the MANET to suppress unnecessary replies. More speciﬁcally, each

request must convey: (i) a unique request identiﬁer (reqID), (ii) the identiﬁca-

tion of the last node that forwarded the message (hopID), and (iii) the number

of service instances needed by the inquiring node (numMaxReplies). Similarly,

each reply must convey: (i) the reqID matching the one of the corresponding

request, and (ii) the identiﬁcation of the node which the corresponding request

was received from (retPath).

Note that most of the aforementioned information is readily available from

either SDP messages or their encapsulating packets at the link level. More spe-

ciﬁcally: (i) the reqID ﬁeld is commonly present in all query-based SDPs we

have surveyed so far, (ii) the value of hopID in service requests and of ret-

Path in service replies can be inferred from the source and destination address

ﬁelds in their encapsulating packets, and (iii) the value of numMaxReplies in

32 A.T.A. Gomes et al.

service requests can be deduced implicitly depending on the service of interest.2

Therefore, there is virtually no interference of the SbV mechanism in the format

of existing SDP messages (see Subsection 3.3).

Our second assumption is that each node in the MANET hosts a local data

structure (pendingList) used to control reply suppressions. In addition to re-

qID,numMaxReplies,andhopID, which are obtained from service requests,

each entry of pendingList has a numReplies ﬁeld (initially set to 0) that

records the amount of replies overheard by the node, and an associated timer

(cleanUp) that deﬁnes the lifetime of this entry in pendingList. Upon recep-

tion of a service request, a node records it as a pending request in pendingList

before rebroadcasting it to neighboring nodes in the MANET. It is important

to note that a rebroadcast service request has its hopID information (i.e.the

source address ﬁeld in its encapsulating packet) updated with the identiﬁcation

of the current rebroadcasting node, which allows neighboring nodes to keep track

of the path traversed by the request in their local pendingList structures. This

information will be used as the return path of corresponding replies towards the

inquiring node (as explained in the following subsections), thus reducing the

additional network load generated by ad hoc routing protocols.

3.2 The Proposed Algorithm

Figure 1 shows the pseudocode of the SbV mechanism as executed by each node

as soon as it has received a reply. When a node receives a reply to a request it

has previously originated (line 2), the node processes the message and does not

forward it further in the MANET. If instead the reply is addressed to an inquiring

node other than the receiver, the latter ﬁrst checks whether there is an entry

for the corresponding request in its pendingList (line 7). If so, the receiving

node checks whether NR<N

M,whereNRand NMare (respectively) the values

of the numReplies and numMaxReplies ﬁelds in the corresponding entry of

its pendingList.IfNR=NM, it means enough replies have already been sent

towards the inquiring node, so the receiving node suppresses (i.e. discards) this

reply. Otherwise, the receiving node increments the value of the numReplies

ﬁeld in the corresponding entry of its pendingList. It then compares its own

identiﬁcation with the value of retPath in the reply (line 10). If these values

are equal, it means the receiving node is in the return path of the reply and

hence can forward the message to the next node in the return path, as indicated

by the hopID ﬁeld in the corresponding entry of its pendingList (line 11).

Figure 2 illustrates the operation of the SbV algorithm. In the ﬁgure, only

nodes wand zare within y’s transmission range. Figure 2(a) shows the initial

2Note that all SDPs we have studied so far—with the exception of P2PDP [6] (see

Section 4) and the work by Varshavsky et al. [2]—do not allow any control on the

amount of replies per query nor automatic selection of the most suitable providers.

Users must therefore manually select the service instances they are interested in

from all received replies, possibly leading to bad selection (e.g. rashly selecting non-

localized providers may increase inter-node interference in the MANET).

Mitigating Reply Implosions in Query-Based Service Discovery Protocols 33

Require: msg,localID

1: if ﬁrstCopy(msg)then

2: if myReply(msg)then

3: process(msg)

4: return

5: end if

6: entry ←pendingList[msg.reqID]

7: if entry =NULL then

8: if entry.NR< entry.NMthen

9: entry.NR←entry.NR+1

10: if msg.retP ath =localID then

11: forward(entry.hopID, msg)

12: return

13: end if

14: end if

15: end if

16: discard(msg)

17: else

18: . . . {Deal with duplicate replies}

19: end if

Fig. 1. SbV pseudocode

conﬁguration of zand y’s pendingList.InFig.2(b),yreceives a reply to a re-

quest with reqID= 1000, and increments the value NRof the numReplies ﬁeld

in the corresponding entry of its pendingList.Asyis in the return path of the

reply (Fig. 2(c)), yrebroadcasts the message towards w,whichisy’s next hop

in the return path. zoverhears such rebroadcast and also increments the value

NRof the numReplies ﬁeld in the corresponding entry of its pendingList, but

does not in turn rebroadcast that reply because it is not in the reply’s return

path.InFig.2(d),zreceives another reply to the same request, but suppresses

such a reply because NR=NMin the corresponding entry of its pendingList.

To summarize, the SbV mechanism reduces the total number of replies con-

veyed in the MANET by eliminating unnecessary additional replies alongside

the return path from replying nodes to the inquiring one. This alleviates the

reply implosion problem, which is intrinsic of query-based SDPs.

3.3 Application-Level Forwarding Scheme

Using the SbV mechanism, the service replies are sent towards the inquiring node

through application-level forwarding. There are two alternative mappings of this

scheme onto the link level: using unicast or broadcast/multicast transmissions.

For link-level unicast mappings, the retPath value associated with replies is

inferred from the destination address ﬁeld in the encapsulating packets (e.g.the

destination MAC address in IEEE 802.11 packets). This address ﬁeld is ﬁlled

with the value of the hopID ﬁeld in the corresponding entry of pendingList

(which indicates the link-level address of the next node in the return path), as

34 A.T.A. Gomes et al.

(a) Initial conﬁguration (b) yreceivesareplytoarequest

request

Fig. 2. Scenario illustrating the SbV mechanism

part of the forward operation (line 11 in Fig. 1). For a participating node to

overhear replies from its neighbors, however, its network interface must work

in promiscuous mode. Besides the security issues involved, this alternative has

the drawback that, in promiscuous mode, the node must process the payload of

all packets (not only those pertaining to the SDP) at the higher levels, which

results in waste of resources (CPU, memory and energy) that are crucial to

computational services.

For link-level broadcast/multicast mappings, nodes do not need to work in

promiscuous mode; however, the destination link address ﬁeld in packets en-

capsulating reply messages do not specify a single recipient, so an additional

retPath ﬁeld (with the link-level address of the next node in the return path)

is needed in such messages. Further, a statement like msg.retP ath ←entry.hop

ID must be added as part of the forward operation in Fig. 1; such a statement

allows the receiving node to update the reply’s retPath ﬁeld with the value

of the hopID ﬁeld in the corresponding entry of pendingList, thus allowing

the correct node to forward the reply to the inquiring node. As link-level broad-

cast/multicast mappings consume less computational resources, we have adopted

them in our implementation of SbV for the P2PDP protocol.

It is worth noting that for MANETs in which the media access control is based

on CSMA/CA (Carrier Sense Multiple Access/ Collision Avoidance), broadcast

transmissions are less reliable and prone to collisions in comparison with unicast

transmissions. This is mainly due to the lack of acknowledgments, RTS/CTS

Mitigating Reply Implosions in Query-Based Service Discovery Protocols 35

(Request/ Consent to Send) dialogues, and a mechanism for collision detection.

The problem of collisions in link-level broadcast transmissions may be rather

alleviated if nodes are prevented from all replying at around the same time. In-

terestingly, the single-hop version of P2PDP already implements an algorithm

in which replies from diﬀerent collaborators are time-shifted, as discussed in the

following section. Regarding the lack of acknowledgments, an implicit acknowl-

edgment mechanism for broadcast transmissions could be used. To understand

this, consider again the example of Fig. 2. When wreceives the reply message

from y(Fig. 2(c)), being in the return path, it will forward the message. Such

a transmission will be overheard by y(asitiswithinw’s range); ycould then

regard this transmission as a higher-level acknowledgement from w.Nonethe-

less, many subtle issues arise if a retransmission policy based on such implicit

acknowledgments is devised to improve the reliability of the discovery protocol.

We argue that such additional complexity is not worthwhile, as reply messages

are always subject to suppression along the remaining path towards an inquir-

ing node. In fact, the experimental results presented in Section 5.2 demonstrate

that, in scenarios of pedestrian mobility, the discovery eﬃciency in the presence

of the SbV algorithm is kept high even without such a retransmission policy.

4 Implementation

We have implemented our SbV mechanism as part of the P2PDP protocol [6].

Along this section, we give a quick overview of the protocol, emphasizing the

points where changes were made to accommodate the SbV mechanism.

4.1 Peer-to-Peer Discovery Protocol

Nodes can play two main roles in P2PDP: collaborators or initiators. Initiators

demand computational services from collaborators, which oﬀer their resources—

e.g. CPU cycles, memory and disk space—for the provisioning of such services.

An initiator sends service requests (IReq messages) to the collaborators and,

based on the received replies (CRep messages), deﬁne a list containing the col-

laborators that are more suitable to provide the service. Figure 3 depicts the

format of IReq and CRep messages and illustrates an example of the protocol

operation in multihop MANETs.

A collaborator adopts two criteria to decide whether it is able to provide

the requested service. The ﬁrst criterion acts as an admission control, checking

weather the collaborator indeed oﬀers the service (e.g. if it hosts a speciﬁc Web

service or a Java virtual machine). The second criterion deﬁnes the suitability

of the collaborator in providing the service. Crucially, the initiator maps the re-

quired service onto the amount of resources needed for its provision. The context

of interest—indicated in the ctxtInfo ﬁeld of IReq messages—allows the ini-

tiator to ask collaborators about the desired service, which resources are needed

for the service provisioning, and the relative importance among such resources.

The initiator also determines in the numMaxReplies ﬁeld of IReq messages

36 A.T.A. Gomes et al.

Fig. 3. Example of P2PDP messages

the number of service instances to be involved. Based on such information, a col-

laborator builds its CRep message, informing in the resInfo ﬁeld the address

of the service (e.g. a URL to a Web service or the network-level address of the

node), and the resource availability related to the provisioning of such service.

We have introduced new ﬁelds in the IReq and CRep messages to allow the

operation of P2PDP in multihop MANETs. The numHops and maxHops ﬁelds

in IReq messages indicate respectively the current and maximum number of

hops associated with such messages, and are used to constrain the diameter of

service requests. The retPath ﬁeld in CRep messages is used for forwarding

such messages to inquiring nodes, and it is necessary due to the adoption of

link-level broadcast transmissions in our application-level forwarding scheme, as

discussed in Section 3.3.

4.2 Controlled Delay of CRep Messages

In the P2PDP protocol, each device willing to collaborate with the provision

of a particular service delays the transmission of its CRep messages according

to a timer. This timer is set to be inversely proportional to the availability

of the required resources at the collaborating node. This way, nodes that are

more resourceful reply earlier to service requests. If the total number of replies

generated in the MANET is larger than the requested maximum number of

replies NM(which is set by the numMaxReplies ﬁeld in IReq messages), the

initiator selects the ﬁrst NMreceived messages as the most suitable replies. When

a node receives a request, it gathers its current state in terms of the resources of

interest for the given request to compute the reply delay. Importantly, all devices

in the MANET must employ the same criterion for such computation. In the

implementation of P2PDP, a collaborating nodes sets the reply delay to τtime

units as given by

τ=1−ω



i=1 αiPi

N

j=1 PjDmax −2HS, 0≤α≤1

0<ω≤1,(1)

Mitigating Reply Implosions in Query-Based Service Discovery Protocols 37

where Nrepresents the number of diﬀerent resource types the collaborating

node should take into account. Piis the weight that describes the relative im-

portance of each resource type i,1≤i≤N.BothNand Piare described as

part of the ctxtInfo ﬁeld in the request. αiis the normalized level of cur-

rent availability (in the interval [0,1]) of resource type iat the collaborating

node. Dmax is the maximum reply delay, which is also obtained from the re-

quest (maxReplyDelay ﬁeld). Hand Sare used for considering the transfer

delays that IReq and CRep messages may experience. His the distance in hops

(obtained from the hopCount ﬁeld in the IReq message) between the collab-

orating node and the inquiring node, and Sis a tuning parameter representing

the transfer delay at each transmission. Finally, ωindicates the willingness (also

in the interval [0,1]) of the collaborating node to participate in the resource

provisioning. τis undeﬁned for ω= 0; such a value means the user is not willing

to participate, thus the collaborating node will not send replies. In this case, the

node will only act as an intermediate in the message forwarding process.

We highlight that the delay reply mechanism provides a time shift in the

transmission of replies, thus allowing for a reduction in the number of collisions

of these messages when link-level broadcast transmissions are used.

5 Performance Evaluation

We carried out a set of experiments with the SbV mechanism. These experiments

were conducted with two diﬀerent simulators to evaluate two diﬀerent aspects

of our approach: scalability and discovery eﬃciency.

5.1 Scalability Analysis

We analyzed the scalability of the SbV mechanism using the ns-2 simulator [9].

All experiments in this simulator consider a ﬁxed node density within the

MANET (using topologies with a constant number of nodes within the same

transmission range) so the impact of increasing the number of nodes in the

MANET could be properly evaluated. The results presented in this section cor-

respond to the average of a hundred sample runs per simulated scenario with a

95% conﬁdence level. This analysis was mainly focused on the evaluation of two

metrics: the number of reply messages in the MANET and the suppression diam-

eter of these messages. Table 1 presents the parameters adopted in the simulated

scenarios.

The average load of reply messages in the MANET was computed using,

for each scenario, the mean number of packets involving these messages. Impor-

tantly, this metric also allows us to deduce whether there is a signiﬁcant reduction

in the energy consumption of devices in the MANET due to the suppression of

replies, given that transmissions are known to be responsible for a high energy

consumption. Using this metric, we compared two purely query-based SDPs:

one in which service replies are sent by unicast to inquiring nodes (we called

38 A.T.A. Gomes et al.

Table 1 . Parameters for ns-2 simulations

Parameter Value

Number of nodes (N) 10to240

Percentage of collaborating nodes (p) 20% to 80%

Maximum number of replies (R)1to10

Node density 5

Distance between nodes 10m

it UCast), and another in which replies are sent through application-level for-

warding, with the SbV mechanism incorporated in the forwarding process. In

both protocols, the inquiring nodes broadcast service requests by ﬂooding, and

no service announcements are employed. Figure 4 presents the number of re-

ply messages as a function of the number of nodes for diﬀerent percentages of

replying devices. The vertical error bars indicate the conﬁdence intervals. The

results show that the adoption of the SbV mechanism allows for an increasing

reduction—with respect to the UCast protocol—in the total number of trans-

missions, as the number of devices in the MANET increases. We also observe an

even higher level of suppressions when there is a larger percentage of nodes (p)in

the MANET with interest in collaborating on service provisioning. These results

give a clear idea of the scalability that protocols adopting the SbV mechanism

can achieve, such as in our implementation of P2PDP.

The suppression diameter of reply messages measures the distance (in number

of hops) between the inquiring node and the nodes where suppressions occurred.

This metric allows us to evaluate the degree of distribution of the load alleviation

provided by SbV among the nodes in the MANET, and consequently the energy

savings among the nodes due to the reduction in the amount of transmissions.

Figure 5 presents the distribution of suppressions as a cumulative distribution

function (CDF) for diﬀerent numbers of nodes and percentages of replying nodes.

To better illustrate the distribution of suppressions through the MANET, the

results presented in Fig. 5 are contrasted with a uniform CDF (represented by

the straight line in the ﬁgure). We observe a better distribution of suppressions

as the number of nodes and the percentage of replying nodes (p) increase. Again,

this suggests the scalability of our proposed approach.

100

150

200

250

300

350

400

50 100 150 200

number of transmissions

number of nodes

Percentage of replying nodes (p)= 20%

SbV (R = 1)

SbV (R = 2)

SbV (R = 4)

SbV (R = 6)

SbV (R = 8)

SbV (R = 10)

UCast

200

400

600

800

1000

1200

1400

1600

20 40 60 80 100 120 140 160 180 200 220 240

number of transmissions

number of nodes

Percentage of replying nodes (p)= 80%

SbV (R = 1)

SbV (R = 2)

SbV (R = 4)

SbV (R = 6)

SbV (R = 8)

SbV (R = 10)

UCast

Fig. 4. Network load in the MANET due to reply messages

Mitigating Reply Implosions in Query-Based Service Discovery Protocols 39

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 1 2 3 4 5 6 7

suppression CDF

suppression diameter

Number of nodes = 60

Percentage of replying nodes (p)= 20%

Uniform CDF

SbV (R = 1)

SbV (R = 2)

SbV (R = 4)

SbV (R = 6)

SbV (R = 8)

SbV (R = 10) 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 1 2 3 4 5 6 7

suppression CDF

suppression diameter

Number of nodes = 60

Percentage of replying nodes (p)= 60%

Uniform CDF

SbV (R = 1)

SbV (R = 2)

SbV (R = 4)

SbV (R = 6)

SbV (R = 8)

SbV (R = 10)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

suppression CDF

suppression diameter

Number of nodes = 240

Percentage of replying nodes (p)= 20%

Uniform CDF

SbV (R = 1)

SbV (R = 2)

SbV (R = 4)

SbV (R = 6)

SbV (R = 8)

SbV (R = 10) 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

suppression CDF

suppression diameter

Number of nodes = 240

Percentage of replying nodes (p)= 60%

Uniform CDF

SbV (R = 1)

SbV (R = 2)

SbV (R = 4)

SbV (R = 6)

SbV (R = 8)

SbV (R = 10)

Fig. 5. Distribution of reply suppressions in the MANET

5.2 Discovery Eﬃciency

To observe the impact of mobility on the eﬃciency of the P2PDP discovery

process using the SbV mechanism, we have implemented a modiﬁed version of

this protocol for multihop MANETs, as well as a testing application to run on

top of it. Both implementations were done in Java, using the CDC (Connected

Device Conﬁguration) J2ME proﬁle as our reference platform. Our testing appli-

cation consisted of a master-worker matrix-matrix multiplication program. For

the purposes of our evaluation, we employed a very simple distributed multi-

plication algorithm: given matrices Am×nand Bn×p, a master node computes

Cm×p=AB by selecting pworker nodes with the P2PDP protocol and sending

to each worker node i(1 ≤i≤p)acopyofmatrixAalong with matrix bi

n×1

(transposed vector whose elements are those of the i-thcolumnofB). Each

worker node icomputes matrix ci

n×1=Abi

n×1and returns it to the master

node, which then builds each i-th column of Cfrom ci

n×1. The selection of the

worker nodes in the MANET that take part in the task is made by only con-

sidering those nodes with the most available CPU and memory resources—more

speciﬁcally, N=2,PCPU =4,andPmem =1inEq.1.

We deployed our implementation in the NCTUns simulator and emulator [10].

To do so, we performed some changes to the underlying monitoring service

that is part of the original P2PDP implementation. This service3is responsible

for gathering information about the current state of a mobile node, including

3The monitoring service used by P2PDP corresponds to the implementation available

at the MoCA architecture [11].

40 A.T.A. Gomes et al.

connectivity, CPU load, available energy and memory, and disk storage space.

In the NCTUns platform, a single machine runs several (virtual) nodes inter-

connected by a simulated MANET, but with no kernel isolation between them.

Thus, the use of the original monitoring service would lead to unrealistic sce-

narios in which all nodes in a simulated MANET would have the same state

information. To tackle this, we have implemented a “fake” monitoring service

that provides randomly generated state information for each diﬀerent node in a

simulated MANET.

The simulation scenarios consisted of 40 nodes placed in an obstacle-free,

500m X 500m area. The initial position of each node was set at random, with the

constraint that at the beginning of the simulation the nodes formed a connected

topology. The ﬁrst scenario consisted of a stationary topology. In the remaining

scenarios, the movement of nodes followed the random walk model. In such a

model, each node moves in a random direction for some seconds—in a speed

that is uniformly distributed in the range ]0,S

max]—then chooses a new random

direction, with no pause between the direction changes. This corresponds to

a worst-case mobility scenario for each speed range. Table 2 summarizes the

parameters adopted in the scenarios simulated with the NCTUns platform.

Table 2 . Parameters for NCTUns simulations

Parameter Value

Number of nodes (N)40

Number of resource providers 10

Maximum number of replies (R)4

Transmission range 100m

Maximum node speed (Smax ) 0 to 5m/s

The discovery eﬃciency for each simulation scenario was measured as a sam-

ple proportion calculated over 100 runs. Each run consisted of a single resource

consumer issuing a single IReq message to a set of resource providers. The sam-

ple proportion indicates the percentage of runs in which the protocol delivered at

least Rreplies to the resource consumer, as determined by the numMaxReplies

ﬁeld in the IReq message. The number of resource providers at each run was

ﬁxed to 10, which corresponds to 25% of the nodes in the simulated scenarios.

Such a percentage was chosen based on the study by Hughes et al. [12], which

states that in Gnutella—a famous P2P, collaboration-based ﬁle-sharing system—

this percentage of participants is responsible for 98% of all service provisions.

Figure 6 presents the discovery eﬃciency of the P2PDP protocol extended

with the SbV algorithm as a function of the maximum node speed (Smax ). The

vertical error bars correspond to the 95% conﬁdence intervals for each sample

proportion. The results show that the protocol behaves well under situations of

human mobility (from 0.8 to 1.2m/s).

As it can be observed in Fig. 6, even for the stationary scenario (Smax =0)

the protocol does not reach 100% eﬃciency—the sample proportion is 92%, with

Mitigating Reply Implosions in Query-Based Service Discovery Protocols 41

100

0 1 2 3 4 5

discovery efficiency (%)

node speed (m/s)

Fig. 6. Discovery eﬃciency in a mobile scenario

±4.13 conﬁdence intervals. This is due to the drawbacks stated in Section 3.3

regarding the application-level forwarding scheme being mapped onto link-level

broadcast transmissions in CSMA/CA enabled nodes.

6 Conclusions

In this paper, we have presented the design and implementation of a mechanism

called Suppression by Vicinity (SbV) to reduce the implosion of reply messages

in purely query-based SDPs for multihop MANETs. Our experimental results

show that the proposed SbV mechanism is eﬃcient in controlling the amount of

service replies transmitted in the MANET. Moreover, the additional processing

the SbV mechanism generates is well distributed among the nodes. In particular,

this prevents greater energy drain rates on nodes nearby the inquiring node, thus

promoting an indirect balance on energy consumption due to transmissions.

Finally, the SbV mechanism behaves well in the mobile application scenarios we

are interested in, which involves pedestrian (walking) mobility.

During the development of this work, some aspects have been identiﬁed for

future investigation. The ﬁrst one is the impact of the maxReplyDelay par-

ameter on the eﬃciency of the SbV mechanism in the P2PDP protocol. Fine-

tuning this parameter—e.g. as a function of the transmission delay of messages—

is essential to reduce the discovery time without increasing the number of reply

collisions, which is achieved through the asynchrony in the transmission of these

messages. Still in this context, we believe it is important to investigate the in-

ﬂuence of clock drifts among diﬀerent equipment on the timers associated with

the SbV mechanism and its implementation on the P2PDP protocol. A second

point is that we have considered only low-mobility scenarios in our simulations.

In more dynamic scenarios, the concept of return path the SbV algorithm uses for

conveying reply messages is likely to reduce the discovery eﬃciency considerably.

To deal with this, we are currently investigating alternative implementations of

the SbV mechanism that automatically resort to using traditional ad hoc routing

protocols whenever a failure is detected in the return path.

42 A.T.A. Gomes et al.

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D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 43–57, 2008.

Adaptive MANET Routing: A Case Study

Liang Qin and Thomas Kunz

Systems and Computer Engineering, Carleton University, Ottawa, Ontario, Canada

tkunz@sce.carleton.ca

Abstract. Node mobility plays an important role in the routing performance for

MANETs. Many protocols provide parameters to adapt to different levels of

mobility, but this is a global optimization (i.e., typically all nodes choose the

same parameter values and they use these parameters throughout their participa-

tion in a MANET). We choose the monitored number of link breaks as key mo-

bility metric and observe that the relative observable mobility varies widely for

different nodes and over time for the same node. We utilize this (simple) mobil-

ity metric to allow a node using OLSR as routing protocol to dynamically adapt

its behavior (changing the Hello Interval, selecting MPRs, etc.). Simulations

with different mobility scenarios show that Adaptive OLSR can improve packet

delivery ratio, reduce packet latency, and reduce routing overhead, especially in

high mobility scenarios. As a general conclusion, we believe that designing

adaptive routing protocols (protocols that change their behavior based on mo-

bility and potentially traffic patterns) holds great promise in resource-

constrained environments.

Keywords: MANET, routing, OLSR, mobility, simulation, NS2.

1 Introduction

A Mobile Ad Hoc Network (MANET) is defined by the MANET Working Group as

“an autonomous system of mobile routers (and associated hosts) connected by wire-

less links - the union of which forms an arbitrary graph”. Because of the antenna’s

limited transmission range, the nodes in the network may act as a router to forward

packets to other nodes, and then a routing protocol is needed. The main characteristics

of a MANET are:

– Packets may need to be forwarded by several nodes to reach the destination.

– Dynamic topology due to the nodes' mobility or nodes leaving/joining the net-

work, which causes packet loss and route change.

– Resource constrains: wireless medium bandwidth, device’s battery, processing

speed and memory.

To obtain the correct network topology, frequent control message exchanges between

nodes are required; on the other hand, these control messages will consume valuable

wireless bandwidth resources. This tension poses a challenge for developing routing

protocols. Existing MANET routing protocols basically can be classified as proactive

44 L. Qin and T. Kunz

(table-driven), reactive (on-demand) and hybrid. Examples of proactive routing proto-

cols are Destination-Sequenced Distance-Vector Routing (DSDV) [1] and Optimized

Link State Routing Protocol (OLSR) [2]. Examples of reactive routing protocols are

Ad hoc On-Demand Distance Vector (AODV) Routing [3] and Dynamic Source

Routing (DSR) [4]. The Zone Routing Protocol (ZRP) [5] is a hybrid of proactive and

reactive routing protocols. It applies proactive routing on a node’s neighbors, and

searches through the network using a reactive protocol. Detailed reviews and per-

formance comparisons of these protocols can be found in [6] [7] [8].

The MANET routing protocol performance depends on the network conditions.

For example, the simulation results in [9] show that under high network load proac-

tive routing techniques outperform reactive routing techniques. Existing MANET

routing protocols assume specific network conditions and preset certain parameters

for all nodes. Because of the characteristics of a MANET, mobile nodes may experi-

ence a very dynamic environment over time, and different nodes may experience very

different conditions at the same time. The term environment here not only refers to

physical environment, which could impact on the transmission of wireless signal, but

also includes the mobility of nodes, and traffic that is routed through nodes them-

selves or shares the wireless medium with the node. The dynamic nature implies that

a node’s environment changes with space and time. If nodes can apply routing pa-

rameters individually and be adaptive to the network environment based on observ-

able metrics, the network performance might be improved.

The basic steps for adaptive routing consist of: monitor the current network charac-

teristics based on some appropriate metrics; map these metrics to related routing pa-

rameters and adjust the parameters if necessary. In a MANET, the environment pa-

rameters that a node may monitor include the mobility of nodes in its neighborhood,

the current number of flows or volume of traffic, the busy/idle time of the (shared)

medium, the received signal strength, etc. These parameters impact the routing proto-

col performance in a number of ways. For example, high mobility typically causes

frequent link breakage and invalid routes; high traffic on certain links will cause con-

gestion; fluctuating signal strength makes route discovery and maintenance difficult.

In this paper, first we propose a simple mobility metric that individual nodes can use

to sense the mobility level changes around them. We then apply this mobility metric

by redesigning OLSR so that nodes adjust their routing behavior individually. Our

simulation results, using a range of mobility scenarios, show that this “Adaptive

OLSR” protocol improves the routing performance in terms of packet delivery ratio,

packet latency, and routing overhead.

The rest of the paper is organized as follows: Section 2 discusses the impact of

mobility on routing protocol performance and how to adequately measure mobility

with little overhead on a given node. Section 3 reviews related work and describes

Adaptive OLSR, our case study for an adaptive routing protocol. Section 4 presents

the simulation results, showing that enabling nodes to individually adapt their routing

behavior in response to the locally observed mobility level does indeed increase pro-

tocol performance. Our conclusions and future work are listed in Section 5.

Adaptive MANET Routing: A Case Study 45

2 Mobility and Mobility Metrics

Packet loss is an important performance metric for MANET routing protocols. The

main causes of packet loss are transmission errors, mobility and congestion. In this

paper we focus on the mobility effect. A number of mobility metrics have been pro-

posed in the literature and are used in the generation of mobility scenarios, such as

node speed, pause time etc. They are useful for generating mobility scenarios for

simulation purposes, but are not appropriate metrics for adaptive routing. For starters,

link changes do not only depend on the mobility metrics of the node itself but also the

(relative) speed of its neighbors. In addition, parameters such as “pause time” are

mobility-model-dependent and therefore hard to generalize. A unifying mobility met-

ric is proposed in [9]: “Mobility is defined as the average change in distance over time

between all nodes (in m/s).”[9], which we use as well. By appropriately modifying the

relevant mobility model parameters, we are thus able to generate mobility scenarios

that show comparable levels of relative node mobility.

Fig. 1. PDR vs. Mobility for the MH Mobility Model

We first ran a series of simulations with different routing protocols and mobility

models to explore the relationship between the overall performance and the mobility

metrics. The purpose of these simulations is to (re-)confirm the impact of mobility on

the performance of routing protocols. We experimented with two entity mobility

models: Random Waypoint (RW) [8] and the Manhattan Grid (MH) [11], and one

group model: Reference Point Group Mobility (RPGM) [12]. We conducted all our

simulations in NS2 (the Network Simulator [13], which provides routing protocols

such as AODV and DSR. In addition, we installed the UM-OLSR implementation

[14] for NS2. The simulation area is 1000x1000 m, 25 CBR sources are sending 4

packets/s of size 64 bytes. Simulation time is 900 seconds. For each protocol (AODV,

DSR, and OLSR), we repeated each run 5 times for each mobility scenario. We

02.5 57. 5 10

100

Manhattan Grid

AODV

DSR

OLSR

Mobility (m /s)

PDR ( %)

46 L. Qin and T. Kunz

generated and analyzed the mobility scenarios with BonnMotion [15], which can

generate RWP, MH and RPGM model scenarios and compute statistical data on the

generated mobility scenarios (including the average relative mobility). We set the

total number of nodes in MH model to 170, and RWP to 80 (to achieve consistent

node degrees). For the RPGM simulations, on average 5 nodes are in a group, the

maximum distance from the center of the group is set to 25 m.

Figure 1 shows the packet delivery ratio (PDR) for AODV, DSR and OLSR for the

MH mobility model with different mobility scenarios with increasing relative mobil-

ity. In all scenarios and for all mobility models AODV achieved the highest PDR,

DSR has the worst performance, and OLSR falls somewhere in between. Also, we

can see that the PDR has some correlation with mobility: when mobility increases,

normally PDR decreases, but the rate of decrease (the sensitivity of the protocol to

mobility) varies for different protocols in different mobility models. For example, we

observed that the PDR of DSR, using the RW mobility model, decreases quickly

when relative mobility exceeds 3m/s.

To allow a node to adapt to the level of relative mobility, it needs to monitor this

parameter. Mobility metrics focus on a node and changes in its neighborhood. There

are basically two ways to collect neighbor information: a mobile node can be

equipped with some positioning device such as GPS and exchange its position infor-

mation periodically; alternatively a node simply depends on exchanging “Hello” mes-

sages to sense the neighbors. In this paper we assume that mobile nodes do not have a

positioning device, and only depend on message exchange to sense the neighbor

changes. Based on this assumption, the relative mobility metric we used above to

evaluate the overall protocol performance is not feasible because it requires that every

node knows all nodes’ positions and speeds all the time.

Fig. 2. Total Number of Link Breaks vs. Different Mobility Models

Link duration [10] is a mobility metric defined as the time period that two mobile

are within transmission range. We explored the relationship between relative mobility

and link duration and found that, in general, as mobility increases, the average link

02.5 57. 5 10

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

Manhattan Grid

Mobility (m /s)

No. of Link Breaks

Adaptive MANET Routing: A Case Study 47

duration decreases, indicationg that the links become less stable. However, average

link duration alone does not accurately represent the current mobility status either.

First, it is an average value; second, although we know that longer link duration

means stable links, the exact value is mobility-model and network configuration de-

pendent. Link duration may also need to be compared with historic data, which is the

average value during a much longer period of time, in order to make judgments with

respect to the mobility status.

As [9] observed, mobility has a good correlation with the number of link breaks.

Our results in Figure 2 show a similar relationship (again showing only the results for

the MH model, but a similar pattern shows for the other models). In addition, the

number of link breaks is an easily obtained parameter from the routing table or by

periodically exchanging Hello messages. From Figure 2, the total number of link

breaks has nearly linear correlation with the relative mobility, which is strongly re-

lated to the protocol performance, so it is a good choice as mobility metric. However,

some routing protocols such as DSR do not employ periodic Hello messages, in par-

ticular in networks where alternative mechanisms can provide indication of link fail-

ure (link-level callbacks, for example). However, in these cases alternative sensing

mechanism based on promiscuous listening can be used instead. In DSR for example,

to collect neighbor information, a DSR node can operate in promiscuous mode, moni-

toring packets that are not the destined for it to learn about new routes. So the node

can periodically check its route cache to obtain the neighbor list (nodes one hop

away), and monitor the change in the neighbor list over time.

As a final step, to confirm that nodes experience vastly different environmental

conditions, Figure 3 shows the node degree for three randomly selected nodes over

time for a mobility scenario generated with the MH mobility model at medium rela-

tive mobility. Different nodes experience very different neighborhood densities over

time, and the number of neighbors of a node at any given point in time fluctuates

widely as well.

Fig. 3. Node Degree vs. Time for Three Randomly Selected Nodes

0250 500 750

Manhattan Grid

Simulat ion Tim e ( s)

Node Degr ee

48 L. Qin and T. Kunz

3 Adaptive OLSR

Most current MANET routing protocols preset certain parameters for a “typical”

MANET scenario and apply the same parameters to all mobile nodes after protocol

deployment. As hinted at by Figure 3, mobile nodes experience very different envi-

ronmental conditions over time. Using a fixed set of identical parameter values will

most likely not achieve the best possible routing protocol performance. The basic idea

of adaptive routing is for each node in a MANET to adjust its routing behavior based

on the sensed network environment around it.

3.1 Related Work

In [22][23], some simulations were run by varying HELLO_INTERVAL values for

OLSR, and the same value is applied to every node in the network. The results show

the tradeoff between packet delivery ratio and control message overhead. In the

ARM (Adapting to Route Demand and Mobility) protocol [21], the rate of neighbor

change is used as mobility metric. The routing messages contain a sender ID, update

period and the sender’s mobility metric. Each mobile node will average the mobility

metrics of itself and its neighbors over time interval TW-SMOOTH and adjust the

routing update period based on this average mobility value. The authors implemented

ARM in DSDV, but only showed simulation results with two mobility patterns. In

[17], the HELLO_INTERVAL of AODV changes according to the node mobility of

its neighbors. The node mobility is determined by periodically checking the routing

table, summing up the new and lost neighbors since the last check. This mobility

metric will be used to decide the value of the HELLO_INTERVAL. The simulation

results show that the packet delivery ratio and latency of adaptive AODV improve,

but the improvement is rather limited and typically occurs only for scenarios with

high node density or a high number of data sources. Fast-OLSR [18] [19] uses the

number of neighbor changes as mobility metric. A node reduces its Hello-Interval

when this metric reaches a predefined threshold. The papers only show simulation

results for a network with 7 nodes, and without a performance comparison with the

original OLSR protocol.

The purpose of Adaptive OLSR is to sense the link changes and adapt the routing

behavior accordingly, increasing the protocol performance. We choose OLSR as an

example for adaptive routing because it is a table-driven routing protocol and ex-

changes Hello messages between neighbors. It is therefore relatively straightforward

to determine the number of link breaks and use it as mobility metric. Our Adaptive

OLSR is inspired by Fast-OLSR [19], but with some major differences. First we use

the number of link breaks as the mobility metric as discussed in Section 2. Second, in

applying this mobility metric to OLSR, each node not only adjusts its

HELLO_INTERVAL based on the mobility level it monitored, but also changes the

MPR selection, a key component of the protocol. We conducted extensive simulation

validation with different mobility scenarios. The simulation results show that our

Adaptive OLSR can significantly increase packet delivery ratio, reduce packet la-

tency, and reduce control message overhead.

Adaptive MANET Routing: A Case Study 49

3.2 OLSR Basics

OLSR is a proactive routing protocol; nodes exchange the topology information with

other nodes in the network regularly. Every node will send a Hello message at least

every HELLO_INTERVAL period. A node only broadcasts its Hello messages to its

one-hop neighbors. The Hello message includes the list of a node’s one-hop

neighbors, and the corresponding link states, and is used for link sensing, neighbor

detection and MPR (Multipoint Relay) selection signaling. Each node selects MPR

nodes among its one hop symmetric neighbors; this set of MPRs will cover its strict

two-hop neighbors. A node also declares its MPR set in its Hello messages, so that an

MPR node can know the set of nodes that select it as their MPR, which is called MPR

selector set of this MPR node. Finding the optimal MPR set is a NP complete prob-

lem, [2] proposes a simple heuristic for MPR selection. OLSR uses MPRs to optimize

the flooding of control messages throughout the network, significantly reducing the

number of retransmissions to reach every node. In addition, a node maintains a Link

Set and Neighbor Set. The Link Set is populated with information about links to its

neighbors and the Neighbor Set is updated according to the changes in Link Set. Ac-

cording to [2], the default HELLO_INTERVAL value is 2 seconds. Hello messages

are used for link sensing. When node mobility is high, this default value may be too

long, causing a node’s MPR set or routing table entries to be inaccurate and resulting

in packet loss. On the other hand, in low-mobility environments, there is no reason for

nodes to frequently broadcast Hello messages, as the set of neighboring nodes is

changing relatively slowly.

Each MPR node periodically broadcasts Topology Control (TC) messages, which

includes links to its MPR selector set. TC messages are flooded throughout the net-

work using the MPR optimization. Because all reachable nodes will select their MPR

sets, all reachable destinations will be declared. Every node in the network uses TC

messages to build a (partial) representation of the network topology, and to calculate

the shortest paths to the destinations in the network. The protocol ensures that the

partial knowledge is sufficient to determine the shortest path, and each path between

two nodes is a sequence of MPR nodes.

3.3 Protocol Changes

The basic idea of Adaptive OLSR is that every node in the network adjusts its routing

behavior based on the environment it experiences, which is the number of link breaks

in this study. A mobile node will change its HELLO_INTERVAL according to the

number of monitored link breaks. We define two HELLO_INTERVAL values: a

default HELLO_INTERVAL of 2 seconds and a FAST_OLSR_HELLO_INTERVAL

of 1 second. Each node checks its link table every second, and compares the number

of its symmetric neighbors with the ones it stored when it checked last time. This

allows it to determine the number of link breaks during this period of time. The node

keeps records of link breaks over the past three seconds. When the number of link

breaks reaches a threshold, a node will change its HELLO_INTERVAL to

FAST_OLSR_HELLO_INTERVAL.

In addition, nodes adapt their MPR selection strategy. To model this, we introduce

node states. Every node operates in one of three modes: Default, Fast-Response, and

50 L. Qin and T. Kunz

Fast-OLSR, as shown in Figure 4. Nodes in different modes co-exist in the same net-

work because they use the same message formats. Initially, every node is in Default

mode, which refers to the original OLSR specification, exchanging control messages

based on the default or configured protocol parameters. A node changes to Fast-OLSR

mode once the number of link breaks reaches the UPPER_LINKBREAKS threshold,

which we set to 2. In Fast-OLSR mode, a node changes its HELLO_INTERVAL to

FAST_OLSR_HELLO_INTERVAL. On the other hand, when a node is in Fast-

OLSR mode and the monitored number of link breaks is equal to or less than a lower

threshold LOWER_LINKBREAKS, which is set to 1, for three consecutive periods,

the node switches back to Default mode. The reason a node does not switch to default

mode immediately once its mobility metric reaches the lower threshold is to reduce

frequent mode switches.

Fast Response

Fast OLSR

Default OLSR

Receive Fast

OLSR

No Fast

OLSR Neighbor

Link Breaks No

Upper

Threshold

Link Breaks No

Lower

Threshold

Link Breaks No

Upper

Threshold

Fig. 4. Modes and Mode Transitions for Adaptive OLSR

The Hello message sent by a node in Fast-OLSR mode is called Fast-Hello mes-

sage, which is in the same format as the default Hello message. However, the message

only contains a node’s MPR set and neighbors in Fast-Response mode. When a node

in Default mode receives a Fast-Hello message, it switches to Fast-Response

mode (which indicates that at least one of its neighbors is in FAST_OLSR

mode, but not this node itself), changes its HELLO_INTERVAL to

FAST_OLSR_HELLO_INTERVAL and sends empty Hello messages called

OLSR_RESPONSE_FAST_HELLO_MSG. The purpose of the empty Hello is for the

nodes in Fast-OLSR mode to sense neighbor changes quickly. A node in Fast-

Response mode also sends regular Hello messages. To reduce the traffic overhead, we

limit the node to only send one empty Hello message per second. A node in Fast-

Response mode switches to Fast-OLSR mode when its number of link breaks is equal

to or greater than the UPPER_LINKBREAKS threshold (same as a node in Default

mode). On the other hand, when a Fast-Response node has not further neighbors in

Fast-OLSR mode, it will switch back to Default mode.

Adaptive MANET Routing: A Case Study 51

Nodes in Default and Fast-Response mode select MPRs based on the heuristic

in [2] and are candidates for being selected as MPRs themselves. Nodes in Fast-

OLSR mode should not be an MPR node as they are experiencing rapid changes in

their neighborhood. They therefore set their willingness to OLSR_WILL_LOW in

their Fast-Hello message to avoid being selected as an MPR. In addition, a Fast-OLSR

node only selects a limited number (currently up to 2) of MPRs, which should be

neighbors in Fast-Response mode. We exclude neighbors in Default mode as poten-

tial MPR node because such nodes have not yet learned about the existence of this

Fast-OLSR neighbors.

Every node in Fast-OLSR has an MPR set and an MPR candidate set. Every

neighbor in Fast-Response mode but not in its MPR set will be in its MPR candidate

set. When a node switches to Fast-OLSR mode, its first MPR set is built from its

current MPR set with reduced size, the remaining MPR nodes are moved to the MPR

candidate set if that MPR node is in Fast-Response mode. When a Fast-OLSR node

receives a OLSR_RESPONSE_FAST_HELLO_MSG from one of its neighbors

(which indicates that this neighbor is in Fast-Response mode), and this neighbor is

not yet in its MPR or MPR candidate set, it adds it either to its MPR set (if it is not

full) or to its MPR candidate set. When a neighbor in Fast-Response mode switches to

Fast-OLSR mode and therefore becomes ineligible as an MPR, it is removed from

either the MPR or MPR candidate sets. In the former case, a new node is moved from

the MPR candidate set to the MPR set.

4 Simulation Results

Our adaptive version of the OLSR protocol is implemented using the UM-OLSR

version 0.8.8 for NS2 version 2.29 (which we will refer to in the remainder of this

paper as “Default OLSR”). In the following simulations, we used the Random Way-

point model, all the mobility scenarios are generated by the Random Trip Model Tool

[20]. We summarize our mobility scenarios in the format speedMean-speedDelta-

pauseMean-pauseDelta, based on the parameters for the Random Trip Model. For

example, 10-5-1-1 is a mobility scenario with mean node speed of 10m/s, speed varia-

tion of 5m/s, mean pause time of 1 second and pause time variation of 1 second. The

simulation area is 1000x1000m with 80 mobile nodes. The data rate is 4 packet/s with

25 data sources; each packet is 64 bytes in size. Simulation time is 900 seconds.

First we calculated the total number of link breaks for each mobility scenario dur-

ing the simulation time. The calculation is based on a 250 m transmission range,

comparing neighbors every second with the ones recorded a second earlier. Then we

ran simulations in ns2 using the Default OLSR implementation with 5 cases for each

mobility scenario and determined the average PDR. These values are shown in

Table 1, showing as expected a strong correlation between PDR and the number of

link breaks.

In a next step, rather than having nodes individually adjust their behavior based on

the observed mobility level, we explored whether globally tuning protocol parameters

can increase performance. The most relevant parameter related to mobility is the

HELLO_INTERVAL, as this is the basis for link sensing in OSLR. We conducted a

series of simulations with various global HELLO_INTERVAL values for the mobility

52 L. Qin and T. Kunz

Table 1. Number of Link Breaks and Default OLSR PDR for Different Mobility Scenarios

Mobility Scenario 3-2-1-1 10-5-1-1 12-6-5-2 15-4-10-5

No. of Link Breaks 10422 35142 40202 46570

PDR (%) 94.98 81.07 74.07 64.02

scenarios listed in Table 1. The simulation results are shown in Table 2, where we

varied the HELLO_INTERVAL from 1 second to 6 seconds in steps of 1 second. In

all cases, all nodes use the specified Hello interval for the whole duration of the simu-

lation. The results show that the PDR values change little when tuning the Hello-

Interval globally, except for high mobility scenarios and for longer interval values. In

these cases, the protocol performance (not surprisingly) deteriorated. In addition, with

the exception of the most dynamic mobility scenario, a global HELLO_INTERVAL

of 1 second performed slightly worse (on average) than the default value of 2 seconds.

Table 2. PDRs of Default OLSR with Different Global HELLO_INTERVAL Values

Hello-Interval (s) 1 2 3 4 5 6

3-2-1-1 92.43 93.37 93.83 93.66 93.40 93.19

10-5-1-1 81.54 81.95 80.81 80.45 78.08 77.11

12-6-5-2 77.49 78.30 76.62 77.09 73.69 72.47

15-4-10-5 65.98 64.62 64.46 64.01 61.61 60.03

PDR for Different OLSR Versions

3-2-1-1:

Def ault

OLSR

3-2-1-1:

Adaptiv e

OLSR

10-5-1-1:

Def ault

OLSR

10-5-1-1:

Adaptive

OLSR

12-6-5-2:

Def ault

OLSR

12-6-5-2:

Adaptiv e

OLSR

15-4- 10-5:

Def ault

OLSR

15-4-10-5:

Adaptive

OLSR

PDR %

100

Fig. 5. PDR for Default OLSR and Adaptive OLSR

Figure 5 compares the simulation results for Default OSLR and Adaptive OLSR in

terms of PDR, averaged over 5 cases for each of our mobility scenario, together with

the 95% confidence interval for the average PDR. The results show that Adaptive

OLSR consistently achieves higher PDR than Default OLSR, especially in higher

mobility scenarios.

Adaptive MANET Routing: A Case Study 53

PDR for Different Thresholds

3-2- 1-1:H2

3-2- 1-1: H3

10-5-1-1: H2

10-5-1-1: H3

12-6-5-2: H2

12-6-5-2: H3

15-4-10-5:

H2 L 1

15-4-10-5:

H3 L 1

PDR

100

Fig. 6. PDR for Adaptive OLSR with Different Threshold Values

As discussed in Section 3, we defined two thresholds for Adaptive OLSR: UP-

PER_LINKBREAKS and LOWER_LINKBREAKS, which determine when a node

switches in and out of Fast-OLSR mode. Initially, the values were set to 2 and 1 re-

spectively. We also ran experiments where we increased UPPER_LINKBREAKS from 2

to 3. The results for both sets of threshold values are shown in Figure 6, together with the

95% confidence interval (Lx donates the value of LOWER_LINKBREAKS, Hx simi-

larly donates the value of UPPER_LINKBREAKS). We can see that with the higher

upper threshold, higher mobility scenarios can achieve even higher PDRs, though the

lowest mobility scenarios suffer a slight degradation.

Table 3. Comparisons of Routing Performance Metrics

Mobility Scenario OLSR Type No Route Link Broken Control Message

Default 394 3269 183486

H2, L1 357 2299 188753

3-2-1-1

H3, L1 332 2824 192236

Default 609 13103 218829

H2, L1 4294 4676 133841

10-5-1-1

H3, L1 1859 5825 161861

Default 700 17232 228621

H2, L1 8769 4952 124697

12-6-5-2

H3, L1 3376 6685 150217

Default 801 22982 248283

H2, L1 16743 4909 115316

15-4-10-5

H3, L1 7438 7202 135047

54 L. Qin and T. Kunz

Table 3 provides further details about the packet losses and routing overhead for

Default OLSR and Adaptive OLSR. The first column describes the mobility scenario;

the second column lists the protocol version (Default OLSR and Adaptive OLSR with

different upper and lower threshold values). The numbers in the third and fourth col-

umn are the number of dropped data packets. A packet is either dropped because a

node cannot find the destination address in its routing table (“No Route”), or because

the link to the next hop broke (“Link Broken”). The last column shows the total num-

ber of protocol control message transmissions (sending and forwarding).

Table 4 summarizes the average packet latency for Default OLSR and Adaptive

OLSR for the H2 L1 case. The values are averaged over all the data packets that

reached their destination.

Table 4. Comparison of Packet Latency (in seconds): Default and Adaptive OLSR

Mobility Scenario Default OLSR Adaptive OLSR

3-2-1-1 0.0687 0.0427

10-5-1-1 0.2586 0.0681

12-6-5-2 0.4064 0.1043

15-4-10-5 0.580 0.1005

From these results, we draw the following conclusions:

– Using the number of link breaks as the mobility metric, a mobile node can adjust

its routing parameter (HELLO_INTERVAL) to detect link changes quickly, thus

reducing the number of dropped packets (Table 3). In conjunction with a change

in the MPR selection, adaptive routing can significantly improve routing per-

formance (in terms of both PDR and packet latency), especially for high mobility

scenarios (Figures 5 and 6, Table 4).

Fig. 7. Percentage of Neighbors in Fast-OLSR Mode

Percentage of Fast-OLSR Neighbors

100

104

112

120

128

136

144

152

160

168

176

184

192

Simulation Time (s)

Fast-OLSR %

Adaptive MANET Routing: A Case Study 55

– The total number of control messages for Adaptive OLSR is almost always less

than for Default OLSR. Nodes in Fast-OLSR mode select fewer MPRs, thus less

TC messages are generated and flooded throughout the network (Table 3).

– Compared to Default OLSR, the number of dropped packets due to “No Route”

increases. The relatively fewer TC messages in same cases prevent a node from

determining routes. Increasing the upper threshold value will produce fewer Fast-

OLSR nodes, generating more TC messages and reducing the number of packets

lost due to “No Route”. However, it also increases the number of packets dropped

due to a lost link to the next hop (Table 3).

Figure 3 already visualized the highly dynamic neighborhood size of different

nodes.To further indicate the highly variable dynamic environment a single node

experiences, Figure 7 shows the percentage of neighbors in Fast-OLSR mode for a

single node for different UPPER_LINKBREAKS values, during the initial 200 sec-

onds of simulation and a mobility scenario with medium relative mobility. The solid

line shows the H3 L1 case, the dashed line shows the H2 L1 case. Over time, a differ-

ent percentage of neighbors experiences a high number of link breaks, operating in

Fast-OLSR mode, while at the same time other neighbors monitor relatively more

stable links and operate in the Default or Fast-Response modes. These figures graphi-

cally demonstrate the highly variable mobility environment from the point view of a

single node over time. Figure 7 also shows the impact of changing the UP-

PER_LINKBREAKS value.

5 Conclusion and Future Work

In a MANET, a node’s environment, such as its neighborhood, the traffic it carries, or

the transmission conditions, are different for each node and also dynamic throughout

time. However, most routing protocols assume some constant average network condi-

tion and predefine routing parameters for all the nodes in the network. In this paper,

we focus on the impact of node mobility on routing performance, and choose the

number of link breaks as mobility metric. Simulation results reconfirm that this metric

correlates to routing protocol performance (for different mobility models and routing

protocols). In addition, it can be easily measured. We apply this mobility metric to

OLSR so that a node will reduce its HELLO_INTERVAL and change the MPR selec-

tion once the mobility metric exceeds an upper threshold. We conducted extensive

simulations with the Random Waypoint mobility model; all results show that Adap-

tive OLSR can achieve better routing performance in terms of higher PDR, fewer

control messages and reduced packet latency. We also show that tuning the mobility

metric threshold can further improve the performance of Adaptive OLSR, especially

in high mobility scenarios.

This case study confirms to us our general idea: allowing nodes to individually

adapt their routing behavior to the dynamic environment they encounter can signifi-

cantly improve the overall routing protocol performance. We plan to continue this

work along a number of avenues. First, we are currently investing the performance of

our Adaptive OLSR implementation over other mobility models. Second, a node’s

adaptive options are currently limited to changing its HELLO_INTERVAL values

and the MPR selection. As part of future work, we will study the impact of adapting

56 L. Qin and T. Kunz

additional routing parameters such as the TC-Interval, the MPR set size for Fast-

OLSR nodes, etc. Finally, we also plan to apply the adaptive routing idea to other

routing protocols such as protocols in the pro-active family of routing protocols.

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Self-interference in Multi-hop Wireless Chains:

Geometric Analysis and Performance Study

Saquib Razak and Nael B. Abu-Ghazaleh

Dept. of Computer Science

State University of New York, Binghamton

and

School of Computer Science

Carnegie Mellon University - Qatar

{srazak,nael}@cs.binghamton.edu

Abstract. In the presence of interference, two single hop links can in-

teract in a number of diﬀerent ways, exhibiting signiﬁcantly diﬀerent

behavior. In this paper, we consider the impact of these two-ﬂow inter-

actions on multi-hop chains. Speciﬁcally, we characterize the diﬀerent

types of interactions that arise in chains between hops that do not share

a common node. We develop closed formed expressions to estimate the

probability of occurrence of these interaction combinations. We use sim-

ulation to characterize the performance of the most common types of

chains. We make a number of interesting observations: (1) the most de-

structive types of two-ﬂow interactions do not arise commonly in chains;

(2) the throughput of chains does not vary signiﬁcantly with the types of

arising interactions, because of the self-regulating eﬀect of packets in the

chain (later hops can only transmit when they receive packets from earlier

ones); however, (3) the chains exhibiting destructive interactions suﬀer

frequent collisions and require many more retransmissions. As such, in

general scenarios, such chains reduce the available bandwidth within the

network.

1 Introduction

Chains are fundamental in multi-hop wireless networks; however, our under-

standing of their behavior is limited. In multi-hop wireless networks, connections

are made across chains of nodes. A chain is a sequence of nodes that a packets

travels in order to go from a source node to a destination. The performance of

chains is aﬀected both by self-interference (diﬀerent nodes in the chain trans-

mitting diﬀerent packets concurrently) [7, 10], as well as interference from other

chains. However, due to the complexity of wireless interference our understand-

ing of the behavior of chains remains limited. More accurate characterization of

chain behavior, and understanding of what makes an eﬀective or poor chain, is

critical for designing routing, QoS and traﬃc engineering protocols for multi-hop

wireless networks.

The CSMA MAC protocol relies on imperfect carrier sense to reduce collisions,

which can, even in simple scenarios, lead to a number of diﬀerent interaction

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 58–71, 2008.

Springer-Verlag Berlin Heidelberg 2008

Self-interference in Multi-hop Wireless Chains 59

modes some of which exhibit ineﬃciency and short or long term unfairness.

Carrier Sense Multiple Access (CSMA) based MAC protocols like IEEE 802.11

are widely used in multi-hop wireless networks. CSMA MAC protocols suﬀer

from imperfect medium access, giving rise to a class of problems generally called

hidden terminal problems [4]; we discuss CSMA MAC protocols in more detail

in Section 2. Recent studies have shown that even with a simple scenario of two

contending single hop ﬂows, a number of diﬀerent interaction modes arise [1, 6, 9].

We discuss these two ﬂow studies and other related works in Section 3.

Self-interference in chains diﬀers signiﬁcantly from the two ﬂow interference

modes that have been previously studied. The structure of the chain changes

the probability of occurrence of the diﬀerent interaction modes. In addition, the

dependent nature of traﬃc in chains leads to diﬀerent behavior than that of

independent traﬃc sources.

This paper contributes the following: (1) Classiﬁcation of the types and fre-

quency of occurrence of chains with respect to self-interaction among the hops;

(2) Analysis of the performance of the types that most commonly occur in a

4-hop chain and generalization of this analysis to n-hops. Based on this anal-

ysis, we discover the following: (1) Some of the most destructive interaction

modes rarely occur because of the structure of the chain (asymmetric interfer-

ence from an upstream hop to a downstream one); (2) In isolation, there is little

diﬀerence in throughput obtainable by the diﬀerent chain types because of the

self-dependent nature of the traﬃc. However, some chains suﬀer from persistent

packet collisions, leading to a large number of retransmissions and therefore,

signiﬁcantly poorer throughput in a general network; (3) Existing routing proto-

cols often pick poor quality chains with respect to self-interference, even in the

presence of high quality ones. This places emphasis on mechanisms for detecting

destructive self-interference and using that information in routing protocols. We

discuss ideas for such mechanisms which form a part of our future work.

2 Background–MAC Protocol

In this section, we ﬁrst brieﬂy review the channel access mechanism and the

IEEE 802.11 MAC protocol. We then discuss the modes of interactions that

arise among two single hop interfering hops. The goal of this paper is to identify

the impact of these interaction modes on a wireless chain.

2.1 IEEE 802.11

The signal power of a wireless transmission attenuates with distance and other

environmental factors. A packet is successfully received if the signal strength at

the receiver is above the receiver sensitivity threshold. Furthermore, the ratio of

the signal to noise and interference power must be above the capture threshold.

The Boolean physical model is a simpliﬁed model of this operation, where a

transmission from a node can be sensed by all the nodes that are within a given

Interference Range(Ri). In the absence of interfering signal, a packet can be

60 S. Razak and N.B. Abu-Ghazaleh

received by all the nodes that are within the Communication Range (Rc,where

Rc<R

i). Under this model, packet collisions occur when a node is receiving a

packet and an interfering node (within a distance of Rifrom the node) transmits

a signal.

The MAC layer protocol regulates access to the channel in an attempt to

reduce collisions. IEEE 802.11 uses a Carrier Sense Multiple Access approach,

augmented with Collision Avoidance (CSMA/CA). Diﬃculties arise in wireless

settings because carrier sense is carried out at the sender, while correct reception

requires the medium to be idle at the receiver. Therefore, IEEE 802.11 optionally

uses small control packets to arbitrate the medium (Request to Send sent by the

sender before a transmission and Clear to Send sent in response by the receiver

if the channel is idle near it) to attempt to reduce collisions. However, since

these packets can only block interferer in reception range (those outside cannot

receive them), they are of limited use in preventing collisions. Finally, in response

to a correctly received packet, the receiver sends an acknowledgement. If the

acknowledgement packet is not received, the receiver attempts to retransmit.

Despite aggressive carrier sense, collisions can still occur between senders that

are outside carrier sense range of each other, but that are in interference range

of their respective receivers. To regulate the load in the presence of collisions,

senders maintains a backoﬀ window (BO) counter. When a collision occurs, the

CW is doubled (up to a maximum limit), a backoﬀ algorithm known as Binary

Exponential Backoﬀ (BEB).

2.2 Two Flow Interaction Modes

It has been recently shown that a number of diﬀerent interaction modes arise

among two interfering single hop ﬂows [1, 9]. In a two ﬂow scenario, two senders

S1and S2communicate with two receivers D1and D2respectively. There ex-

ist four secondary (or cross-ﬂow) channels that lead to the diﬀerent modes of

interactions; these are S1S2S1D2,S2D1and D1D2. The connections interfere

diﬀerently depending on the state of these four secondary links. In this paper

we assume Carrier Sense range and Interference range to be the same. Study-

ing interactions with diﬀerent Carrier Sense and interference ranges is part of

our future work. Under a boolean interference model, the interactions can be

grouped into ﬁve categories as described below [9].

Sender-Connected Symmetric Interference (SCSI): This category in-

cludes all scenarios where the two senders are in range and there is symmetric

interference between opposite source and destination. An example of this sce-

narios is shown in Fig 1(a). In this scenario the channel is shared equally among

the two ﬂows.

Sender-Connected Asymmetric Interference (SCAI): In SCAI, senders

are in communication range and only one destination is in interference range

of the other sender. Fig 1(b) shows an example of this scenario. An ACK sent

by D2 is received by S1 as a corrupted packet. S1assumesthatitisaDATA

Self-interference in Multi-hop Wireless Chains 61

S_1 D_1

D_2

S_2

R_i

(a) SCSI

S_1 D_1

S_2

D_2

(b) SCAI

S_2

D_2

S_1

D_1

R_i

S_1

D_1

D_2

S_2

R_i

(d) IDIS

D_1

D_2

S_1

S_2

R_i

(e) SIS

Fig. 1. Sample scenarios in each category

packet and defers for an Extended Inter Frame Separation (EIFS) period while

S2 defers for the standard DIFS. Since EIFS is much longer than DIFS, S2wins

the channel most of the time. Hence SCAI exhibits severe unfairness problems.

Asymmetric Incomplete State (AIS): In the remaining scenarios the senders

are not connected (Incomplete State) and carrier sense cannot prevent collisions.

In Asymmetric Incomplete State, as shown in Fig 1(c), only one of the senders

interferes with the other destination and only one of the ﬂows experiences colli-

sions, giving rise to unfairness.

Symmetric Incomplete State (SIS): In this category, the senders are not

connected and both senders can interfere with the other destination. Fig 1(e)

shows an example of this kind of interaction. This causes drops at both destina-

tions and severely aﬀects the throughput of both ﬂows.

Interfering Destinations Incomplete State(IDIS): In this mode only des-

tinations are in range as shown in Fig 1(d). The ACK sent by one destination

interferes with packets being received by the other causing packets to be dropped.

This scenario aﬀects the throughput of both links.

In this paper we study the existence of diﬀerent interference groups in a multi

hop chain and its eﬀects on chain throughput and goodput. We denote the

absence of any interaction between twohopsasNI(NoInteraction).

3 Related Work

Analysis of throughput in chains has been studied extensively. Authors in [2, 3,

5, 7] compute the theoretical upper bounds on throughput of multi-hop ad hoc

network. In [11], the authors evaluate the performance of TCP over a mulithop

chain. They demonstrate that TCP traﬃc in a chain has instability problems

that degrade the throughput of the chain.

In [8] the authors present a hop by hop analysis of a multi-hop chain and

study the eﬀects of hidden nodes on the throughput of a chain topology. They

present a quantitative approach towards estimating the throughput of a chain.

They provide two main observations about ﬂows in a chain. Firstly the presence

of hidden nodes cause packet drops that reduce the throughput of the chain

62 S. Razak and N.B. Abu-Ghazaleh

directly, and secondly packet drops cause reporting of broken links to the routing

protocol and hence reducing the throughput indirectly.

Our observations in this study show that in a four-hop chain, packet drops

have very little eﬀect on the throughput of a chain both directly by extra trans-

missions or indirectly by way of rerouting because of false link breakage infor-

mation. Extra lost transmissions come at a cost of decreased goodput of a chain

hence introducing extra noise in the network. We also extend this analysis to an

n-hop chain and conclude that chain interactions do not play vital role in de-

termining the throughput but eﬀect only the goodput of the chain. Cross chain

interference is eﬀected more by these interactions since diﬀerent chains produce

similar throughput but very diﬀerent overall transmission levels.

Most of the studies are focused on ﬁnding the macro level behavior of chains

in order to estimate the overall throughput of the network. Our study is focused

on the micro level interactions in a multi-hop chain between diﬀerent hops in

order to better understand the interference present in a chain topology. In this

paper we study the patterns of self interference in a chain. We feel that a better

understanding of self interference is critical in understanding cross interference

between chains.

4 Chain Self Interference

Links in a chain topology exhibit diﬀerent modes of interference among hops,

leading to signiﬁcant impact on performance. We use, as the base for classifying

the diﬀerent chains, the two ﬂow interference modes presented in an earlier

work [9]. Given the restrictions of chain connectivity, the probability of the

diﬀerent cases changes. Moreover, given the nature of the traﬃc, it is likely that

the impact of these modes will be diﬀerent as well.

4.1 3-Hop Chains

Figure 2 shows a chain with 3 hops. In this chain, hops H1 and H3 are two

link level ﬂows within this chain that interact with each other according to the

probabilities shown in Figure 3.

The plot in Figure 3 is obtained by creating diﬀerent 3-hop chains using

a Monte Carlo approach and then analyzing the existing interference interac-

tions amongst the ﬂows. It can be seen fromtheplotthatattypicalcarrier

sense/interference range of more than twice the communication range, only SCSI

interactions are possible. But at lower ratios of carrier sense to communica-

tion the AIS group is the dominant interaction. AIS interaction has much lower

throughputs than SCSI groups in two ﬂow settings [9] but increasing the carrier

sense range in a network exacerbates the exposed node problem.

H1 H3

I1 I2 D

Fig. 2. AChainwith3hops

Self-interference in Multi-hop Wireless Chains 63

1 1.5 2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Group Probability

Interference to Communication range ratio

SCSI

AIS

SIS

IDIS

Fig. 3. Interaction Probabilities for a 3-Hop Chain

4.2 4-Hop Chains

A 4-hop chain as shown in Figure 4 presents more interesting problems. In

this chain we have three diﬀerent sets of two ﬂow links that can interfere; note

that links that share a node cannot be active at the same time and hence do

not interfere with eachother. Node S can potentially transmit to Node I1 at the

same time when Node I3 is transmitting an older packet to Node D. This makes

hops H1 and H4 one set of simultaneous ﬂows. Similarly H1 and H3, and H2 and

H4 make up the other sets of two-ﬂows. Hence in 4-hop chain we can have three

diﬀerent groups of interactions between the three sets of ﬂows.

H1 H3

I1 I2 I3 D

Fig. 4. AChainwith4hops

Mathematically there can be 53kinds of interactions in a chain. To determine

those interactions that are probable in a 4-hop chain topology we perform an

exhaustive enumeration of all possible scenarios. More speciﬁcally, we ﬁx the

location of the source node Sand move node I1 around it in a circular disc

starting from radius 0 to a radius of Communication Range (250m in this case).

Then we move node I2 around I1 in a circle making sure that I2doesnot

enter the communication range of node S. Similarly node I3 is moved around

I2 and the destination Dis moved to all possible locations around I3. For each

position of these ﬁve nodes, we evaluate the scenario that occurs in this chain.

The following interactions occur non-negligible percentage of times in a chain.

The interactions are referred to in the format A/B/C where A is the interaction

between H1 and H4, B is the interaction between H1 and H3 and C is the

interaction between H2 and H4.

1. SCSI/SCSI/SCSI

2. AIS/SCSI/SCSI

3. NI/SCSI/AIS

4. AIS/AIS/SCSI

5. NI/AIS/AIS

64 S. Razak and N.B. Abu-Ghazaleh

Fig 5(a) plots the occurrence probabilities of the scenarios as carrier sense range

is increased.

4.3 Geometric Models

We develop geometric models for computing the probability of occurrence of the

ﬁve chain interactions listed above. Here we present the complete derivation of

NI/AIS/AIS group while the rest of the groups are derived in a similar fashion.

NI/AIS/AIS. In this set of interactions nodes S and I1 are out of range of

Nodes I3 and D. This Scenario has AIS interaction between H1 and H3, which

requires that I1 to be out of range of I3 (Source of H1 is out of range of destination

of H3). The last interaction AIS between H2 and H4 requires I1 to be out of

range of Node D. This is already implied by the NI interaction between H1 and

H4. For this chain we ﬁnd the probability that for a given distance between

nodes S and I1, I2 lies in an area that is outside the area of interference of S.

Also given the distance between I1 and I2, we ﬁnd the probability that I3 lies

outside the area of interference of I1.

The derivation uses the following terminology: interference range and com-

munication range are represented by riand rcrespectively. C(X) refers to the

area of communication range of Node X (circle of radius rcaround X)andT(X)

refers to the interference range of Node X (circle of radius riaround X).

The probability that I1 is on a circle of radius xaround S where xis always

less than rcis given by

p1=rc

dx (1)

Next we ﬁnd the probability that I2 is out of range of S. Lets say that I2 is on a

circle of radius yfrom I1. The arc length of circle with radius y around I1 that

is intersected by circle with radius riaround Sgives us the portion of circle y

that is within range of S. Subtracting this arclength from the perimeter of circle

y will give us the portion that is out of range of S.

The minimum value of yhas to be ri−xto guarantee that some portion of

the circle is out of range of S. The maximum value of yis rc.

p2=rc

(ri−x)

(2 ∗pi ∗y)−2ycos−1(y2+x2−r2

2xy )dy (2)

Now we calculate the probability that I3 is out of range of I1. I3 has to be within

the communication range of I2. We ﬁnd AreaRiRcythe area of intersection of

circle riaround I1 and rcaround I2 given the distance ybetween I1 and I2,.

This is the portion of Communication range around I2 that is within range of

I1. Subtracting this common area from C(I2) gives the area that is out of range

of I1. Let AreaRcRcybe the area of intersection of circle of radius rcaround I1

and I2. Subtracting this area from C(I2) will give us the area which is within

communication range of I2 but outside the communication range of I1. Note

Self-interference in Multi-hop Wireless Chains 65

that since I3 is the next hop for I2, it can only be in C(I2) - AreaRcRcy. Hence

probability of I3 being out of range of I1 is given

p3=C(I2) −AreaRiRcy

C(I2) −AreaRcRcy(3)

The overall probability of NI/AIS/AIS is calculated by multiplying Eq[1,2,3]

p=rc

0rc

(ri−x)

((2 ∗pi ∗y)−2ycos−1(y2+x2−r2

2xy )) dy dx (4)

4.4 Model Validation

We validate the geometric models for each interaction by comparing against

exhaustive enumeration of all interactions in a chain.

1 1.5 2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Group Probability (Simulation)

Interference to Communication range ratio

SCSI/SCSI/SCSI

AIS/SCSI/SCSI

NI/SCSI/AIS

AIS/AIS/SCSI

NI/AIS/AIS

(a) Simulated

1 1.5 2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Group Probability (Model)

Interference to Communication range ratio

SCSI/SCSI/SCSI

AIS/SCSI/SCSI

NI/SCSI/AIS

AIS/AIS/SCSI

NI/AIS/AIS

(b) Predicted

Fig. 5. 4-Hop Interaction Percentages

Figures 5(a), and 5(b) show the probability of each interaction obtained using

enumeration, and geometric model prediction. The plots indicate that the models

closely match the results of simulation as the ratio of interference range and

communication range is increased. As the ratio increases, the interactions move

towards having all interacting hops Sender Connected. At lower ratios we have

an increased percentage of interactions with hidden terminals.

5 Simulation Study of throughput

In this section we analyze the throughput of a 4-Hop chain under diﬀerent inter-

actions using NS2 Network Simulator. We use a ﬁxed distance of 250m for trans-

mission range and disable RTS/CTS mechanism. All transmissions are based on

802.11 DCF mode at data rates of 2Mbps and packet size of 1000 bytes. We

change the saturation level of the channel by altering the rates at which the

source pumps Constant Bit Rate (CBR) packets into the chain. We perform this

analysis using the standard two-ray ground wireless propagation model which

results in ﬁxed communication and interference/carrier sense ranges.

66 S. Razak and N.B. Abu-Ghazaleh

0 10 20 30 40 50 60 70 80 90 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Chain Throughput (Mbps)

Saturation percentage

SCSI/SCSI/SCSI

AIS/SCSI/SCSI

NI/SCSI/AIS

AIS/AIS/SCSI

NI/AIS/AIS

SCSI/SCSI/AIS

(a) Throughput

0 10 20 30 40 50 60 70 80 90 100

100

Chain Goodput %

Saturation percentage

SCSI/SCSI/SCSI

AIS/SCSI/SCSI

NI/SCSI/AIS

AIS/AIS/SCSI

NI/AIS/AIS

SCSI/SCSI/AIS

(b) Goodput

Fig. 6. Throughput and Goodput of a 4-hop Chain vs Channel Saturation

Fig 6(a) shows the throughput achieved at diﬀerent saturation rates for the

diﬀerent chains. The throughput of a chain increases as we increase the satura-

tion rate until it reaches an asymptotic limit. The limit represents the highest

throughput possible in a chain topology as has been determined to be 1/4 of total

bandwidth [7, 8, 11]. Figure 6(b) shows the percentage goodput of each chain.

Goodput in our case is calculated as percentage of packets that are successfully

transmitted. We analyze these plots of each chain separately.

5.1 SCSI/SCSI/SCSI

In this chain, all the hops are Sender Connected. As the source node competes

for the channel with three other nodes (I1, I2 and I3), it is able to transmit at

one fourth of the total bandwidth. The only drops in this interaction are due

to two sources transmitting within very short duration of each other. Since the

probability of these collisions is very little we see a goodput of more than 90%.

5.2 AIS/SCSI/SCSI

The chain eﬀect dominates the throughput performance of this chain. In the AIS

interaction between the ﬁrst and the last hop, the ﬁrst hop is the weak link and

last hop is the strong link. Packets transmitted together on H1 and H4 cause the

packet on Hop 1 to be dropped. Hence the lack of sender connectedness in the

ﬁrst group just increases the noise produced by wasted transmissions by Node

S. This is depicted in the goodput curve of AIS/SCSI/SCSI in Figure 6(b). This

chain transmits lots of packets on hop1 that are dropped.

5.3 NI/SCSI/AIS

In this chain, several packets are dropped at the AIS connection. The throughput

is not aﬀected severely because of the presence of SCSI in the middle that limits

the transmission of packets from Source and I2 and hence limits the concurrently

active packets in the chain. The goodput of this chain is aﬀected by the lack of

coordination between the hops.

Self-interference in Multi-hop Wireless Chains 67

0 10 20 30 40 50 60 70 80 90 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Chain Throughput (Mbps)

Saturation percentage

SIS/SCSI/SCSI

IDIS/SCSI/SIS

SIS/AIS/SCSI

SCSI/SIS/SCSI

SCSI/SCSI/SIS

IDIS/AIS/SIS

SCSI/SIS/AIS

(a) Throughput with SIS

0 10 20 30 40 50 60 70 80 90 100

100

Chain Goodput %

Saturation percentage

SIS/SCSI/SCSI

IDIS/SCSI/SIS

SIS/AIS/SCSI

SCSI/SIS/SCSI

SCSI/SCSI/SIS

IDIS/AIS/SIS

SCSI/SIS/AIS

(b) Goodput with SIS

0 10 20 30 40 50 60 70 80 90 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Chain Throughput (Mbps)

Saturation percentage

AIS/SCSI/SIS

AIS/AIS/AIS

AIS/SCSI/AIS

AIS/AIS/SIS

0 10 20 30 40 50 60 70 80 90 100

100

Chain Throughput (Mbps)

Saturation percentage

AIS/SCSI/SIS

AIS/AIS/AIS

AIS/SCSI/AIS

AIS/AIS/SIS

(d) Goodput with Reverse AIS

Fig. 7. Throughput and Goodput of Chains with SIS and Reverse AIS interactions

5.4 AIS/AIS/SCSI

In this chain, the packets are sent in bursts because of the two AIS connections.

The connection starts sending packets. When the packet reaches node I3, trans-

missions from I3 to node D cause packets to be dropped on Hop 1. For every

packet sent successfully on Hop1, the next packet will be dropped, increasing

the backoﬀ at Node S. Hence the goodput for this chain is always less than 50%.

5.5 NI/AIS/AIS

This interaction is also dominated by the AIS group in terms of goodput. Since

senders of all interactions are out of range, they will transmit together. This

causes many wasted transmissions without any gain in throughput.

5.6 SIS Cases

In this section we consider those chains that have SIS interaction between any

two hops. The probability of these interactions is really small using the default

NS-2 parameters. Figure 7(a) shows the throughput of seven possible categories

with SIS interactions. This type of interaction is really destructive as packets

are dropped from both links and the throughput is drastically reduced. As can

68 S. Razak and N.B. Abu-Ghazaleh

be seen in Figure 7(b), although the chain transmits many packet, few of these

are successful.

5.7 Reverse AIS Cases

Another interaction that is possible in a chain (although the probability is low

because of the geometry restrictions) is an AIS interaction between the ﬁrst

and the last hop where the ﬁrst hop is the strong link and last hop is the

weak link. The ﬁrst hop transmits packets causing collisions at the last hop,

which cannot empty packets as fast as it receives them (leading to queue drops).

Figures 7(c) and 7(d) show the throughput and goodput of chains with Reverse

AIS interaction.

6 Towards Generalization to n-Hop Chains

In this section we make some observations about generalizing the results from 4-

hops to general chains via an inductive argument. In the future, we will attempt

a more systemic generalization. First we add one more hop to our chain. The

ﬁfth hop can have two possibilities - it either interferes with the ﬁrst hop or it

does not. In the ﬁrst case, the ﬁfth hop interferes with the ﬁrst, second, and third

hops in either AIS or SCSI interactions because of symmetry. Our simulation

results indicate that the throughput of all these scenarios is within 2.5% of each

other.

45678

0.2

0.25

0.3

0.35

0.4

0.45

Chain Throughput (Mbps)

Number of hops

SCSI/SCSI/SCSI

AIS/SCSI/SCSI

(a) Throughput

45678

100

Chain Goodput (Percentage)

Number of hops

SCSI/SCSI/SCSI

AIS/SCSI/SCSI

(b) Goodput

Fig. 8. Throughput and Goodput of 8-Hop Chains

In the second case where the ﬁfth hop does not interact with the ﬁrst hop,

the situation is similar to evaluating a four hop chain where the second node of

the chain is acting as the source of the 4-hop chain. As we have seen in section 5 the

throughput of a chain does not depend on the type of interaction, hence the type

of interaction between the 4 hops starting from the second node of the 5-hop chain

would not eﬀect the chain throughput. Hop count is the only dominating cause that

eﬀects the throughput of the chain. The goodput of the chain on the other hand is

directly eﬀected by the interactions amongst the hops. Chains with a higher number

Self-interference in Multi-hop Wireless Chains 69

of AIS interactions will have higher drops hence lower goodput, while SCSI dom-

inated chains will produce a higher goodput. Figure 8 shows the throughput and

goodput of 8-hop chains. In the SCSI/SCSI/SCSI chain, each group of 4-hops as

obtained by shifting down the chain by one hop has SCSI/SCSI/SCSI interaction

while in AIS/SCSI/SCSI has the same interaction for all sets of four-hops within

the 8-hop chain.

7 Discussion

We have seen in this section that for all diﬀerent interactions in a chain, the

throughput of the chain with AIS and SCSI interactions depends only on the

number of hops. Chains with SIS and Reverse AIS have very little throughput.

The goodput of the chain is more inﬂuenced by the type of interaction. For chains

with higher goodput, the channel utilization is more eﬃcient which translates

into less cross chain interference. Low goodput chains waste a lot of bandwidth

for transmissions that in the end are dropped and hence wasted. Throughput of

a chain should not be the only criteria for determining its performance. As we

have seen from Figures 6(a) and 6(b) that chains that have similar throughput

might have substantial diﬀerence in goodput. In routing decisions it is important

to pick routes that minimize not only the interference within the chain but also

across diﬀerent chains in order to better utilize available channel bandwidth.

Designing routing protocols that take consider chain interaction and pick high

goodput routes is an area of our future research.

In chain interactions that occur more often, the type of interaction does

not substantially aﬀect the throughput of the chain although it does eﬀect the

amount of traﬃc generated. This observation leads us to believe that evaluating

cross-chain interference and its eﬀects on throughput are more important than

self-interference in a chain.

SI1

I2 I3 D

Fig. 9. A chain and an external ﬂow

We consider the eﬀect of noise from a chain on the throughput of other ﬂows.

Fig 9 shows a chain in close proximity to another ﬂow. We determine the eﬀect

of this chain on the ﬂow when the chain has diﬀerent self interference patterns

while the source of the chain has an AIS relationship with the second ﬂow. In

this AIS interaction, the second ﬂow is the weaker link. Fig 10(a) and 10(b)

show the eﬀect of the chain on the throughput and goodput of an external ﬂow.

These are some preliminary results, a detailed study of cross-chain interference

is a topic of our future research.

70 S. Razak and N.B. Abu-Ghazaleh

Chain Flow 2

0.2

0.4

0.6

0.8

1.2

1.4

Throughput Mbps

SCSI/SCSI/SCSI

AIS/SCSI/SCSI

NI/SCSI/AIS

AIS/AIS/SCSI

NI/AIS/AIS

(a) Throughput

Chain Flow 2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Percentage Goodput

SCSI/SCSI/SCSI

AIS/SCSI/SCSI

NI/SCSI/AIS

AIS/AIS/SCSI

NI/AIS/AIS

(b) Goodput

Fig. 10. Eﬀect of a chain on throughput and goodput of an external ﬂow

8Conclusion

This paper makes several contributions to the analysis of interference interac-

tions multi-hop wireless chains. Speciﬁcally, we classify and study of all possible

interactions within a chain and their eﬀects on chain throughput and interfer-

ence generated to other chains. We identify that some chains that produce high

throughput in isolation, also experiences substantial drops hence wasting the

available channel bandwidth with retransmissions and causing cross chain inter-

ference. The characterization of chains is important for routing protocols to be

able to more intelligently select routes.

Our immediate goal is to extend this study to include a more realistic model

where capture eﬀects are taken into consideration. We would like to take the

analysis performed in this paper to develop interference aware routing proto-

cols that can look at a route and determine the types of interaction within the

routes. Based on this study the protocol then decides on picking the best mix

for throughput and goodput from all routes that are available.

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D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 72–85, 2008.

Energy-Efficient Multi-path Routing in

Wireless Sensor Networks

Philipp Hurni and Torsten Braun

Universität Bern, Neubrückstrasse 10, CH-3012 Bern

{hurni,braun}@iam.unibe.ch

Abstract. The paper investigates the usefulness of multi-path routing to achieve

lifetime improvements by load balancing and exploiting cross-layer information

in wireless sensor networks. Performance gains in the order of 10-15 % could

be achieved by altering path update rules of existing on-demand routing

schemes. Problems encountered with concurrent traffic along interfering paths

have been identified as a direct consequence of special MAC protocol

properties.

Keywords: Sensor Networks, Energy Efficiency, Routing Protocols.

1 Introduction

1.1 Benefits of Multi-path Routing

Standard routing protocols in ad hoc wireless networks, such as AODV [3] and DSR

[4] are mainly intended to discover one single route from a source to a destination.

During the route discovery process, these protocols aim to find the best route with the

lowest cost. Multi-path routing protocols aim to find multiple routes. Multiple routes

can be useful to compensate for the dynamic and unpredictable nature of ad hoc net-

works, also in energy and bandwidth constrained sensor networks. Multi-path routing

has been investigated in the Internet, in metropolitan and local area networks, in wire-

less mobile ad hoc networks, as well as in wireless sensor networks. In [6] goals,

problems and recent suggestions for multi-path routing protocols in wireless ad hoc

networks have been discussed. Discovering and maintaining multiple paths causes

certain overhead, but yields several advantages, namely load balancing, fault toler-

ance, bandwidth aggregation, and reduced delay [2].

Load Balancing: Multi-path routing can avoid congestion and improve performance.

When certain nodes and links become over-utilized and cause congestion, multi-path

routing can spread traffic over alternate paths to balance the load over those paths. In

wireless sensor networks, the main focus of multi-path routing is typically on the load

balancing issue. As nodes are constraint to a limited amount of energy, and traffic is

expected to be low, the main concern is to keep the network operable for a maximum

amount of time. In sensor networks, one has to deal with traffic generated by many

leaf nodes attempting to deliver data to one or a few sinks. Usual on-demand routing

schemes tend to utilize always the same set of nodes to forward packets, whereas

Energy-Efficient Multi-path Routing in Wireless Sensor Networks 73

many other nodes remain unused. It has been observed that in such cases nodes that

have to forward traffic from large sub-trees suffer much earlier from energy depletion,

whereas other nodes have only slightly been used. When nodes collaborate in sensing

and data forwarding and packets are not always routed on the same routes, but the

load is balanced over multiple routes, network lifetime can be increased significantly.

Fault Tolerance: Multi-path routing protocols can increase the degree of fault toler-

ance by having redundant information routed to the destination over alternate paths.

This increases the energy overhead, but helps to reduce the probability that communi-

cation is disrupted and data is lost in case of link failures. Sophisticated algorithms

have been developed to increase the degree of reliability. The trade-off between the

additional overhead and the reliability gain has been investigated in [5].

Bandwidth Aggregation: By splitting data to the same destination into multiple

streams, each stream is routed through a different path. The effective bandwidth can

be aggregated. This strategy is especially beneficial when a node has multiple low

bandwidth links but requires higher bandwidth than each individual link can provide.

Reduced Delay: In wireless networks running single path on-demand routing proto-

cols, route failures trigger the path discovery process to find new routes causing route

discovery delay. Delay can be reduced in multi-path routing, as backup routes can be

identified immediately. Furthermore, discovering several paths and observing Qual-

ity-of-Service (QoS) characteristics of both paths permits to switch the load to another

route whenever the service parameters of another route promise better quality.

In wireless sensor networks, the focus of multi-path routing is often on load-

balancing or fault tolerance, rather than on the aggregation of bandwidth. Often, the

goal of multi-path routing protocols is to maximize the time the network is operable

and fulfills its observation task.

1.2 Route Coupling

Using multiple paths in ad hoc networks to achieve higher bandwidth, balance load or

achieve fault tolerance is not as easy as in wired networks. As nodes in the network

communicate through the wireless medium, radio interference must be taken into

account. Transmissions along one path may interfere with transmissions along another

path, even if the paths are link-disjoint or even node-disjoint. The interference may

limit the achievable throughput and lead to two paths with impact on each other for

forwarding packets. This phenomenon is often referred to as route coupling. Route

coupling occurs when two routes are located physically close enough to interfere with

each other during transmission. As a result, the nodes along those two routes are con-

stantly competing for medium access. The advantages of two routes being available

are therefore limited.

Route coupling in wireless networks caused by radio interference between paths

can have serious impact on the performance of multi-path routing protocols, even if

the paths are disjoint [7]. In some cases, route coupling can even lead to worse results

than routing over one single path. The shared transmission medium forces all nodes in

the interference range of a sender to remain silent until completion of a transmission.

The problem even gets worse when applying an RTS/CTS scheme. In [9] the

74 P. Hurni and T. Braun

influence of route coupling in wireless networks applying multi-path routing has

been studied. The following types of routes can be distinguished:

a) routes with no common collision domain

b) routes with a common link

c) routes sharing a common node

Paths of type a) produce the best throughput results, because the common collision

domain of the multiple paths is reduced to source and destination nodes, and trans-

mission along the path are independent to the largest possible extent. Although more

efficient network utilization due to better load balancing can justify the use of a multi-

path routing strategy compared to single path routing, the benefits of multi-path rout-

ing in terms of throughput quickly vanish in case of interference [9].

In [10] it is argued that many multi-path routing protocols mainly find routes that

are too close to each other to actually behave much different than single path routing

schemes. To save energy, multi-path routes must ensure that traffic is routed along

routes that do not interfere with each other at all, which is in most cases hard to

achieve.

None of the established and well-investigated proposals have considered and in-

corporated the route-coupling phenomenon for effective load balancing. Recent re-

search has been pursued on the issue of on-demand construction on non-interfering

multiple paths in sensor networks [8]. The proposed mechanism routes packets along

paths that have a gap of two transmission ranges in between. The mechanism strongly

relies on the position-awareness of the sensor nodes and the knowledge of the position

of the receiver.

1.3 Overview

This paper investigates the usefulness of multi-path routing in wireless sensor net-

works. After discussing related work in Section 2, we propose in Section 3 a multi-

path routing protocol for wireless sensor networks based on the AODV multi-path

extensions called AOMDV. The protocol has been evaluated by simulations as

discussed in Section 4. Section 5 concludes the paper.

2 Related Work

2.1 Multi-path Routing Protocols

Several multi-path protocols for wireless ad-hoc networks such as the Ad-hoc On

Demand Distance Vector Multi-path routing protocol (AODVM) [14] and Split

Multi-path Routing (SMR) [12] have been proposed. The protocol described in this

paper has mainly been influenced by the Ad hoc On-demand Multi-path Distance

Vector protocol (AOMDV) [13], which is an extension of AODV for discovering

node-disjoint or optionally link-disjoint paths. It finds node-disjoint paths by exploit-

ing a particular property of flooding. By appending the first-hop to the RREQ (Route

Request) header, and bookkeeping about the first-hops of the recently received

RREQs, nodes receiving duplicate RREQs by different neighboring nodes can easily

determine whether the routes are node-disjoint. The first-hop is the first node a RREQ

Energy-Efficient Multi-path Routing in Wireless Sensor Networks 75

traverses after the initiating source. To find node-disjoint routes, nodes do not imme-

diately reject RREQs. Each RREQ arriving via a different neighbor of the source has

a different first-hop in the RREQ header, and therefore defines a node-disjoint path.

Nodes do never rebroadcast duplicate RREQs, so any two RREQs arriving at an in-

termediate node via a different neighbor of the source could not have traversed the

same node. As in AODV, RREQ duplicates are discarded in intermediate nodes.

RREQs with equal destination sequence number, but incoming from another interme-

diate node are simply ignored in AODV, unless they advertise a better hop count

value. In AOMDV, intermediate and destination nodes reply to such RREQs with

RREP (Route Reply) messages, if their first-hop is different from the one in the prior

received RREQ. Using this policy, AOMDV guarantees node-disjoint paths whenever

it takes up a second routing entry to the same destination. AOMDV further allows

discovering link-disjoint paths by exploiting RREQ duplicates arriving at the destina-

tion via different intermediate nodes. AOMDV [13] leaves the choice to use the op-

tion to the user.

Figure 1 and Figure 2 illustrate the AOMDV mechanisms to find node-disjoint

paths. The illustration shows node 1 initiating a route request to node 8. The RREQ is

flooded via node 2 and node 3. There, the first-hop field is set accordingly. The

RREQs finally reach destination node 8, where both incoming requests create new path

entries for source node 1, because the incoming RREQs exhibit a different first-hop.

Furthermore, to establish the full bidirectional routes, both RREQs are replied. Node 6

similarly receives two RREQs via nodes 4 and 5. Both RREQs, however, exhibit the

same first-hop. Node 6 therefore knows that the paths to the source node advertised by

these RREQs are not node-disjoint, and does not add a second path entry. To support

multi-path routing, the AOMDV route tables contain a list of intermediate nodes and

hop counts for each destination node. The path entries (cf. Table 1 Table 3) to a desti-

nation have all the same destination sequence number, as they have been obtained in

one single RREQ-RREP query cycle. When receiving a path advertisement with a

higher sequence number, all routes with the old sequence number are removed.

[11] considers how to construct secondary paths, which are in the optimal case node

disjoint. The study is focused on the question how to keep the overhead as small as

possible if only one node or one link in the network fails. The authors argue that when

a small number of paths are kept alive, failures on the primary path can usually be

recovered without invoking network-wide flooding for path discovery. This feature is

important in sensor networks since flooding is very costly and can vastly reduce net-

work lifetime. Node-disjoint paths are a very strong condition when aiming to find

multiple paths between two nodes and may result in rather inefficient and suboptimal

paths in terms of hop count. Long detours around many nodes can be necessary to

fulfill the condition of node-disjoint paths. Alternate node-disjoint paths can become

very long, and therefore require significantly more energy than the primary path. To

overcome this problem, and yet retain the robustness advantages of multiple paths, the

authors suggest the construction of so-called braided paths. Braided paths relax the

requirement for node-disjoint paths. Such paths are only required to leave out some of

the primary path’s nodes. They are free to use other nodes on the primary path. In [11]

it is proposed to construct two different kinds of redundant paths - node-disjoint paths

and braided paths. It depends on the failure patterns which of the two schemes shall be

used. It is claimed to achieve better path resilience with the braided path approach.

76 P. Hurni and T. Braun

Fig. 1. AOMDV Route Request

Fig. 2. AOMDV Route Reply

Table 1. Routing table node #1

dest next hops seq

8 3 3 37

8 2 4 37

Table 2. Routing table node #6

dest next hops seq

1 4 3 11

8 8 1 37

When discovering and maintaining multiple paths from a source to a destination, it

may make sense to occasionally use suboptimal paths in terms of hop count that use

more energy for an end-to-end transmission than the optimal one. Traffic load can be

Energy-Efficient Multi-path Routing in Wireless Sensor Networks 77

Table 3. Routing table node #8

dest next hops seq

1 7 3 11

1 6 4 11

spread over multiple paths, which leads to more nodes participating in the forwarding

process. Using the lowest energy path for all packets is not necessarily best for the

long-term health of a sensor network, as important forwarders might run out of energy

first. In [15] a quite simple approach to probabilistically incorporate suboptimal

routes is suggested. Each node maintains an energy cost estimate for each of its path

entries. This cost estimate determines the probability that a packet is routed over a

certain path. If a node aims to transmit a packet to a certain destination for which it

has multiple paths, it chooses the forwarding node according to a probability assigned

to that path. Each intermediate node does the same and forwards packets according to

the probability assigned to the different paths in the table. This is continued until the

data packet reaches the destination node. Using this simple mechanism to send traffic

over different routes helps in using the nodes’ resources more equally. An overall

gain of ~40% of network lifetime increase with this probabilistic routing scheme has

been achieved. Taking suboptimal paths occasionally into account pays off as nodes

use their scarce resources more equally, which helps to remove load from central

forwarder nodes that would otherwise run out of energy first.

2.2 Sensor MAC Protocols

Routing performance in wireless sensor networks heavily depends on the underlying

MAC protocol. Cross-layer designs are required to optimize performance in terms of

throughput, energy efficiency, delay etc. WiseMAC [1] appears to be one of the most

efficient MAC protocols for wireless sensor networks. It is based on preambles sub-

mitted prior to data. If the receiver’s wake-up pattern is still unknown, the preambles

are slightly longer than the time between two wakeups of a sensor node, such that a

sensor node waking up will discover an upcoming transmission from another node

and remain active until the frame reception (Figure 3). After successful frame recep-

tion, the receiver node piggybacks its own schedule to the respective frame acknowl-

edgement. Received schedule offsets of all neighbor nodes are subsequently kept in a

table and are periodically updated. Based on this table, a node can determine the

wake-up intervals of all its neighbors and minimize the preamble length for upcoming

transmissions.

In previous work we have derived a similar scheme that offers a better protection

against systematic overhearing and does not rely on full-cycle preamble for the

neighborhood discovery [19]. We propose to implement so-called moving wake peri-

ods. Figure 4 shows the approach where a wake period is moving forward and back-

ward within a fixed interval equal to the average time interval between two wakeups

of a node in WiseMAC. Nodes just need to select the same fixed interval value, but

do not need to synchronize further. The moving wake periods scheme ensures that

two nodes can detect each other by periodic transmission of HELLO messages after a

limited time, because their wake periods will sooner or later overlap. If two nodes

78 P. Hurni and T. Braun

have detected each other and learned about their schedule they calculate when the

other node becomes active again in order to schedule pending transmissions. This

scheme proved to avoid overhearing and fairness problems of WiseMAC’s fixed

static wake-up pattern, in particular when two neighbour nodes share a similar wake

pattern. Moving intervals proved to help reducing end-to-end latency over minimum-

hop paths by intelligently choosing gateway nodes to forward packets.

Fig. 3. WiseMAC

Fig. 4. MAC with moving wake periods

3 Energy-Efficient Multi-path Routing for Wireless Sensor

Networks

3.1 AOMDV Inspired Multi-path Routing

Our energy-efficient multi-path routing approach is based on AOMDV, because the

path construction algorithm of AODVM depends on overhearing neighboring nodes’

transmissions. Permanent overhearing requires to keep the receiver constantly in the

receive state, which is contrary to the scope of the energy-efficient MAC. Moreover,

we found in initial experiments that redundant paths detected by multi-path routing

schemes were often much longer than the optimal paths. Long detours of redundant

paths have negative impact on the lifetime, because more transmissions become nec-

essary when paths are suboptimal, and each transmission may influence other nodes

in the carrier sensing range.

AODV is tailored to the use in mobile ad hoc networks and always keeps the

freshest route to every destination. A node receiving a path advertisement for a given

destination node checks whether the advertisement provides a higher destination se-

quence number, or if it provides an equal destination sequence number and a shorter

path to the destination. If it does, the current entry for this destination is deleted and

the packet source is taken as new next node towards the destination node. As AODV

has been designed for use in mobile ad-hoc networks, in which nodes move in and out

Energy-Efficient Multi-path Routing in Wireless Sensor Networks 79

of the transmission range of each other, the sequence number condition ensures that a

node always uses the path known to be the freshest one. However, most wireless

sensor networks can be assumed to be rather static and node mobility does not play a

major role. We therefore weakened the condition of prioritizing route advertisements

with the highest sequence number. Our approach considers route advertisements to a

destination with higher sequence number only, if the route is not longer than the cur-

rent one. The approach incorporates the basic mechanism of the AOMDV protocol to

find node-disjoint paths, but adds such paths only, if they advertise the same hop

count. Incoming RREQ duplicates are treated as in AOMDV: they are answered, if

they advertise a node-disjoint path to a destination and if they advertise the same hop

count. To summarize, we add an additional path entry to the same destination to

which a path is already known if it meets all of the following criteria:

a) The sequence number is equal or higher,

b) The first-hop is different from all already known paths to the same destination

c) The hop count is equal.

When a path advertisement arrives with lower hop count, all existing routes are de-

leted and the new route is added. When receiving a duplicate that fulfils the condition

of a node-disjoint path and is optimal in terms of hop count, the routing table is ex-

tended to contain more than one path entry. The modification of the routing table

entry update rule compared to AOMDV and AODV can be explained by Figure 5,

where the dissemination of a RREQ from node 1 searching a path to node 16 is de-

picted. After flooding the whole network, the destination node receives path adver-

tisements to node 1 from its neighbours 9, 11 and 14. With AODV, the destination

node only answers to the first incoming RREQ with a corresponding RREP, e.g., from

neighbour 9. The duplicate RREQ from neighbour 11 is simply discarded and left

unanswered, as it advertises the same sequence number. Although it took another

route and would provide path redundancy, AODV discards the request and leaves it

unanswered. In contrast, AOMDV considers all routes that are advertised by

neighbours 9, 11 and 14, as the respective RREQs all took another first hop. We

changed the table update policy such that only the optimal routes in terms of hop

count are added to the table and answered with a RREP. In the previous case, the

RREQs received via neighbours 9 and 11 are answered with a RREP, but not the one

received via neighbour 14. The resulting routing tables for source node 1 and destina-

tion node 16 are depicted in Figure 5. With AODV, only one path entry is considered,

whereas AOMDV adds all paths to its table. With our approach, only the hop-count

optimal routes via nodes 9 and 11 are added to the table.

AOMDV only addresses the question how to establish multiple routes, but not how

to spread the load over them. There are probabilistic schemes that assign a certain

probability to a route and choose the route for each packet in a random manner. We

suggest exploiting information provided by the MAC layer to achieve some perform-

ance gains in respect to the latency. As all redundant path entries to a destination

advertise an optimal route in terms of hop count, the next soonest wake-up of the

gateway leading to the destination shall be the only selection criterion, also in each

intermediate node. For a transmission of a packet from source to destination, each

80 P. Hurni and T. Braun

intermediate node shall forward the packet to the node with the soonest wake-up. A

lower latency as well as the desired load balancing among the intermediate nodes can

thus be expected.

Fig. 5. RREQ and different table update policies

As the source knows two paths towards node 16, it chooses the path according to

the delay to the next-wake-up of the gateway node. In the left part of Figure 6, we can

see that the time remaining to the next wake-up of node 2 is 132 ms, and the next

wake-up of node 4 is in 54 ms. Therefore, the source node chooses to send the packet

via node 4, because it can deliver the packet and empty its buffer earlier. The packet

is routed in every intermediate node accordingly. Since we only added hop-count-

optimal routes, packets are never routed away from the destination.

If we would apply WiseMAC with its simple periodic wake-up pattern, nodes

would always forward over the same gateways, because the time shift between two

Energy-Efficient Multi-path Routing in Wireless Sensor Networks 81

Fig. 6. Packet forwarded from 1 to 16 choosing nodes with the soonest wake-up

node’s wake-ups remains constant. With the moving wake-intervals MAC (Figure 4)

nodes will always choose their gateway according to the shortest delay to the next

wake-up. The choice of the gateways may change, because the offset and minimum

delays dynamically change with the moving intervals.

4 Evaluation

4.1 Simulation Parameters and Scenarios

We performed our evaluation using the OMNeT++ network simulator [16] and the

mobility framework [17]. The energy consumption model is based on the amount of

energy that is used by the transceiver unit. We do not take processing costs of the

CPU into account. Each node’s energy consumption is calculated in respect to the

time and input current that the node spends in the respective operation modes

idle/receive, transmit and sleep. Furthermore, state transition delays are taken into

account. The simulation parameters are summarized in Table 4. As the choice of the

network topology may have an impact on the results, we considered the following

three network topologies:

• uniformly distributed network topology of 90 nodes in an area of 300x300 m

• 7x7 nodes lattice square topology (Figure 7)

• 3x10 nodes grid topology (Figure 8)

82 P. Hurni and T. Braun

We defined the lifetime of the network as the time until 10% of the nodes deplete or

the network becomes partitioned. For each topology, we measured two different traf-

fic patterns.

• Evenly distributed traffic: Every node starts reporting data according to the

Poisson model with λ = 0.01. When every node generates the same amount

of traffic, multi-path routing might not pay off, because the load is already

balanced. As common single path routing protocols establish source-sink

trees with some nodes having the burden to forward traffic of large sub-trees,

multi-path routing still might help to redistribute the load over more hops.

• Neuralgic spots traffic: If there are neuralgic spots in the network that gener-

ate much traffic, whereas other parts stay more or less inactive, multi-path

routing can pay off more. We assume that the three most distant nodes from

the sink generate 20 times more traffic (λ = 0.05) than all other nodes

(λ = 0.0025).

Table 4. Simulation Parameters

carrier frequency 868 MHz

bit rate 19.2 kbps

packet size including header 160 bits

transmitter power 0.1 mW

SNR threshold 4 dB

sensitivity -101.2 dBm

sensitivity carrier sensing -112 dBm

communication range 50 m

packet loss coefficient α 3.5

carrier sensing range 100 m

node energy 20 J

supply voltage 3V

current

transmit 12 mA

receive 4.5 mA

sleep 5 µA

state transition delays

receive to transmit 12 µs

transmit to receive 12 µs

sleep to receive 518 µs

receive to sleep 10 µs

transmit to sleep 10 µs

Energy-Efficient Multi-path Routing in Wireless Sensor Networks 83

4.2 Lifetime and Delay Results

The results in Figure 9 and Figure 10 show an overall performance gain when apply-

ing the AOMDV-related scheme coupled with the next-soonest-wake-up routing

paradigm of ~10-15% concerning network lifetime and one-way delay. When consid-

Fig. 7. 7x7 nodes lattice square topology

Fig. 8. 3x10 nodes grid topology

ering the low cost of some additional RREP messages in the initial route discovery

phase, the results show that on-demand multi-path routing may provide limited but

valuable contributions to extend network operability. In our simulation, the mecha-

nism paid off when sticking to the hop count optimal routes only. The performance

improvements are in a similar range as in [18] although the authors focused on wire-

less ad-hoc networks and on throughput optimization.

The exploitation of the MAC layer information about the next-soonest wake-up of

the neighboring nodes paid off in respect to the one-way delay. This might be in con-

flict with the layered design paradigm, but in wireless sensor networks with scarce

energy resources, such cross-layer approaches are acceptable, if higher efficiency can

be achieved. Neither the different traffic patterns nor the topology has a big impact on

the results.

In a second series of experiments, we performed all the experiments with another

lifetime metric. In that case, we measured the first node depletion. The results differed

only slightly from the results using the first lifetime metric. The overall gain also

reached 10-15% in respect to lifetime and to one-way delay for all topologies and

both traffic patterns.

84 P. Hurni and T. Braun

Fig. 9. Network Lifetime

Fig. 10. One-Way Delay

5 Conclusions

The paper proposed to integrate a multi-path routing protocol and appropriate MAC

protocols with periodic wake-up to balance load in a wireless sensor network and

achieve higher network lifetime. The proposed concept achieves this by exploiting

cross-layer optimizations between MAC and routing protocol as well as by altering

path update policies. The evaluation showed that the potential to achieve higher net-

work lifetimes is limited when applying preamble sampling low-power MAC proto-

cols such as WiseMAC. WiseMAC amplifies the performance degrading route

Energy-Efficient Multi-path Routing in Wireless Sensor Networks 85

coupling effect, because it increases its carrier-sensing range with a more prohibitive

carrier access policy. This increased the probability that transmissions along multiple

paths interfere with each other. Load balancing of multipath-routing was deteriorated

by the additional cost of coping with path interference. The mechanism exhibited

performance gains of 10-15% in respect to throughput and average end-to-end delay.

References

[1] El-Hoiydi, A., Decotignie, J.-D.: WiseMAC: An Ultra Low Power MAC Protocol for

Multihop Wireless Sensor Networks. ALGOSENSORS (2004)

[2] Tsai, J., Moors, T.: A Review of Multipath Routing Protocols: From Wireless Ad Hoc to

Mesh Networks. ACoRN Early Career Researcher Workshop on Wireless Multihop Net-

working (2006)

[3] Perkins, C.E., Belding-Royer, M., Ad, E.: hoc On-Demand Distance Vector (AODV)

Routing, RFC 3561 (2003)

[4] Johnson, D.B.: Routing in Ad Hoc Networks of Mobile Hosts. In: Workshop on Mobile

Computing Systems and Applications. IEEE Computer Society, Los Alamitos (1994)

[5] Dulman, S., Nieberg, T., Wu, J., Havinga, P.: Trade-off between Traffic Overhead and Reli-

ability in Multi-path Routing for Wireless Sensor Networks. In: WCNC Workshop (2003)

[6] Mueller, S., Ghosal, D.: Multi-path Routing in Mobile Ad Hoc Networks: Issues and

Challenges. MASCOTS Tutorials (2003)

[7] Pearlman, M.R., Haas, Z.J., Sholander, P., Tabrizi, S.S.: On the impact of alternate path

routing for load balancing in mobile ad hoc networks. In: ACM international symposium

on Mobile ad hoc networking & computing, Boston (2000)

[8] Voigt Th., Dunkels A., Braun, T.: On-demand Construction of Non-interfering Multiple

Paths in Wireless Sensor Networks 2nd Workshop on Sensor Networks, Informatik (2005)

[9] Waharte, S., Boutaba, R.: Totally Disjoint Multi-path Routing in Multihop Wireless Net-

works. IEEE International Conference on Communications (2006)

[10] Ganjali, Y., Keshavarzian, A.: Load Balancing in Ad hoc Networks: Single-path Routing

vs. Multi-path Routing. IEEE Infocom (2004)

[11] Ganesan, D., Govindan, R., Shenker, S., Estrin, D.: Highly Resilient, Energy-Efficient

Multi-path Routing in Wireless Sensor Networks. Mobile Computing and Communica-

tions Review (2001)

[12] Lee, S.-J., Gerla, M.: Split Multi-path Routing with Maximally Disjoint Paths in Ad Hoc

Networks. In: IEEE International Conference on Communications (2001)

[13] Marina, M.K., Das, S.R.: On Demand Multi-path Distance Vector Routing in Ad hoc

Networks. In: IEEE International Conference on Network Protocols (2001)

[14] Ye, Z., Krishnamurthy, S.V., Tripathi, S.K.: A Framework for Reliable Routing in Mo-

bile Ad Hoc Networks. IEEE Infocom (2003)

[15] Shah, R.C., Rabaey, J.: Energy Aware Routing for Low Energy Ad Hoc Sensor Net-

works. In: IEEE Wireless Communications and Networking Conference WCNC (2002)

[16] Varga, A.: The OMNeT++ Discrete Event Simulation System European Simulation Mul-

ticonference (ESM 2001), Prague, Czech Republic (June 2001),

http://www.omnetpp.org

[17] Mobility Framework for OMNeT++, http://mobility-fw.sourceforge.net

[18] Bononi, L., Di Felice, M.: Performance Analysis of Cross-Layered Multipath Routing

and MAC Layer Solutions for Multi-hop Ad Hoc Networks. ACM MobiWAC (2006)

[19] Hurni, P., Braun, T.: Improving Unsynchronized MAC Mechanisms in Wireless Sensor

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Approximating Minimum-Power k-Connectivity

ZeevNutov

The Open University of Israel, Raanana, Israel

nutov@openu.ac.il

Abstract. The Minimum-Power k-Connected Subgraph (MPkCS)prob-

lem seeks a power (range) assignment to the nodes of a given wireless net-

work such that the resulting communication (sub)network is k-connected

and the total power is minimum. We give a new very simple approxima-

tion algorithm for this problem that signiﬁcantly improves the previously

best known approximation ratios. Speciﬁcally, the approximation ratios

of our algorithm are:

- 3 (improving (3 + 2/3)) for k=2,

- 4 (improving (5 + 2/3)) for k=3,

-k+3 for k∈{4,5}and k+5 for k∈{6,7}(improving k+2(k+1)/2),

-3(k−1) (improving 3k) for any constant k.

Our results are based on a (k+ 1)-approximation algorithm (improving

the ratio k+ 4) for the problem of ﬁnding a Min-Power k-Inconnected

Subgraph, which is of independent interest.

1 Introduction

1.1 Preliminaries

Wireless networks are studied extensively due totheirwide applications.The

power consumption ofastation determines its transmission range,andthus

alsothe stationsitcansend messages to; the power typically increases at least

quadratically in the transmission range.Assigningpower levelstothe stations

(nodes)determines the resultingcommunication network.Conversely, givena

communication network,the cost required at vonly depends on the furthest

node that is reached directly byv.Thisisin contrast with wired networks,in

which everypairofstationsthatneed tocommunicate directly incurs a cost.

In network designproblems one seeks todesigna“cheap”communication

(sub)network that satisﬁes some prescribed properties.Animportantnetwork

propertyisfault-tolerance,oftenmeasured bynode-connectivityofthenetwork.

Node-connectivityismuchmore centralhere thanedge-connectivity, as itmod-

elsstationsfailures.Such problems were vastly studied;see [1,3,4,9,11,12,17,21]

foronly asmall sampleofpapersin thisarea.Weconsider the Min-Power k-

Connected Subgraph (MPkCS)problem which isthepower variantoftheclassic

Min-Cost k-Connected Subgraph (MCkCS)problem.Wegiveanapproximation

algorithm forMPkCS that signiﬁcantly improves the previously best known ones.

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 86–93, 2008.

Springer-Verlag Berlin Heidelberg 2008

Approximating Minimum-Power k-Connectivity 87

Deﬁnition 1. Let H=(V, I)be a graph with edge-costs {c(e):e∈I}.For

v∈V,thepower p(v)=pH(v)ofvin H(w.r.t. c) is the maximum cost of an

edge in Ileaving v, i.e., p(v)=pI(v)=maxvu∈Ic(vu). The power of the graph

is the sum of the powers of its nodes.

Note that p(H)diﬀers fromthecost c(H)=e∈Ic(e)ofHevenforunitcosts;

forunitcosts,ifHisundirected,thenc(H)=|I|and(ifHhas no isolated nodes)

p(H)=|V|.Forexample,ifIis a perfect matchingon Vthenp(H)=2c(H).

IfHisaclique thenp(H)isroughly c(H)/|I|/2.Fordirected graphs,the

ratio ofthecost over the power canbe equaltothe maximum outdegree,e.g.,

forstarswith unitcosts.The following statement,parts ofwhich appeared in

various papers,c.f., [9,11], shows that these are the extremalcases forgeneral

edge costs.

Proposition 1. c(H)/|I|/2≤p(H)≤2c(H)for any undirected graph H=

(V,I),andifHis a forest then c(H)≤p(H)≤2c(H). For any directed graph

Dholds: c(D)/∆(D)≤p(D)≤c(D),where∆(D)is the maximum outdegree of

anodeinD.

Minimum-power problems are usually harder thantheirminimum-cost versions.

The Minimum-Power Spanning Tree problem isAPX-hard.The problem ofﬁnding

minimum-cost kpairwise edge-disjointpathsisin P (thisistheMinimum-Cost

k-Flow problem,c.f., [22]) whileboth directed andundirected minimum-power

variants are unlikely tohaveevenapolylogarithmic approximation [9,17]. An-

other exampleisﬁndinganarborescence rooted at s,that is,a subgraph that

containsansv-path foreverynode v.The minimum-cost case isin P (c.f., [22]),

whiletheminimum-power variantisatleast as hard as the Set-Cover problem.

Formore examples see [1,21].

Anetwork isa(possibly directed)graph with edge costs.ForagraphH=

(V,I)andX⊆V,let dI(X)=dH(X)denote the degree ofXin H,that isthe

number ofedgesfromXtoV−X.Allthe graphs in the paper are assumed to

be simple,and,unless stated otherwise,undirected.

Agraph H=(V,I)isk-connected ifitcontainskinternally-disjointuv-paths

forall u, v ∈V.Weconsider the min-power variantoftheextensively studied

classicMin-Cost k-Connected Subgraph (MCkCS)problem.

Minimum-Power k-Connected Subgraph (MPkCS)

Instance:Agraph G=(V, E)with edge costs {c(e):e∈E), andaninteger k.

Objective:Findaminimum-power k-connected spanning subgraph HofG.

1.2 Previous and Related Work

Wenow introduce some additionalrelated problems,that will alsoplayanim-

portantrolelater.The ﬁrst problem isthemin-power variantoftheMin-Cost

k-Flow problem (with unitnode capacities).

Min-Power kDisjoint Paths (MPkDP)

Instance: Agraph G=(V, E), edge-costs {c(e):e∈E},u, v ∈V,aninteger k.

Objective: Findamin-power subgraph HofGwith kinternally-disjointuv-paths.

88 Z. Nutov

A(possibly directed)graph H=(V, I)isk-inconnected to sifitcontainsk

internally-disjointvs-paths forall v∈V−s.

Min-Power k-Inconnected Subgraph (MPkIS)

Instance: Agraph G=(V, E), edge-costs {c(e):e∈E},s∈V,aninteger k.

Objective: Findamin-power k-inconnected tosspanning subgraph HofG.

Min-Power k-Edge-Cover (MPkEC)

Instance: Agraph G=(V, E), edge-costs {c(e):e∈E},aninteger k.

Objective: Findamin-power edge set I⊆Esothat dI(v)≥kforall v∈V.

Itiseasytosee (c.f., [11,9]) that the simplest heuristicforMPkEC that forevery

node v∈Vtakes the kcheapest edges incidenttovisa(k+1)-approximation

algorithm forMPkEC.In[12]the approximation ratio O(logn)was derived.Fo

k=1a3/2-approximation algorithm isgivenin[13].

Itturnsout that approximatingMPkCS isclosely related toapproximating

MCkCS andMPkEC as showsthefollowingobservation from[9], which ﬁrst part

was implicitly observed independently in [11].

Theorem 1 ([9,11])

(i) An α-approximation for MCkCS and a β-approximation for MP(k−1)EC

implies a (2α+β)-approximation for MPkCS.

(ii) Aρ-approximation for MPkCS implies a (2ρ+1)-approximation for MCkCS.

Onecancombinevarious values ofα, β with Theorem 1(i) toget approximation

algorithms forMPkCS.Aswas mentioned,currently β=min{k, O(logn)}[9],

andβ=3/2fork=2[13] (note that here βistheratio forMP(k−1)EC and

notforMPkEC). The best known values forαare:α=(k+1)/2for2≤k≤7

(see [2]fork=2,3, [6] fork=4,5, and[14]fork=6,7), α=kforother small

values ofk[14], andα=Ologk·logn

n−kotherwise [20]. Thus forundirected

MPkCS the followingratiosfollow: 3kforany k,k+2(k+1)/2for2≤k≤7,

O(logn)unless k=n−o(n), andO(log2n)ifk=n−o(n).

Improvements over the aboveratiosforMPkCS are known only fork≤5:

(2k−1/3) fork∈{2,3}[13], and9fork=4[11].

Forfurtherresults on other min-power connectivityproblems,amongthem

problems on directed graphs see [9,21,17]. Forresults on min-cost k-connectivity

problems see [2,6,14,5,15,7,20,18]; see alsoa recentsurveyin[16]onvarious

min-cost connectivityproblems.

1.3 Results

The previously best known ratio forMPkIS was min{k+4,O(logn)}[17]. We

improvetheratio k+4fork=O(logn)as follows:

Theorem 2. Undirected MPkIS admits a (k+1)-approximation algorithm.

CombiningTheorem 2 with a direct analysisofthealgorithms in [2,6,14]for

MCkCS,weobtain the followingresult:

Approximating Minimum-Power k-Connectivity 89

Theorem 3. Suppose that MPkIS admits a γ-approximation algorithm and that

MPkDP admits a θ-approximation algorithm. Then MPkCS admits the following

approximation ratios: γ+θ(k−2)for any constant kand γ+θ(k/2−1)

for k≤7.Inparticular,fork≤7the ratios are: γfor k∈{2,3},γ+θfor

k∈{4,5},andγ+2θfor k∈{6,7}.

AsMPkDP admits a 2-approximation algorithm (c.f., [9,17]), thenbycombining

Theorems 2 and3weobtain:

Theorem 4. MPkCS admits the following approximation ratios: k+1 for k∈

{2,3},k+3 for k∈{4,5},k+5 for k∈{6,7},and3(k−1) for any constant k.

Theorem 4 signiﬁcantly improves the previously best known ratiosforMPkCS

with 2 ≤k≤7,as summarized in the followingtable:

Table 1 . Approximation ratios for MPkCS

kPrior art This paper

1(5/3+ε)[1] −

2(3 + 2/3) [13] 3

3(5 + 2/3) [13] 4

49[11] 7

511 [11,9] 8

614 [11,9] 11

715 [11,9] 12

constant k3k[11,9] 3k−3

Theorems 2 and3are proved in Sections2and3, respectively.

2 Algorithm for MPkIS (Proof of Theorem 2)

Abi-direction ofanundirected network Hisadirected network obtained by

replacingeveryedge e=uv ofHbytwo opposite directed edges uv, vu each

havingthesamecost as e.Clearly, ifDisabi-direction ofH,thenp(H)=p(D).

The underlying network ofadirected network Disanetwork Hobtained from

Dbyignoringthedirections(but keepingcosts)oftheedges,andthenkeeping

one(arbitrary) edge fromeverymaximalset ofparalleledges,ifnon-empty. If

Histheunderlyingnetwork ofadirected star Dwith unitcosts,thenp(H)=

(∆(D)+1)p(D). The following statementshowsthatthisistheextremalcase

forgeneralcosts.

Lemma 1. p(H)≤(∆(D)+1)p(D)for the underlying network Hof a directed

network D.

Proof. By induction on the number mofedgesin D.Form=1the statement

isobvious.Assume that the statementistruefordigraphs with at most m−1

90 Z. Nutov

edges.Let v∈Vbe a node in Dofmaximum power cmax .Let Dbe obtained

fromDbyremovingtheedgesleavingv,andlet Hbe the underlyinggraphof

D.Clearly, p(D)=p(D)−cmax andp(H)≥p(H)−(∆(D)+1)cmax.Combining

with the induction hypothesisgives:

p(H)≤p(H)+(∆(D)+1)cmax

≤(∆(D)+1)(p(D)+cmax)

=(∆(D)+1)p(D).

Weneed severalresults from[17].

Theorem 5 ([17]). Directed MPkIS can be solved in polynomial time.

Deﬁnition 2. An edge eof a k-inconnected to sgraph Jis criticalif J−eis

not k-inconnected to s. A graph is minimally k-inconnected to sif all its edges

are critical.

Theorem 6 ([17]). Let uvand uv be two distinct critical edges of a

k-inconnected to sdirected graph J.ThendJ(u)=k.Inparticular,dJ(u)=k

for every node u=sif Jis minimallyk-inconnected to s.

The (k+1)-approximation algorithm forMPkIS isasfollows:

1. Let Dbe the bi-direction ofG.

2.Compute a min-power k-inconnected tosspanning subgraph JofD.

3. Returnthe underlyinggraphHofJ.

Step 2 canbe implemented in polynomialtime usingthealgorithm of[17]

(Theorem 5). Wenow show that the approximation ratio ofthealgorithm is

k+1. Let H∗be anoptimalsolution toMPkIS instance (sop(H∗)=opt)and

let J∗be the bi-direction ofH∗.Let HandJbe as in the algorithm.Combining

Theorem 6with Lemma 1weget:

p(H)≤(∆(J)+1)p(J)

≤(k+1)p(J)

≤(k+1)p(J∗)

≤(k+1)p(H∗)

=(k+1)opt .

The proofofTheorem 2 iscomplete.

3 Algorithm for MPkCS (Proof of Theorem 3)

Weneed the following summaryofseveralstatements from[2,6,14].

Lemma 2 ([2,6,14]). Let H=(V,I)be k-inconnected to sgraph with dH(s)=

k. Then one can ﬁnd in polynomial time a set Fof at most k−2new edges on the

neighbors of sin Hso that H+Fis k-connected. Furthermore, |F|≤k/2−1

for k≤7.

Approximating Minimum-Power k-Connectivity 91

Halin [10] proved that any minimally k-connected graph has a node ofdegreek.

Astronger statementwas proved byMader [19]:

Theorem 7 ([19]). A minimally k-connected graph contains at least (k−1)n+2

2k−1

nodes of degree k.

Thismotivates the followingauxiliaryproblem,which min-cost variantisthe

basisforthealgorithms in [2,6,14].

Restricted MPkIS

Instance: Agraph G=(V, E), edge costs {c(e):e∈E},s∈V,aninteger k.

Objective: Findamin-power k-inconnected tosspanning subgraph HofG

with dH(s)=k.

Lemma 3. If MPkIS admits a γ-approximation algorithm then Restricted MPkIS

admits a γ-approximation algorithm for any constant k.

Proof. The algorithm forRestricted MPkIS isderived fromthealgorithm for

MPkIS by”guessing”the kedges incidenttosin some optimalsolution for

Restricted MPkIS.Forany subset K⊆Eofkedges incidenttos,weremovethe

other edges incidenttos,andcompute a γ-approximate solution HKtoMPkIS

(ordeclare that the resultinggraphisnotk-inconnected tos). Then, amongthe

subgraphs HKcomputed,weoutput oneHoftheminimum power.The running

time isn

k=O(nk)times the runningtime oftheγ-approximation algorithm

forMPkIS,hence polynomialforany constantk.

Remark: In [6], itwas shown that the min-cost version ofdirected Restricted

MPkIS issolvablein polynomialtime;thiswas donebyusingthealgorithm

of[8]forthemin-cost version ofdirected MPkIS andpenaltymethods.Although

MPkIS issolvablein polynomialtime [17], itseemsthatthepenaltymethod

used in [6] does notwork fordirected Restricted MPkIS.

Wenow ﬁnish the proofofTheorem 3. The algorithm isasfollows:

1. Foreverys∈V,compute a γ-approximate solution HstoRestricted MPkIS

with G, s.

Among the subgraphs Hscomputed,let Hbe oneoftheminimum power.

2.Compute anedge set Fas in Lemma 2.

3. Foreveryuv ∈Fcompute a 2-approximate solution forMPkDP in G, {u, v}.

4.ReturnH+{Fuv :uv ∈F}.

The fact that the returned graph isk-connected was alreadyestablished in [2,14],

andeasily followsfrom the deﬁnition ofF.Forany constantk,Step 1can

be implemented in polynomialtime,byLemma 3. All the other steps canbe

implemented in polynomialtime forany k.Thus the runningtime ispolynomial

forany constantk,as claimed.

Weprove the approximation ratio. Note that a k-connected graph isalsok-

inconnected tosforeverys∈V.Let H∗be some optimalsolution toMPkCS;

92 Z. Nutov

clearly, wemayassume that H∗isminimally k-connected.FromTheorem 7 it

follows that there isanode s∈Vsothat the degree ofsin Hisk.Thus for

the graph Hcomputed at Step 1wehavep(H)≤γp(H∗)=γopt.Also, H∗

containskinternally disjointuv forall u, v ∈V.Thus Fuv ≤θopt forall uv ∈F.

Consequently,

pH+{Fuv :uv ∈F}≤p(H)+ 

uv∈F

p(Fuv)

≤γopt +θ|F|opt

=(γ+θ|F|)opt .

Substitutingthesizes ofFfromLemma 2 weobtain the following.Forany kwe

have|F|≤k−2,andthusin this case the approximation ratio isγ+θ|F|=

γ+θ(k−2). Fork≤7wehave|F|≤k/2−1, andthusin thiscasethe

approximation ratio isγ+θ|F|=γ+θ(k/2−1). Substitutingthespeciﬁc

values ofk,weobtain the last statementoftheTheorem.

The proofofTheorem 3iscomplete.

4OpenProblems

The main openproblem in the contextofthispaperistodeterminewhether the

undirected MPkDP isin P orisNP-hard (the directed MPkDP isin P, c.f., [9]).

IfMPkDP isin P, thenwecansubstitute θ=1inTheorem 3andobtain the

followingratiosforMPkCS:2k−1(instead of3k−3) forany constantk,and

k+k/2(improvingk−1+2k/2)fork≤7.

Wenote that wedonotknow the answer eventothe following”easier”ques-

tion. Let MPkDP Augmentation be the restriction ofMPkDP toinstances where

E0={e∈E:c(e)=0}containsk−1pairwise internally disjointpaths.Wedo

notknow if(undirected)MPkDP Augmentation isin P, but weconjecture this

isso. A polynomialalgorithm forMPkDP Augmentation canbe used toimprove

the ratiosforMPkCS fork=4,5: from7to6fork=4andfrom8to7fork=5.

Thisissince in [2,6] itisshown that ifHisk-inconnected tosanddH(s)=k

thenHis(k/2+1)-connected.Thus fork=4,5, Hisk−1-connected,and,by

Lemma 2,Hcontainstwo nodes u, v sothat increasingtheconnectivitybetween

them byoneresults in ak-connected graph.

Except directed MPkDP andMPkIS that are in P, there isstill alarge gap be-

tweenupper andlower bounds of approximation formany other min-power node

connectivityproblems,forboth directed andundirected graphs,see [21,17,12].

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Berlin (2004)

A Secure Cross-Layer Protocol for

Multi-hop Wireless Body Area Networks

Dave Singel´ee1,Benoˆıt Latr´e2,BartBraem

3, Michael Peeters4,

Marijke De Soete4, Peter De Cleyn3, Bart Preneel1, Ingrid Moerman2,

and Chris Blondia3

1ESAT–SCD–COSIC, Katholieke Universiteit Leuven — IBBT,

Kasteelpark Arenberg 10, 3001 Heverlee-Leuven, Belgium

dave.singelee@esat.kuleuven.be

2IBCN, Dept. of Information Technology (INTEC), Ghent University — IBBT,

Gaston Crommenlaan 8, bus 201, 9050 Gent, Belgium

3PATS, Dept. of Mathematics and Computer Sc., University of Antwerp — IBBT,

Middelheimlaan 1, B-2020, Antwerp, Belgium

4NXP Semiconductors, Competence Center System Security & DRM,

A&I Innovation & Development Center Leuven,

Interleuvenlaan 74–82, 3001 Leuven, Belgium

Abstract. The development of Wireless Body Area Networks (WBANs)

for wireless sensing and monitoring of a person’s vital functions, is an

enabler in providing better personal health care whilst enhancing the

quality of life. A critical factor in the acceptance of WBANs is provid-

ing appropriate security and privacy protection of the wireless commu-

nication. This paper ﬁrst describes a general health care platform and

pinpoints the security challenges and requirements. Further it proposes

and analyzes the CICADA-S protocol, a secure cross-layer protocol for

WBANs. It is an extension of CICADA, which is a cross-layer protocol

that handles both medium access and the routing of data in WBANs.

The CICADA-S protocol is the ﬁrst integrated solution that copes with

threats that occur in this mobile medical monitoring scenario. It is shown

that the integration of key management and secure, privacy preserving

communication techniques within the CICADA-S protocol has low im-

pact on the power consumption and throughput.

1 Introduction

Recent progress in wireless sensing and monitoring, and the development of

small wearable or implantable biosensors, have led to the use of Wireless Body

Area Networks (WBANs). The research on communication within a WBAN

is still in its early stages. Only few protocols designed speciﬁcally for multi-

hop communication in WBANs exist. They try to minimize the thermal eﬀects

of the implanted devices by balancing the traﬃc over the network [1] or by

forming clusters [2,3] or a tree network [4].

Wireless Body Area Networks can be seen as an enabling technology for mobile

health care [5]. Medical readings from sensors on the body are sent to servers at

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 94–107, 2008.

Springer-Verlag Berlin Heidelberg 2008

A Secure Cross-Layer Protocol Multi-hop WBAN 95

the hospital or medical centers where the data can be analyzed by professionals.

These systems reduce the enormous costs associated to ambulant patients in

hospitals as monitoring can take place even at home in real-time and over a

longer period.

In this paper, we propose and analyze CICADA-S, a secure protocol for

WBANs. It is based on an existing multi-hop protocol for WBANs, called CI-

CADA [4]. This is a cross-layer protocol that sets up a data gathering tree in

a reliable manner, oﬀering low delay and high energy eﬃciency. The communi-

cation of health related information between sensors in a WBAN and over the

Internet to servers is strictly private and conﬁdential and should therefore be

encrypted to protect the patient’s privacy. Furthermore, the medical staﬀ who

collects the data must be conﬁdent that the data is not tampered with, and

indeed originates from that patient.

The CICADA-S protocol is designed within the scope of the IBBT IM3-project

(Interactive Mobile Medical Monitoring), which focuses on the research and im-

plementation of a wearable system for health monitoring [6]. Patient data is

collected using a WBAN and analyzed at the gateway (also called medical hub)

worn by the patient. If an event (e.g., heart rhythm problems) is detected, a

signal is sent to a health care practitioner who can view and analyze the patient

data remotely.

The remainder of this paper is organized as follows. Section 2 gives an overview

of related work. The general architecture and the necessary security assumptions

are described in section 3. A short description of CICADA is given, followed by

the integration of the security mechanisms in the protocol and a description

of the key management aspects in section 4. The analysis of the integration in

terms of performance overhead and security properties are dealt with in section 5.

Finally, section 6 provides a ﬁnal conclusion on the paper.

2 Related Work

Security is essential for broad acceptance and further growth of Wireless Sensor

Networks. These networks pose unique challenges as security techniques used in

traditional networks cannot be directly applied. Indeed, to make sensor networks

economically viable, sensor devices should be limited in their energy consump-

tion, computation, and communication capabilities. Since most of the existing

security mechanisms have major drawbacks in that respect, new ideas are needed

to address these requirements in an appropriate way [7].

One of the most crucial components to support the security architecture of a

Wireless Sensor Network is its key management. During the last years, a num-

ber of pairwise key establishment schemes have been proposed. Zhou and Haas

propose to secure ad-hoc networks using asymmetric cryptography [8]. They use

threshold cryptography to distribute trust among a set of servers. This scheme

achieves a high level of security, but is too energy consuming to be used in

practice in a Wireless Sensor Network. Eschenauer and Gligor introduce a key

management scheme for distributed sensor networks [9]. It relies on probabilistic

96 D. Singel´ee et al.

WBAN

Medical Serve

Physician

External Network

Personal Device – Medical Hub

Sensor

Fig. 1. General overview of the IM3 health care architecture

key sharing among the nodes of a random graph. Perrig et al. present SPINS,

a suite of security building blocks optimized for resource-constrained environ-

ments and wireless communication [10]. It has two secure building blocks: SNEP

and µTESLA. SNEP provides data conﬁdentiality, two-party data authentication

and data freshness, while µTESLA oﬀers authenticated broadcast in constrained

environments.

The security mechanisms employed in Wireless Sensor Networks do generally

not oﬀer the best solutions to be used in Wireless Body Area Networks for the

latter have speciﬁc features that should be taken into account when designing the

security architecture. The number of sensors on the human body, and the range

between the diﬀerent nodes, is typically quite limited. Furthermore, the sensors

deployed in a WBAN are under surveillance of the person carrying these devices.

This means that it is diﬃcult for an attacker to physically access the nodes

without this being detected. When designing security protocols for WBANs,

these characteristics should be taken into account in order to deﬁne optimized

solutions with respect to the available resources in this speciﬁc environment.

Although providing adequate security is a crucial factor in the acceptance

of WBANs, little research has been done in this speciﬁc ﬁeld [11]. In [12] an

algorithm based on biometric data is described that can be employed to ensure

the authenticity, conﬁdentiality and integrity of the data transmission between

the personal device and all the other nodes. Another method is presented in [13]

where body-coupled communication (BCC) is used to associate new sensors in

a WBAN.

None of the current protocols oﬀer a solution where appropriate security mech-

anisms are incorporated into the communication protocol while addressing the

lifecycle of the sensors. Further, security and privacy protection mechanisms use

a signiﬁcant part of the available resources and should therefore be energy eﬃ-

cient and lightweight. The mechanisms proposed in this paper aim to cover these

challenges.

3 Architecture

3.1 General Overview

Fig. 1 shows the health care architecture used by the IM3 pro ject. There are

three main components: the Wireless Body Area Network (WBAN), the external

A Secure Cross-Layer Protocol Multi-hop WBAN 97

network and the back-end server. In this scenario, the WBAN contains several

sensors that measure medical data such as ECG, body movement etc. These

sensors send their measurements, directly or via several hops, to the gateway.

Each WBAN (and hence every patient) has its unique gateway. In other words,

the sensors shall only send their data to the unique gateway they are linked with

and this needs to be enforced by speciﬁc security mechanisms. The gateway

processes the medical data, and sends the result via the external network to

the back-end server at the hospital, where it can be observed and analyzed by

medical staﬀ.

Although the architecture was originally designed for and is fully adapted to

a medical environment, it may also be used in other applications. Indeed, as

long as the (security) relations between the diﬀerent devices remain valid, the

protocol remains applicable, which increases the generality of our solution. In

the remainder of this paper, the medical scenario will be further used to explain

the architecture and the secure cross-layer protocol for multi-hop WBANs.

3.2 Security Assumptions

This section aims to address the securityoftheentiresystem,andtheWBAN

in particular.

The most security critical device in the entire architecture is the back-end

server. This server, which is managed by the hospital or medical center, will

receive the medical data sent by all active WBANs. It is assumed that this server

is physically protected (e.g., put in a secure place in the hospital where it can

not be stolen or tampered with), and that an adequate access control system

is implemented (i.e. only authorized medical personnel has (partial) access to

the server through appropriate identiﬁcation/authentication mechanisms). The

back-end server is considered to be a trusted third party, which means that

it is known and trusted by all other devices in the network after a successful

authentication.

Since potentially security critical data will be transferred through the exter-

nal network, end-to-end security between the gateway and the back-end server

is required. For eﬃciency reasons, it is assumed that both devices share a sym-

metric session key to secure their communication. This symmetric session key

can be manually installed (e.g., pre-installed during manufacturing), or (prefer-

ably) established via a symmetric key establishment protocol. The description

of such protocols can be found in the ISO 9798–2 standard, and is out of scope

of this article. The symmetric session key is updated regularly. The end-to-end

channel between gateway and back-end server should also be anonymized using

temporary pseudonyms. This avoids privacy problems like (location) tracking.

In the remainder of the paper, it is assumed that the secure end-to-end channel

between gateway and back-end server is already established after a successful

mutual authentication. As mentioned before, each gateway belongs to a speciﬁc

WBAN (i.e. a patient, who is carrying this device). To enforce this, the gateway

is registered in advance at the back-end server.

98 D. Singel´ee et al.

It is assumed that it is impossible to alter or read the memory of a (securely

initialized) node that is put on the patient’s body, or to modify the behavior of

a node without this being detected. This is not a strong assumption, since the

patient is carrying the nodes on its body, and an attacker is not able to access

the nodes without this being detected. It is also assumed that the attacker has

no access to the sensors that yet have to be securely initialized (e.g., because

they are stored in a safe place). However, an attacker can put a malicious node in

the presence of a WBAN, and try to join the network. He can also eavesdrop on

all data transmitted in the WBAN, and insert/delete/modify (malicious) data

into the network. The attacker is hence assumed to be active.

4ProtocolDesign

4.1 CICADA

CICADA is a cross-layer protocol as it handles both medium access and the

routing of data [4]. The protocol sets up a spanning tree in a distributed manner,

which is subsequently used to guarantee collision free access to the medium and

to route data toward the gateway. The time axis is divided in slots grouped in

cycles, to lower the interference and avoid idle listening. Slot assignment is done

in a distributed way where each node informs its children when they are allowed

to send their data using a SCHEME. Slot synchronization is possible because a

node knows the length of each cycle. During a cycle, a node is allowed to send

all of its data to its parent node. CICADA is designed in such a way that all

packets arrive at the source in only one cycle. Routing itself is not complicated

in CICADA anyway as data packets are routed up the tree which is set up to

control the medium access, no special control packets are needed.

Level 0

Level 1

Level 2

(a) Sample topology

0 20 40 60 80 100 120

Node number

time (ms)

Control subcycle

Data subcycle

(b) Packet streams in this network. Notice

the down- and upstream traﬃc

Fig. 2. Communication in CICADA for a sample network of 5 nodes

A cycle is divided in a control subcycle consisting of control slots, and a data

subcycle consisting of data slots. The former is used to broadcast a SCHEME

A Secure Cross-Layer Protocol Multi-hop WBAN 99

message from parent to child, i.e. to let the children know when they are allowed

to send in the data subcycle. In the data subcycle, data is forwarded from the

nodes to the gateway. In each data subcycle, a contention slot is included to allow

nodes to join the tree. New children hear the SCHEME message of the desired

parent and send a JOIN-REQUEST message in the contention slot. When the

parent hears the JOIN-REQUEST message, it will include the node in the next

cycle. Each node will send at least two packets per cycle: a data packet or HELLO

packet (if no data is sent) and a SCHEME packet. If a parent does not receive

a packet from a child for Nor more consecutive cycles, the parent will consider

the child to be lost. If a child does not receive packets from its parent for Nor

more consecutive cycles, the child will assume that the parent is gone and will

try to join another node. An example of communication in CICADA is given in

Fig. 2, for a network of 5 nodes. The control and data subcycles can be seen

clearly.

A node informs its parent node of the number of slots it needs to send its own

data and forward data coming from its children, by calculating two parameters:

αand β. The former gives the number of slots needed for sending data (including

forwarded data) to its parent, the latter gives the number of slots the node has

to wait until it has received all data from its children. Based on the αand β

from its children, a node can calculate the slot allocation for the next cycle.

4.2 CICADA-S

The CICADA protocol, as described in the previous section, does not guaran-

tee any form of security and privacy. Unauthorized nodes can easily join the

WBAN, and all communication in the network is sent in plain text and is not

integrity protected. The ﬁxed identity of the sensors is not kept conﬁdential,

and can hence be used to track sensors (and patients carrying these sensors). To

counter these problems, appropriate security mechanisms have to be added to

the CICADA protocol. The result is the CICADA-S protocol, the secure version

of the CICADA protocol.

From a security point of view, there are four main states which take place dur-

ing the lifetime of a sensor: the secure initialization phase, the sensor (re)joining

the WBAN, a key update procedure in the WBAN, and the sensor leaving the

WBAN. The security mechanisms used in these phases and their integration into

the CICADA-S protocol, based on the results of [6], will now be described.

Secure Initialization Phase: Initially, each sensor has to be securely initial-

ized by the back-end server before it can join the WBAN in a later stage. During

this initialization phase, the sensor and the back-end server will agree on a shared

symmetric key. This can be done via asymmetric cryptographic techniques, but

this is typically too energy (and computation) consuming for a regular sensor.

Another way of establishing a shared key, is by using a private and authen-

tic out-of-band channel. Such a channel is typically cheap to setup. It has the

interesting property that all data transmitted on the channel remains conﬁden-

tial for eavesdroppers, and that the integrity and authenticity is protected too.

100 D. Singel´ee et al.

A private and authentic channel can be created in several ways, depending on

the exact hardware and (physical) characteristics of the sensors. It can be es-

tablished by connecting the sensor directly to the back-end server, via an extra

electrical contact available on both devices. Other techniques to create such a se-

cure out-of-band channel is by employing distance bounding protocols, by having

the user manually enter the data on both devices etc. More information on these

and other techniques to establish a private and authentic out-of-band channel

can be found in the literature [14, 15, 16].

Let us assume that sensor Ahas to be initialized. The data transfer via the

secure out-of-band channel takes place in two steps. First, the sensor sends its

ﬁxed identity to the back-end server. This can be done explicitly or implicitly

(the identity of the sensor can be implicitly known because of the speciﬁc char-

acteristics of the out-of-band channel). In the second step of the protocol, the

back-end server generates a random secret key (kA), and sends this key securely

to the sensor. The sensor and the back-end server store this secret key in their

memory. The key is (conceptually) composed out of 2 subkeys: the encryption

key kAencr and the integrity key kAint. Note that each new node is assigned a

new and unique secret key.

Each sensor iis also assigned a unique counter CTRi,whichis

initialized to 0 and stored in the sensor’s memory. The value of this counter

is included in all key management messages, and is used to avoid replay attacks

and assure freshness. Every time the counter is used, the value gets incremented

by 1.

Sensor (Re)joining the WBAN: After the initialization procedure, the sen-

sor is ready to be put on the patient’s body. It will detect the WBAN, and start

the join procedure, which will now be discussed.

Sensor A Gateway

A || E_kA_encr (CTRA) + MAC_kA_int

Sensor A Gateway

A || E_kA_encr (CTRA) + MAC_kA_int

Fig. 3. Secure JOIN-REQUEST originating from sensor A

When the sensor (with ﬁxed identity A) hears the SCHEME of the desired par-

ent, it sends a secure JOIN-REQUEST message, as shown in Fig. 3, in the con-

tention slot. This message is forwarded to the gateway. It is basically a HELLO

message containing the unique (global) identity of the sensor and the value of

its unique counter CTRA. The counter is encrypted for privacy reasons (since it

is used in all key management messages). The gateway stores (and updates) this

value of the counter. The integrity and authenticity of the entire secure JOIN-

REQUEST message is protected by a message authentication code (MAC )[17],

computed with the key kAint.

When the gateway receives the secure JOIN-REQUEST message of sensor A,

it forwards this request to the back-end server via the secure end-to-end channel.

This triggers a protocol in which the key kAis securely transported from the

A Secure Cross-Layer Protocol Multi-hop WBAN 101

Sensor i Gateway

localIDi|| E_ki_encr (CTRi|| s) + MAC_ki_int

E_ki_encr (CTR’i) + MAC_ki_int

Sensor i Gateway

localIDi|| E_ki_encr (CTRi|| s) + MAC_ki_int

E_ki_encr (CTR’i) + MAC_ki_int

Fig. 4. Secure key transport to all the sensors in the WBAN

back-end server to the gateway. More information on how to accomplish this, can

be found in the ISO 9798–2 standard [18]. In some scenarios, and this is often

the case in a medical environment, it is known in advance (e.g., already during

the initialization procedure) in which WBAN the sensor will be deployed. In this

case, the back-end server can already transport the key kAto the correct gateway,

and does not have to wait until it receives the secure JOIN-REQUEST message.

This makes the join procedure faster. In the case a sensor leaves the network,

and (not much) later rejoins it, the gateway may still have the key kAin its

memory and does not have to forward the request to the back-end server. From

the moment the gateway has access to the key, it can check the validity of the

JOIN-REQUEST by verifying the message authentication code, and in case of a

rejoin, also the value of the counter CTRA(the new value should be higher than

the current value shared by sensor and gateway). If this veriﬁcation is successful,

the sensor is allowed to join the WBAN and is assigned a temporary identity

localID A. This temporary identity, which is chosen by the gateway, is established

in order to preserve the privacy. It is only unique within the environment of the

WBAN. Other networks can reuse the same identiﬁer. Since the bitlength of

such a local identiﬁer can be smaller than the full identity of the sensor (A), it

also improves the eﬃciency. A joining sensor in the WBAN is informed about

its temporary identity during the key transport procedure, which takes place

immediately after the approval of the secure JOIN-REQUEST message.

Key Update Procedure in the WBAN: Except for the key management

messages, the data traveling in the WBAN consists of schemes sent during the

control subcycle, and medical data sent during the data subcycle from the sensors

to the gateway. The former is only integrity protected (to allow a new node

to inform itself about the contention slot), while the latter is both integrity

protected and encrypted. All these operations are performed by employing a

secret group key s, that is shared between all the sensors in the WBAN. Every

time a node joins or leaves the network, the group key is updated in order

to avoid an attacker recovering the key. Even when the topology of the network

remains constant for a long time, the group key should still be updated at regular

intervals. The exact period is determined by the cryptographic strength of the

encryption and integrity algorithms used to protect the data in the WBAN, and

the length of the key. We will brieﬂy come back to this in section. 5.1.

The update process works as follows. First, the gateway randomly generates a

new group key s. Next, it performs a secure key transport procedure with all the

nodes in the WBAN, as shown in Fig. 4. The gateway constructs a key

102 D. Singel´ee et al.

update message, unique for every sensor, which contains the encrypted valueof the

updated group key s. For each node i, the message also contains the new value of

the counter CTRi(which is the current value of the counter incremented by 1),

in order to avoid replay attacks, and the local identiﬁer localIDi. The authentic-

ity and the integrity of the message is protected by a message authentication code.

Nodes that have been excluded from the WBAN, can not decrypt the key transport

messages anymore, and are hence not able to obtain the new group key s.

The key update message is uniquely constructed for every sensor, and for-

warded from the gateway to the correct node during the control subcycle. Each

node takes the message containing its local identiﬁer, checks the validity of the

message (by verifying the value of the counter and the message authentication

code) and decrypts the encrypted part in order to recover the new value of the

group key s. It also forwards all other key update messages to its children, who

perform the same procedure. A new joining node Adoes not yet know its local

identiﬁer localIDA, and therefore has to check the message authentication code

(and the counter) of all the key update messages using its key kAint until the

test succeeds. This only has to be done once, and is easily feasible since com-

puting a message authentication code can be done very eﬃciently. The joining

sensor stores its local identiﬁer localID Ain its memory, and recovers the group

key sfrom the encrypted part of the key update message. Finally, all sensors

send a secure acknowledgement back to the gateway during the next data sub-

cycle, to inform that they received the key well. This key conﬁrmation message

only contains the encrypted value of the updated counter CTRi, concatenated

with a message authentication code. After having received the key conﬁrmation

message, the gateway knows it can deﬁnitively update the group key. When a

node does not send its key conﬁrmation message within a certain period, e.g.,

because it did not receive the new group key sdue to packet loss, the gateway

retransmits the key transport message to that particular node.

Sensor leaving the WBAN: When a node detects that a particular sensor A

is not part anymore of the WBAN, it forwards this information to the gateway.

This automatically triggers a group key update procedure. This has to be done

in order to avoid that an attacker stealing a sensor from the network, would

be able to read or modify the data in the WBAN. After a certain interval (or

even immediately, depending on the policy), the gateway deletes the key kAand

the identiﬁer localID Afrom its memory. If the medical staﬀ removes sensor A

from the patient, or if the sensor is reported lost or stolen, the key kAshould

also be deleted from the memory of the back-end server. This way, the sensor

can not rejoin any network anymore in a later stage, until it has been securely

reinitialized by the back-end server.

5Analysis

5.1 Performance Evaluation

The addition of these security mechanisms to CICADA undoubtedly inﬂuences

the performance as it leads to an increased overhead and higher delay. The

A Secure Cross-Layer Protocol Multi-hop WBAN 103

exact impact strongly depends on the choice of the cryptographic algorithms

that are deployed in the WBAN, and it is hence diﬃcult to formulate results

that are generally applicable. That is why a worst case analysis will be given, in

which we assume that a secure block cipher, such as the Advanced Encryption

Standard (AES) [19], is employed in an authenticated encryption mode (e.g.,

CCM or GCM mode of operation). The numbers used below are based on the

guidelines of the National Institute of Standards and Technology (NIST) [20,21].

In practice, it would be better to employ a low-cost encryption and integrity

algorithm, which has a slightly lower security level, but is more eﬃcient.

The combined encryption and authentication algorithm uses a symmetric key

of 16 bytes (the group key sor the shared key ki). The output of this method

are encrypted blocks of 16 bytes, and a message authentication code of at least

8 bytes. Furthermore, the unique hardware address of the sensor is assumed to

be 6 bytes (e.g., as in Bluetooth), and a counter of 4 bytes is employed to avoid

replay attacks. Note that encrypting the counter results in an encryption block

of 16 bytes. Using these parameters oﬀers a high level of security as long as the

keys are updated regularly, which depends on the strength of the cryptographic

algorithm that is being used. E.g., when AES is used in the GCM mode of

operation, the group key sshould be updated at least at every 232th invocation

of the encryption algorithm [21]. In this section, we will now brieﬂy discuss the

(worst case) impact of the security mechanisms on the CICADA protocol, using

the numbers stated above.

In the (re)joining phase, additional information is sent to the gateway in

the JOIN-REQUEST message. The original CICADA-message only contains

localID Aand localID P(i.e. the local ID of node Ajoining the network and

the local ID of the desired parent Prespectively). The length of these IDs is 1

byte, which is suﬃcient for a WBAN. In CICADA-S the unique hardware address

of the sensor is sent, together with the encrypted synchronized counter and a

message authentication code. The length of the JOIN-REQUEST message thus

is longer, but still only 30 bytes. As this information is sent in a contention slot

with ﬁxed size, this will not inﬂuence the throughput of the system. However,

this secure JOIN-REQUEST message needs to be forwarded to the gateway. As

the contention slot of a node is in the beginning of a data subcycle, the message

can be sent to the gateway directly. E.g., the JOIN-REQUEST message can be

piggybacked on a data packet that is sent to the gateway. As the length of the

message is small, this may not inﬂuence the overall throughput signiﬁcantly.

The number of bytes that can be sent in one slot depends on the size of the slot

and the raw bit rate of the radio technology used. If the number of bytes in the

data packet and the secure JOIN-REQUEST message is too large, the slot size

will have to be altered. This will lower the throughput of the network. A better

solution is to send the JOIN-REQUEST message in a separate data slot. This

will hardly impact the throughput of the network. If the key is already present

at the gateway, the gateway can immediately start the key update procedure. If

not, the gateway has to wait for a response from the back-end server. This will

add extra delay to the joining procedure.

104 D. Singel´ee et al.

In the key update procedure, the gateway sends a new key to all the nodes

in the control subcycle. This message contains localID A, the new key group

key sconcatenated with an increased counter (both encrypted), and a message

authentication code. For each node, this is an additional 41 bytes. Due to the

broadcast mechanism in the control subcycle, these messages all need to be

broadcasted by every node sending its SCHEME in the control subcycle. This

will lead to a larger slot length in the control subcycle, and subsequently a lower

throughput. In CICADA, the slot length in the control subcycle is smaller than

the data slot length as the SCHEME-messages sent in the control subcycle are

very short. The slot length can be up to ten times smaller. This improves the

energy throughput of CICADA. As the key is only updated after several cycles,

we opt to change the control slot dynamically. When the key is updated, the

control slot length has the same length as the data slot. At any other time,

the control slot has its shorter length. When the key is about to be updated,

the gateway broadcasts a warning in the previous cycle by setting a bit in the

header. The nodes receive this warning and adapt their control slot lengths for

one cycle.

When a node leaves the network or is no longer attached to it, the (former)

parent node sends a message to the gateway. This can be added to a data packet

and will not inﬂuence the throughput.

It is very important to note that the key management messages are sent

rarely (only when a node (re)joins the network, or when the group key has to

be updated), and hardly aﬀect the global throughput in the network. Most data

traveling in the WBAN is medical data, sent by the sensors to the gateway. These

messages are protected by employing the group key s. The data is encrypted

in blocks of 16 bytes, and a message authentication code of 8 bytes is added.

The SCHEME packets sent during the control subcycle are not encrypted, but

integrity protected. For both types of data, the length of the messages is hardly

inﬂuenced. Overall, the security mechanisms will have a minor impact on the

performance of CICADA-S.

5.2 Security Properties

One of the design goals of the CICADA-S protocol is to secure the wireless

communication in the WBAN while preserving privacy. The most interesting

security properties of our protocol will now be brieﬂy discussed (without formal

proof). It has to be stressed that the following statements are based on the

assumptions stated in section 3.2, and that all devices in the network, including

the attacker, are computationally bounded.

–The CICADA-S protocol provides forward security. A node that leaves the

network can not successfully read/modify/insert/delete data in the WBAN,

since the group key sis always updated in case the topology of the network

changes.

–Nodes that are not securely initialized, can not join the WBAN. Only nodes

that share a symmetric key with the back-end server, can construct a valid

secure JOIN-REQUEST message, which is needed to join the WBAN.

A Secure Cross-Layer Protocol Multi-hop WBAN 105

–Since the group key is transported in an encrypted format from the gateway

to the nodes in the WBAN, it is practically not feasible for an eavesdropper

to recover the key. Only an attacker that can break the encryption scheme

used to protect data in the WBAN, is able to ﬁnd the group key s.

–The CICADA-S protocol oﬀers key conﬁrmation, which is important for se-

curity and performance reasons. After receiving the new group key s, a node

sends a key conﬁrmation message to the gateway, to inform that the key was

received well. This avoids certain Denial-of-Service attacks (e.g., blocking

key update messages). Due to packet loss and bit errors, key conﬁrmation is

also an important and necessary property of network protocols for wireless

media.

–A sensor that is a member of a WBAN can not join another WBAN at the

same time. The second secure JOIN-REQUEST message sent by the sensor

will be refused by the back-end server, because this device will detect that

the sensor already belongs to another network.

–Nodes that are part of a particular WBAN, are not able to read, modify,

insert or delete encrypted data in other WBANs without this being detected,

since these other networks do not share the same group key s.

–Since the conﬁdentiality and integrity of data traveling in the WBAN is

cryptographically protected, a device that does not possess the group key

will not succeed in decrypting the enciphered communication, nor success-

fully modifying/inserting/deleting data into the network without this being

detected.

–Replay attacks are detected because of the use of the synchronized counter,

that is shared between sensor and gateway.

–Location privacy has been taken into account during the design of the

CICADA-S protocol. The communication between gateway and back-end

server is assumed to be completely secured (end-to-end) and anonymized.

Using the data in the WBAN to trace a patient is not possible, because it

only contains local identiﬁers, and these are not unique across WBANs. Only

in the ﬁrst message of the join procedure, the exact identity of the sensor

is exposed. It is however not used in the other key management messages.

Neither is it possible to link other messages to the initial key management

message of the join procedure (since the synchronized counter is encrypted).

As a result, the data in the WBAN can not be used to trace patients.

6Conclusion

Wireless Body Area Networks are an enabling technology for mobile health care.

These systems reduce the enormous costs associated to patients in hospitals as

monitoring can take place even at home in real-time and over a longer period.

A critical factor in the acceptance of WBANs is the provision of appropriate

security and privacy protection of the wireless communication medium. The data

traveling between the sensors should be kept conﬁdential and integrity protected.

Certainly in the mobile monitoring scenario, this is of uttermost importance.

106 D. Singel´ee et al.

InthispaperwehavepresentedCICADA-S, a security enabled cross-layer

multi-hop protocol for Wireless Body Area Networks. It is a secure extension of

the CICADA protocol, and was designed within the scope of the IM3-project

(Interactive Mobile Medical Monitoring), which focuses on the research and im-

plementation of a wearable system for health monitoring. The CICADA-S proto-

col is the ﬁrst integrated solution to cope with the threats of interactive mobile

monitoring and the life cycle of the sensors. It combines key management and se-

cure privacy preserving communication techniques. We have presented the main

security properties of CICADA-S, and shown that the addition of security mech-

anisms to the CICADA-S protocol has low impact on the power consumption

and throughput. The security mechanisms integrated in the protocol are sim-

ple, yet very eﬀective. The CICADA-S protocol can be implemented on today’s

devices as it only requires low-cost and minimal hardware changes.

The authors strongly believe that adding suﬃcient security mechanisms to

Wireless Body Area Networks will work as a trigger in the acceptance of this

technology for health care purposes.

Acknowledgments. This work is partially funded by a research grant of the

Katholieke Universiteit Leuven for D. Singel´ee, by the Concerted Research Ac-

tion (GOA) Ambiorics 2005/11 of the Flemish Government, by the IAP Pro-

gramme P6/26 BCRYPT of the Belgian State (Belgian Science Policy), by the

Fund for Scientiﬁc Research — Flanders (F.W.O.-V.,Belgium) project G.0531.05

(FWO-BAN) and by the Flemish IBBT project IM3.

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Communication in Random Geometric Radio

Networks with Positively Correlated Random

Fault s

Evangelos Kranakis1, Michel Paquette1, and Andrzej Pelc2

1School of Computer Science, Carleton University, Ottawa, Ontario,

K1S 5B6, Canada

kranakis@scs.carleton.ca, michel.paquette@polymtl.ca

2D´epartement d’informatique et d’ing´enierie, Universit´eduQu´ebec en Outaouais

Gatineau, Qu´ebec, J8X 3X7, Canada

pelc@uqo.ca

Abstract. We study the feasibility and time of communication in ran-

dom geometric radio networks, where nodes fail randomly with positive

correlation. We consider a set of radio stations with the same commu-

nication range, distributed in a random uniform way on a unit square

region. In order to capture fault dependencies, we introduce the ranged

spot model in which damaging events, called spots, occur randomly and

independently on the region, causing faults in all nodes located within

distance sfrom them. Node faults within distance 2sbecome dependent

in this model and are positively correlated. We investigate the impact

of the spot arrival rate on the feasibility and the time of communication

in the fault-free part of the network. We provide an algorithm which

broadcasts correctly with probability 1 −in faulty random geometric

radio networks of diameter Din time O(D+log1/).

Keywords: Fault-tolerance, dependent faults, broadcast, crash faults,

random, geometric radio network.

1 Introduction

Wireless networks have received much attention in recent years because of ap-

plications where wired networks are impractical or impossible to deploy. These

networks are now so common that the idea of large scale wireless networks has

become natural. However, as they grow in size, complexity, and area, wireless

networks become increasingly vulnerable to component failures and damaging

environmental phenomena. Nodes of a network may fail and the communication

medium may become too noisy to support correct message transmissions. These

failures often result in delaying, blocking, or even distorting transmitted mes-

sages. Hence, it becomes important that the desired tasks may be accomplished

eﬃciently in spite of these faults, usually without knowing their location ahead

of time. Networks with this property are called fault-tolerant.

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 108–121, 2008.

Springer-Verlag Berlin Heidelberg 2008

Communication in Random Geometric Radio Networks 109

An important type of wireless network is obtained from a set of stations in the

plane where each station uhas communication range ru. The resulting network

is modeled as a directed graph in which stations are nodes and a directed edge

from uto vexists if vis at distance at most rufrom u. Such networks are called

geometric radio networks (GRN).

One of the most important communication tasks is broadcasting. In this pro-

cess, a source node attempts to transmit a message to all other nodes of the

network. This process is successful if, upon termination, all functional nodes,

connected to the source by a fault-free path, have received the source message.

Although the question of fault-tolerant broadcasting has been widely studied for

faulty point-to-point networks, few results are known about this process in geo-

metric radio networks. To the best of our knowledge, all existing analytic results

examine the general problem of broadcasting in networks where the number of

faults is bounded above (cf., e.g., [8]), or faults are distributed randomly and

independently (cf., e.g., [9,14]). Hence, the present paper is the ﬁrst to address

the problem of broadcasting in GRNs in the presence of positively correlated

faults.

1.1 Model and Problem Deﬁnitions

We seek to model a network composed of mobile stations moving under the

Random Waypoint mobility model [7] inside an open region, e.g., a train station

or a plaza. Under this mobility model, mobile stations alternately move and

pause for random amounts of time, choosing a direction, distance and speed at

random at every movement phase. Here, we assume that the mobile stations move

at low, pedestrian-like speeds, making the network appear static for the short

duration of communication processes; the distance and directions are chosen

in some uniform way. We further assume that neither the boundaries of the

open region nor the other mobile stations have any eﬀect on the mobile station

movements. Hence, any snapshot of the graph is a set of stations distributed on

a plane by a Poisson process. Due to the short duration of the communication

processes, we consider that the faults are permanent. The proposed static model

also applies to networks of sensors spread randomly in hostile environments

where individual placement and replacement of units is not possible.

We focus attention on a unit square region of the plane. Node locations occur

with Poisson arrival rate n.Weﬁxaparameterr, called the communication

range. Any two nodes at Euclidean distance at most rfrom one another can

communicate directly. We now deﬁne the ranged spot fault model. Damaging

phenomena, called spots, occur on the plane with Poisson arrival rate λ.Some

examples of damaging phenomena are lightning strikes (and other electrostatic

discharges), electromagnetic pulses and explosions. We ﬁx a parameter s>0,

called the spot range. Each spot causes permanent crash faults in all nodes

within distance sof it, i.e., inside the disk of radius scentered at it, which we

call the spot disk.Foraﬁxedspoti, we denote the corresponding spot disk by Di.

Faulty nodes can neither send nor receive messages for the entire communication

process. More formally, consider the undirected fault-free graph G(V,E), where

110 E. Kranakis, M. Paquette, and A. Pelc

Vis the random set of nodes occurring on the unit square with Poisson arrival

rate n,andEis the set of all node pairs {u, v}for which the Euclidean distance

is at most r.LetSbe the set of spots which occur on the unit square with

Poisson arrival rate λ.LetFbe the set of faulty nodes, i.e., all the nodes in

Vwhose location is within distance sfrom at least one spot in S.Weconsider

the graph G[V] induced on Gby the set V=V\Fof all functional nodes.

To remind the reader how it is built, throughout this paper, we will denote the

graph G[V]byU(n, r, λ, s).

As usual in wireless network algorithms, communication in U(n, r, λ, s)is

assumed synchronous; nodes have synchronized clocks and the communication

process is executed in ﬁxed time steps, called rounds. All communication is

done using the same base frequency, modulation and encoding, hence using a

single channel. In each round, each node either sends a message or listens to

the channel. In the ﬁrst case, we say that the node is a sender, otherwise, it

is a receiver. In a ﬁxed round t, a node vreceives a message if and only if it

is a receiver and precisely one of its neighbors is a sender. If no neighbor of

vis a sender, then there is no message on the channel which vcan receive. If

more than one neighbor of vsends a message, we say that a collision occurs

at vand vcan only perceive noise on the channel. Nodes do not have collision

detection abilities, i.e., they cannot distinguish collision noise from background

noise (which is apparent when no messages are heard).

We say that an event occurs in the graph with high probability (w.h.p.) if

its probability converges to 1 as the node arrival rate ngrows to inﬁnity. We

say that an event occurs on the graph with constant (positive) probability if its

probability pis bounded away from 0 and from 1 as ngrows to inﬁnity, i.e.,

if there exist positive constants 1,

2such that 0 <

1<p<

2<1 for all

n. Speciﬁcally, we say that a graph is connected w.h.p. when the event that

it is connected occurs w.h.p. On the other hand, we say that a graph is not

connected w.h.p. when the event that it is disconnected occurs at least with

constant probability.

In this paper, we study the question of feasibility and eﬃciency of communi-

cation in the fault-free graph U(n, r, λ, s).

1.2 Our Results

We ﬁrst give answers to the question for which parameters s=s(n)andλ=

λ(n, s) there exist any fault-free nodes in the unit square, i.e., when the fault-free

graph U(n, r, λ, s) is non-empty, w.h.p. For s∈o(1), we ﬁnd a threshold function

l(n, s) and constants L1,L

2such that, for λ≥L1·l(n, s) fault-free nodes do not

exist, w.h.p., while for λ≤L2·l(n, s) they do exist w.h.p. For s∈Ω(1), we show

that, for λ∈ω(1/s2) fault-free nodes do not exist, w.h.p., and for λ∈o(1/s2)

they do exist, w.h.p.

We then give answers to the question for which parameters s=s(n), r=r(n)

and λ=λ(n, s, r), the fault-free graph U(n, r, λ, s) is connected, w.h.p. Connec-

tivity is equivalent to feasibility of communication in our setting. We restrict

attention to the case of small spot range, more precisely, we work under the

Communication in Random Geometric Radio Networks 111

assumption s∈o(r). In the case r∈o(1), we ﬁnd a threshold function c(n, s, r)

and constants C1,C

2such that, for λ≥C1·c(n, s, r) the graph U(n, r, λ, s)isnot

connected w.h.p., and for λ≤C2·c(n, s, r) it is connected, w.h.p. Then, in the

case r∈Ω(1), and for λ∈o(1/s2), we show that for the values of λfor which the

graph U(n, r, λ, s) contains at least one node w.h.p., it is also connected w.h.p.

Finally, under the additional restriction on spot range, when s∈o(1/√n), we

show an algorithm which accomplishes broadcast with probability at least 1 −

in time O(D+log1/) in the graph U(n, r, λ, s)ofdiameterD.

Due to lack of space, the proofs of several lemmas and theorems are omitted.

1.3 Related Work

The fundamental questions of network reliability have received much attention

in the context of point-to-point networks, under the assumption that compo-

nents fail randomly and independently (cf., e.g. [1,2,3,11] and the survey [12]).

On the other hand, empirical work has shown that positive correlation of faults

is a more reasonable assumption for networks [6,15,16]. In particular, in [16], the

authors provide empirical evidence that data packets losses are spatially cor-

related in networks. Moreover, in [6], the authors simulate failures in a sensor

network using a model similar to that of the present paper; according to these au-

thors, the environment provides many spatially correlated phenomena resulting

in such fault patterns. More recently, in [10], a gap was demonstrated between

the fault-tolerance of networks when faults occur independently as opposed to

when they occur with positive correlation. To the best of our knowledge, this

was the ﬁrst paper to provide analytic results concerning network fault-tolerant

communication in the presence of positively correlated faults.

In contrast, few results are known about fault-tolerant communication in geo-

metric radio networks. To the best of our knowledge, all existing analytic results

examine the problem of broadcasting in networks where, either the number of

faults is bounded above (cf., e.g., [8]), or faults occur randomly and indepen-

dently (cf., e.g., [9,14]). In particular, in [14], the authors consider the problem

of connectivity of a square grid of nsensors with communication range ron a

unit square when faults occur at the nodes randomly and independently with

probability 1−p. They show that if pr2≈log n

n, then the functional nodes are all

part of a connected component w.h.p. In [8], the authors consider the problem

of broadcasting in a fault-free connected component of a radio network whose

nodes are located at grid points of square grids and can communicate within a

square of size r. For an upper bound ton the number of faulty nodes, in worst-

case location, the authors propose a Θ(D+t)-time oblivious broadcast algorithm

and a Θ(D+ log(min(r, t)))-time adaptive broadcast algorithm, both operating

on a connected fault-free component of diameter D.

The question of communication in networks of unknown topology has been

widely studied in recent years. In fact, in [4], the authors state that broadcast-

ing algorithms which function in unknown GRNs also function in the resulting

fault-free connected components of faulty GRNs. A basic performance evalua-

tion criterion of broadcasting algorithms is the time necessary for the algorithm

112 E. Kranakis, M. Paquette, and A. Pelc

to terminate; in synchronous networks, this time is measured as the number

of communication rounds. For networks whose fault-free part has a diameter

D,Ω(D) is a trivial lower bound on broadcast time, but optimal running time

is a function of the information available to the algorithms (cf., e.g., [5]). For

instance, in [5], an algorithm was obtained which accomplishes broadcast in

arbitrary GRNs in time O(D) under the assumption that nodes have a large

amount of knowledge about the network, i.e. given that all nodes have a knowl-

edge radius larger than R, the largest communication radius. The authors also

show that algorithms broadcasting in time O(D+logn) are asymptotically op-

timal, for unknown GRNs when nodes can communicate spontaneously (before

receiving the source message) and either can detect collisions or have knowledge

of node locations at some positive distance δ, arbitrarily small. In the present

paper, we assume that nodes communicate spontaneously, but know nothing of

the network, other than their own location, and cannot detect collisions. Under

these assumptions, we show an O(D+log1/)-time algorithm which correctly

broadcasts in the random graph U(n, r, λ, s) with probability at least 1 −.

2 Liveness of the Graph

In this section, we show bounds on the spot arrival rate λfor which functional

nodes exist in the unit square, i.e., the graph U(n, r, λ, s)containsatleast

one node, w.h.p. We say that the graph U(n, r, λ, s)isalive if it contains at

least one node; otherwise, we say that it is dead.

Theorem 1. For s∈o(1), there exist two positive constants, L1and L2,such

that if the spot arrival rate λ≥L1ln(min{n,1/s2})

s2, then the graph U(n, r, λ, s)is

dead, w.h.p., and if λ≤L2ln(min{n,1/s2})

s2,thenU(n, r, λ, s)is alive, w.h.p.

Theorem 2. For s∈Ω(1), the graph U(n, r, λ, s)is dead w.h.p. if λ∈ω(1/s2)

and alive w.h.p. if λ∈o(1/s2).

Remark 1. Fo r s∈o(1/√n)andλ=ln(cn)

πs2,wherecis a positive constant, the

graph U(n, r, λ, s) is dead with constant probability.

3 Connectivity of U(n, r, λ, s)

In the preceding section, we gave a threshold for the spot arrival rate for which

the graph U(n, r, λ, s) is non-empty w.h.p. We now answer the next natural

question: for which spot arrival rate is the graph U(n, r, λ, s) connected w.h.p.?

It has been shown, in [13], that for any real number c,ifr≥ln n+c

πn ,then

the probability that the graph U(n, r, λ, s), with λ= 0, is connected is at least

e−e−c,asn→∞. If we substitute e−c=f(n), assume that f(n)∈o(1) and

recall that e−f(n)=1−f(n)+f(n)2/2−...≥1−f(n), then we see that if

r≥ln n+ln1/f(n)

πn

Communication in Random Geometric Radio Networks 113

then

Pr[U(n, r, 0,s) is connected] ≥1−f(n).

Hence, it is natural to investigate the connectivity of the graph U(n, r, λ, s)

under the assumption r2≥ln n+ln 1/f (n)

πn ,forsomef(n)∈o(1), when we know

that connectivity is guaranteed w.h.p. without faults. In what follows we make

this assumption.

The main results of this section are Theorems 3 and 4. In Theorem 3, for spot

range sof lower order of magnitude than the communication range rand for

r∈o(1), we show a threshold for the spot arrival rate λbelow which the graph

U(n, r, λ, s) is connected w.h.p. and above which it is not. For the case r∈Ω(1),

the separation is diﬀerent: in Theorem 4, we show thresholds for the spot arrival

rate λbelow which the graph U(n, r, λ, s) is connected w.h.p. and above which

it is dead w.h.p.

Theorem 3. For s∈o(r)and r∈o(1), there exist two positive constants, C1

and C2, such that if spots appear with arrival rate λ≥C1ln r2min{n,1/s2}

ln(1/r2)/s2,

then the graph U(n, r, λ, s)is not connected w.h.p., and if the spot arrival rate

λ≤C2ln r2min{n,1/s2}

ln(1/r2)/s2, then the graph U(n, r, λ, s)is connected, w.h.p.

Theorem 3 will follow from Lemmas 2, 3, 4, and 5.

Theorem 4. For s∈o(r)and r∈Ω(1),

1. if s∈o(1), then there exist two positive constants, C3and C4, such that

(a) for λ≤C3ln(min{n, 1/s2})/s2,U(n, r, λ, s)is connected, w.h.p.,

(b) for λ≥C4ln(min{n, 1/s2})/s2, the graph U(n, r, λ, s)is dead w.h.p.,

2. if s∈Ω(1),then

(a) for λ∈o(1/s2), the graph U(n, r, λ, s)is connected, w.h.p.

(b) for λ∈ω(1/s2), the graph U(n, r, λ, s)is dead w.h.p.,

Theorem 4 will follow from Theorems 1 and 2 and from Lemmas 6 and 7.

3.1 Non-connectivity Results

In this section, we show conditions on spot arrival rate implying, w.h.p., non-

connectivity of the graph U(n, r, λ, s) by the existence of two functional nodes

which cannot communicate with one another in the unit square.

Denote by Pleft and Pright the two rectangular halves of the unit square.

Partition Pleft and Pright respectively into meshes of r×rsquares. Group these

squares in matrices of 5×5 squares, called blocks; let Blef t and Bright be the sets

of these blocks. For each block b,denotebycbthe central square in this block

and by pbthe union of 8 squares adjacent to cb.Letalivebbe the event that cb

contains at least one functional node. Let surroundbbe the event that pbcontains

no functional node. Let isolationbbe the intersection of events surroundband

aliveb.Ifisolationboccurs, and there is at least one functional node outside

b,thennodesincbhave no functional path to this external functional node,

114 E. Kranakis, M. Paquette, and A. Pelc

and then, the graph U(n, r, λ, s) is disconnected. In particular, we show non-

connectivity w.h.p. by proving that events isolationb1and isolationb2,b1∈B

left

and b2∈B

right, occur w.h.p. Note that, for distinct blocks b1and b2,events

surroundb1and surroundb2are independent.

We ﬁrst examine non-connectivity in the case when r∈o(1) and s∈o(1/√n),

in Lemma 2. Non-connectivity for r∈o(1) and for larger values of s∈o(r) will

be addressed in Lemma 3. The case s∈Ω(1) is treated in the next section.

We show that for these values of r, the graph is connected w.h.p. for those spot

arrival rates for which it is alive w.h.p.

Let Fvbe the event that a ﬁxed node vis faulty, i.e., that there exists at least

one spot within distance sof it. Then, for spot arrival rate λwe have

Pr[Fv]=1−e−λπs2.

While distant faults are independent, the presence of a faulty node within dis-

tance 2sfrom a ﬁxed node vimplies that there is a spot which might be close

enough to vto make it faulty, i.e., the occurrence of a fault at a node can

never decrease the probability of a fault on another node. This is why faults are

positively correlated. Hence, the following fact applies to the events Fv.

Fact 1 . For any set Zof nodes,

Pr[ 

v∈Z

Fv]≥

v∈Z

Pr[Fv].

AsetSof nodes whose elements have a distance greater than 2sfrom one

another is called sparse. Such a set has the property that the events Fv,for

v∈S, are independent. The following lemma states that there exist large sparse

sets, w.h.p.

Lemma 1. AsquareAwith area |A|contains a sparse set Sof size at least

k|A|min{n, 1/s2}, for some positive constant k, w.h.p., if |A|min{n, 1/s2}→∞

as n→∞.

Lemma 2. Fix any constants α>8and β>1.Fors∈o(1/√n)and r∈o(1),

the graph U(n, r, λ, s)is not connected w.h.p. when λ=βln αnr2

ln(1/r2)/πs2.

Proof. Consider f(n)∈ω(1) and the set Λof spot arrival rates of the form

λ=ln

αr2n

ln(1/(r2f(n))) /(πs2). Consider two subsets of Λ:Λ1consisting of these

λof the form λ=ln(g(n)r2n)/(πs2), with g(n)∈O(1) and Λ2consisting of

these λof the same form with g(n)∈Ω(1). In each case, we show that there

exists at least one occurrence of the event isolationbin each set Blef t and Bright

and thus, that the graph U(n, r, λ, s) is disconnected.

Case 1: λ=ln(g(n)r2n)/(πs2), with g(n)∈O(1)

Fix a block band consider the event aliveb. Consider the subsquare c

b⊂cb

whose points are at distance greater than 2sfrom pb, i.e. for which the contained

Communication in Random Geometric Radio Networks 115

nodes become faulty independently from nodes in pb.Fors/r →0asn→∞,

|c

b|>0.9r2,forlargen. From Lemma 1, since 0.9nr2>0.9logn∈ω(1), it

follows that, w.h.p., there is a sparse set of nodes Sb,inc

b,ofsizeatleastknr2,

for some positive constant k.EventsFv,v∈Sb, occur independently. Let A

be the event that the above lower bound on the size of the sparse set Sbholds.

Assume A. Then,

Pr[aliveb]=1−Pr[∀v∈cbFv]≥1−Pr[∀v∈c

bFv]

≥1−Pr[∀v∈SbFv]≥1−(Pr[Fv])knr2=1−(1 −e−λπs2)knr2

=1−(1 −e−ln(g(n)r2n))knr2

=1−(1 −1/g(n)r2n)knr2≥c∈Θ(1)

since g(n)∈O(1). Since Pr[A]→1forlargen, this implies that the probability

of event alivebis at least a positive constant c.LetAleft be the set of all blocks

bin Bleft for which the event aliveboccurs. Since the probability of the event

alivebis a constant, the expected size of the set Aleft is a constant fraction of

grows to inﬁnity as n→∞and thus, under the preceding assumptions, we use

Chernoﬀ bounds to show that |Alef t|≥(0.9)c/(50r2) w.h.p. Assume this bound

on |Aleft |and let k/r2=(0.9)c/(50r2) for the remainder of the proof.

Fix a block band consider the event surroundb. Using Chernoﬀ Bounds

adapted to Poisson distributions, we can show that, w.h.p., at most αnr2nodes

are in pb;letEbe the event that this bound holds. Assume E. Then, we have,

by Fact 1,

Pr[surroundb]=Pr[

v∈pb

Fv]≥

v∈pb

Pr[Fv]≥(1 −e−λπs2)αnr2

and since Pr[E]→1forlargen,wehavePr[surroundb]≥(0.9)(1 −e−λπs2)αnr2,

for large n. Then, the probability that there exists a block b∈B

left for which

event isolationboccurs is

Pr[∃b∈B

left isolationb]=Pr[∃b∈A

left surroundb]

=1−Pr[∀b∈A

left ¬surroundb]

=1−(Pr[¬surroundb])|Alef t |

≥1−1−(0.9) 1−ln(1/(r2f(n)))

αr2nαr2nk/r2

=1−(1 −(0.9)r2f(n))k/r2→1asn→∞.

The same calculations apply to the second half of the unit square, thus showing

the occurrence of at least 2 events isolationbw.h.p. This concludes the argument

in the ﬁrst case.

116 E. Kranakis, M. Paquette, and A. Pelc

Case 2: λ=ln(g(n)r2n)/(πs2), with g(n)∈Ω(1)

Consider again the event surroundb.Forλ=ln(g(n)r2n)/(πs2), with g(n)∈

Ω(1), the same argument as in case 1 implies

Pr[surroundb]≥(0.9)(1 −e−λπs2)αnr2=(0.9)(1 −1/(g(n)r2n))αnr2

≥c∈Θ(1).

Let Sleft be the set of all blocks in Bleft for which the event surroundboccurs.

Since the probability of surroundbis constant, the expected size of the set Slef t

is a constant fraction of |Bleft|. The number of blocks in Bleft is |Blef t |=1/50r2.

For r∈o(1), |Blef t|grows to inﬁnity as n→∞and thus, under the preceding

assumptions, we use Chernoﬀ bounds to show that |Sleft |≥(0.9)c/(50r2) w.h.p.

Assume this bound on |Slef t |and let k/r2=(0.9)c/(50r2) for the remainder of

the proof.

From Remark 1, if the spot arrival rate is λ=ln(nh(n))/(πs2), h(n)∈Ω(1),

we ﬁnd a positive constant probability that the graph U(n, r, λ, s) is dead. Hence,

consider the subset of spot arrival rates of the form λ=ln(nh(n))/(πs2), h(n)∈

o(1). Then, for these values of λ, the probability that there exists a block b∈B

left

for which event isolationboccurs is

Pr[∃b∈B

left isolationb]=Pr[∃b∈S

left aliveb]=1−Pr[∀b∈S

left ¬aliveb]

=1−(Pr[¬aliveb])|Sleft |

≥1−(1 −(1 −(1 −e−λπs2)knr2))k/r2

=1−((1 −e−ln(nh(n)))knr2)k/r2

=1−(1 −1/(nh(n)))kkn →1asn→∞.

The same calculations apply to the second half of the unit square, thus showing

the occurrence of at least 2 events isolationbw.h.p. This concludes the argument

in the second case.

To conclude the proof, ﬁx the function f(n)=1/r.Sincer∈o(1), we

have f(n)∈ω(1). Hence the corresponding ˜

λ=ln

αr2n

ln(1/(r2f(n))) /(πs2)=

ln αr2n

ln(1/r)/(πs2)isinΛ. We show that ˜

λ<βln αr2n

ln(1/r2)/(πs2), for any con-

stant β>1. Indeed,

λ=lnαr2n

ln(1/r)/(πs2)=lnαr2n

0.5ln(1/r2)/(πs2)

=ln αr2n

ln(1/r2)+ln2

/(πs2)≤βln αr2n

ln(1/r2)/(πs2).

It follows that all λ=βln αr2n

ln(1/r2)/(πs2), for any constant β>1, are also in

Λwhich proves the lemma. Note that, under the assumption s∈o(1/√n)), we

have min{n, 1/s2}=n.

The proof of Lemma 3 diﬀers from the proof of Lemma 2 only in the use of a

partition to obtain the probability of the event surroundb.

Communication in Random Geometric Radio Networks 117

Lemma 3. Fix any constant β>1.Fors∈o(r)and r∈o(1), the graph

U(n, r, λ, s)is disconnected w.h.p. when λ=4βln 8r2/s2

ln(1/r2)/πs2.

The preceding lemmas concern only the case when r∈o(1). As stated in Theo-

rem 4, for r∈Ω(1), thresholds on spot arrival rate separate the case of connected

U(n, r, λ, s) from the case when it is dead. Hence, we do not provide any non-

connectivity result for r∈Ω(1) and defer this case to the next section.

3.2 Connectivity Results

In this section, we show conditions on spot arrival rate guaranteeing connectivity

of the graph U(n, r, λ, s) w.h.p. We show connectivity of U(n, r, λ, s)byproving

the existence of a fault-free node in each square of a suﬃciently ﬁne partition

of the unit square w.h.p. This implies the existence of a fault-free path between

any pair of nodes of the graph U(n, r, λ, s) and hence this graph is connected.

Partition the unit square into a mesh of r/√5×r/√5 squares, called blocks.

Let Bbe the set of all blocks. The distance between any two points in blocks

which are adjacent by an edge (edge-adjacent) is at most r. Hence, functional

nodes in adjacent blocks can communicate with each other.

Partition each block b∈Binto a mesh of 3s×3ssquares called tiles. Let

Tbbe the set of all these r2/(45s2) tiles for the block b. For a ﬁxed tile t∈Tb,

let freetbe the event that it contains no spot. Under the event freet,the

central s×ssquare ct⊂tis at distance greater than sfrom all spots. Let at

be the event that ctcontains at least one node. Since node arrivals and spot

arrivals are independent, the events freetand atare independent. Moreover, for

all t=s∈Tb, the events at,a

s(freet,free

s) are independent since they are

respectively the result of arrivals inside non-overlapping tiles tand s.

Consider the event alivebthat a ﬁxed block bcontains at least one functional

node. The event alivebis implied by the existence of a tile t∈Tbwhere both

the events freetand atoccur. Let alive

b={∃t∈Tbs.t. freet∩at}be this

sub-event of aliveb. Hence, the probability of event alivebthat a ﬁxed block b

contains at least one functional node is

Pr[aliveb]≥Pr[alive

b]=Pr[∃t∈Tbfreet∩at]=1−Pr[∀t∈Tb¬freet∪¬at]

=1−(Pr[¬freet∪¬at])|Tb|=1−(1 −Pr[freet∩at])|Tb|

=1−(1 −Pr[freet]Pr[at])|Tb|=1−(1 −e−λ9s2(1 −e−ns2))r2/(45s2).

Let connect be the event that each block bin Bcontains at least one functional

node. We have Pr[connect]≥Pr[∀b∈Balive

b]. The next two lemmas are easily

derived from the above estimates.

Lemma 4. For s∈o(1/√n)and any constant α<1, the graph U(n, r, λ, s)is

connected, w.h.p., when the spot arrival rate is λ=αln nr2

45 ln(1/r2)/9s2.

Lemma 5. For s∈Ω(1/√n)∩o(r)and any constant α<1,U(n, r, λ, s)is

connected, w.h.p., when the spot arrival rate is λ=αln r2/s2

45 ln(1/r2)/9s2.

118 E. Kranakis, M. Paquette, and A. Pelc

For large values of r, we show connectivity for the same range of λfor which we

have shown the graph U(n, r, λ, s) to be alive w.h.p.

Lemma 6. For r∈Ω(1) and s∈o(1), the graph U(n, r, λ, s)is connected,

w.h.p., when the spot arrival rate is λ=αln(min{n,1/s2})

πs2, for any constant α<1.

For r∈Ω(1) and s∈Ω(1) ∩o(r), we observe that if r∈Θ(1), then the condition

s∈o(r) is impossible. Hence, necessarily, r∈ω(1). Since the unit square has a

diameter of √2, if it is alive, then it is also connected for r∈ω(1) and suﬃciently

large n. Hence Lemma 7 follows from Theorem 2.

Lemma 7. For r∈ω(1) and s∈Ω(1)∩o(r), the graph U(n, r, λ, s)is connected,

w.h.p., when the spot arrival rate is λ∈o(1/s2).

4 Broadcasting Algorithm

We propose a deterministic algorithm which completes broadcast with prob-

ability 1 −in time O(D+log1/), in the fault-free graph U(n, r, λ, s)for

s∈o(1/√n). The algorithm consists of two parts: a preprocessing part called

spokesman election, and a message transmission part. In the spokesman election

part a unique node, called the spokesman, is selected in each square of a partition

deﬁned below. Only the spokesman of a square relays messages in the following

part.

Partition the unit square into a mesh of r/√5×r/√5 squares called boxes

and let Sbe the set of these boxes. Group the boxes in 5 ×5 matrices, called

blocks and let Bbe the set of all these blocks. For all blocks, label its boxes 1

through 25, row by row. Further partition each box into a mesh of 1/√n×1/√n

squares, called tiles. Let Tibe the set of all tiles in a box i.Forallboxes,label

the tiles 1 through t=r2n/5, row by row.

Algorithm A∗

Spokesman Election Part

Nodes know their location and hence, they can compute the labels i, j of their

box, and tile, respectively. Nodes label themselves (i, j) accordingly.

In parallel for all blocks, the algorithm executes rounds i=1,2,...,25. In a

round i, the algorithm sequentially goes through steps j=1,2,...,t. In a round

i,atstepj, all nodes with label (i, j )(inboxiand tile j) transmit their label

and the list of labels heard from adjacent boxes. At any given step j, when only

one node transmits its label (i, j), the message is heard by all other nodes in

the box iand all edge-adjacent boxes; The ﬁrst node whose message is heard

is chosen as the spokesman for box iby all other nodes in the box i(the node

itself does not know it yet) and in edge-adjacent boxes. In subsequent steps in

round i,nodesintheboxicontaining this node (i, j) are silent. The node (i, j)

will learn that it is the spokesman for the box iwhen, in an edge adjacent box,

a unique node transmits its own label and the list of labels heard from adjacent

boxes. Since all boxes, except box 25, are edge-adjacent to a box with a larger

label, by the end of round 25, if a spokesman is chosen for each box, then all

Communication in Random Geometric Radio Networks 119

spokesmen, with the exception of the spokesman in box 25 are conﬁrmed, i.e.,

they know that they are spokesmen. Hence, after round 25, a single transmission

from the spokesman in box 24 is suﬃcient to conﬁrm the spokesman of box 25.

This transmission is done in parallel by all spokesmen in boxes labeled 24, right

after the end of round 25.

Hence, the spokesman election part chooses and conﬁrms one spokesman in ev-

ery box if there is, in every box, a tile which contains exactly one functional node.

Message Transmission Part

In the ﬁrst step of this part, the source transmits its message. Then, in parallel

for all blocks, the algorithm is executed in identical phases ρ=1,2,.... In phase

ρ,stepsj=1,2,...,25 are executed sequentially. In a step j,aspokesmanof

box jwhich has received the source message but has not relayed it yet, transmits

the message. This completes the description of algorithm A∗.SeeFigure1.

(q, 4)

(b) In each box with the same label,

spokesmen transmit the message in

parallel, for all blocks

(a)thenode(q, 4)(intile4ofboxq)

is elected spokesman in box q

box

block

(q, 1) (q, 2) (q, 3)

Fig. 1. Algorithm A∗: (a) Spokesman Election part (b) Message Transmission part

Let be the tolerated error probability for the algorithm, i.e., we wish to

broadcast with probability at least 1 −.LetAbe the algorithm A∗modiﬁed

so that the spokesman election part uses only the ﬁrst ln(2D2/)

ln(1/(1−(0.9)e−(c+1))) tiles

of each box.

Theorem 5. Let cbe a positive constant and d=ln(1/(1 −(0.9)e−(c+1))).For

s∈o(1/√n),r2≥5ln(5D2/)

dn ,andλ≤c/(πs2), the algorithm Abroadcasts a

message in time O(D+log1/), with probability at least 1−.

Proof. Consider a tile t. There exists a subsquare aof tof area (1/√n−s)2=

1/n −2s/√n+s2whose nodes are not aﬀected by spots in other tiles; the

remaining subset aof the tile has area 2s/√n−s2.Letgoodtbe the event that

thereexistsexactlyonenodeina,nonodeina, and that the node in ais not

within distance sof a spot. We have

120 E. Kranakis, M. Paquette, and A. Pelc

Pr[goodt]=e−(1/n−2s/√n+s2)n((1/n −2s/√n+s2)n)·e−(2s/√n−s2)n·e−λπs2

≥(1 −2s√n+s2n)e−1+(2s√n−s2n)−(2s√n−s2n)−c

πs2πs2≥0.9e−(c+1)

for large n.Letspokesmanqbe the event that the spokesman election part is

successful in a ﬁxed box q.Sincer2≥5ln(5D2/)

dn ,thereareatleastnr2/5=

ln(5D2/)

dtiles in each box. Hence, the algorithm Acan execute its spokesman

election part. Then, we have

Pr[spokesmanq]=1−(1 −Pr[goodt])ln(5D2/)/d

≥1−(1 −0.9e−(c+1))ln(5D2/)/d

=1−5D2

ln(1−0.9e−(c+1))/d

=1−5D2

−ln(1/(1−0.9e−(c+1)))

ln(1/(1−0.9e−(c+1))) =1−

5D2.

There are at most 5D2boxes.Hence, the event spokesmen that each box contains

one spokesman occurs with probability

Pr[spokesmen]≥1−

5D25D2

≥1−.

We now show that, assuming the event spokesmen, all functional nodes are

informed and we estimate the total time of the algorithm. Consider the Message

Transmission part. For each phase, 25 time steps are elapsed. We say that a box

with label jis active if the algorithm step is j, i.e., when its spokesman may

transmit. All boxes with the same label are located at distance at least 4r/√5

from each other. Only spokesmen in active boxes (with the same label j,ata

step j) transmit. Hence all nodes in boxes adjacent to active boxes will receive

the message correctly at every time stepwhenaspokesmantransmitsinthis

active box (due to large distances between boxes with the same label, there are

no collisions in adjacent boxes). It follows that if a message is received by any

box in a block iat time t, then there exists a positive constant δsuch that at

time t+δall nodes in the block iwill know the message. Moreover, at time t+δ,

the nodes in boxes outside the block i, but adjacent to the boxes in block ialso

have received the message. Consider two nodes in diﬀerent blocks iand jsuch

that there is a sequence of edge-adjacent blocks of length k−1 between them.

If all nodes in block ihave received the message by time t, it follows from the

above that, at the time t+kδ, the message will also be received by all nodes

in block j. Since the unit square is partitioned in rows and columns of √5/(5r)

blocks, there is a sequence of, at most, 2√5/(5r) blocks between any two blocks

iand j, so that consecutive blocks are edge-adjacent. Hence, the total broadcast

time is at most 2δ√5/(5r). Since the diameter of the graph is at least 1/r,the

message transmission part is completed in time O(D). The spokesman election

Communication in Random Geometric Radio Networks 121

part of the algorithm terminates in O(log(5D2/)) = O(1 + log D+log1/)time

steps. Hence, the total execution time of the algorithm is O(D+log1/), and

the algorithm is correct with probability at least 1 −.

Acknowledgements. Evangelos Kranakis and Michel Paquette were supported

by MITACS and NSERC. Andrzej Pelc was supported by the Research Chair in

Distributed Computing of the Universit´eduQu´ebec en Outaouais and NSERC.

References

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2. Chlebus, B.S., Diks, K., Pelc, A.: Sparse networks supporting eﬃcient reliable

broadcasting. Nordic Journal of Computing 1, 332–345 (1994)

3. Chlebus, B.S., Diks, K., Pelc, A.: Reliable broadcasting in hypercubes with random

link and node failures. Comb. Prob. and Computing 5, 337–350 (1996)

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The Mathematics of Routing in Massively Dense Ad-Hoc

Networks

Eitan Altman1, Pierre Bernhard2, and Alonso Silva1

1INRIA, 2004 Route des Lucioles - BP 93, 06902 – Sophia Antipolis, France

{eitan.altman,alonso.silva}@sophia.inria.fr

2I3S, University of Nice-Sophia Antipolis and CNRS, France

Pierre.Bernhard@polytech.unice.fr

Abstract. Computing optimal routes in massively dense adhoc networks be-

comes intractable as the number of nodes becomes very large. One recent ap-

proach to solve this problem is to use a ﬂuid type approximation in which the

whole network is replaced by a continuum plain. Various paradigms from physics

have been used recently in order to solve the continuum model. We propose in

this paper an alternative modeling and solution approach similar to a model by

Beckmann [3] developed more than ﬁfty years ago from the area of road trafﬁc.

1 Introduction

An important approach to routing in ad-hoc network has been to to design trafﬁc de-

pendent adaptive protocols that send packets along paths that have smallest delays. This

metrics goes back to an early paperby Gupta and Kumar [8] who showthat by doing so,

resequensing delays (that are undesirablein real time trafﬁc and that are very harmful in

data transfers using the TCP protocol) are minimized. A recent line of research has been

to study the such protocols in massively dense static ad-hoc networks that are character-

ized by the property that each node has many other nodes in its transmission range. We

are interested here in the recent ﬂuid limit approach in which the nodes are modeled as a

continuum, and where the discrete graphdescribing the links and their costs is replaced

by a cost density (which depends on the trafﬁc intensity) over the plain. The rational

of using such ﬂuid limit approximations is that whereas the complexity of ﬁnding opti-

mal routes grows with the number nof nodes, the ﬂuid limit does not depend on nand

hence the complexity of ﬁnding optimal routesin the ﬂuid approximation does not grow

with n.

Various approaches inspired by physics have been proposed starting with the pi-

oneering work of Jacquet (see [10]) who used ideas from geometrical optics1.Ap-

proaches based on electrostatics have been designed in [20,21,18,17,9] (see the survey

[19] and references therein).

The physics-inspired paradigmsallow one to minimize various metrics related to the

routing. In contrast, Hyytia and Virtamo propose in [15] an approach based on load

balancing arguing that if shortest path (or cost minimization) arguments were used,

then some parts of the network would carry more trafﬁc than others and may use more

1We note that this approach is restricted to costs that do not depend on the congestion.

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 122–134, 2008.

Springer-Verlag Berlin Heidelberg 2008

The Mathematics of Routing in Massively Dense Ad-Hoc Networks 123

energy than others. This would result in a shorter lifetime of the network since some

parts would be out of energy earlier than others and earlier than any part in a load

balanced network.

The development of the original theory of routing in massively dense ad-hoc net-

works has emerged in a complete independent way of the related theory developed

within the community of road trafﬁc engineers, introduced in 1952 by Wardrop [22]

and by Beckmann [3]2, and which is still an active research area among that commu-

nity, see [5,6,13,14,24] and references therein.

This community further developed numerical approaches to solve the continuous

approximation model through discretization3.

Inspired by Dafermos [5] who considered routing over two possible directions (North

to South and West to East), we havestudied in [1] routing in staticad-hoc networks (e.g.

sensor networks) where the limitation to two directions can be justiﬁed by the use of

directional antennas. In the present work, we study the case where any general direction

can be chosen at any point.

Two types of objectives are sought in the research on routing in the road trafﬁc con-

text. The ﬁrst is to maximize the global utility for the whole society, and the second is

to ﬁnd a routing conﬁguration (called “trafﬁc assignment”) such that each transmission

uses only paths with minimum costs. Conﬁgurations satisfying this property are known

as “Wardrop Equilibrium”, and they coincide with the solution concept used by Gupta

and Kumar [8]. We study the two types of objectives in this paper in the context of

massively dense ad-hoc networks. For the ﬁrst objective (which corresponds to a co-

operation between nodes) we use and strengthen results of Beckmann by using tools

from optimization and control theory that have not been available at the middle of the

last century. We further study the Wardrop equilibrium and establish conditions under

which it coincides with the global optimization.

The paper is structured as follows. After describing the model in the next section,

we provide in Section 3 the mathematical foundations for globally optimizing the ﬂuid

model. The mathematical foundation for describing and solving the non-cooperative

case (i.e. the Wardrop equilibrium) are introduced in Section 4. This is followed by

Section 5 with two examples for congestion cost. We end with a concluding section

that summarizes our contributions.

2TheProblem

2.1 Routing in a Dense Network

We consider a routing problem in a dense ad-hoc network. A domain Ωof the plane

(x, y)is densely covered by potential routers. Messages have to ﬂow from a region S

of the boundary Γof Ωto a disjoint region Rof Γ. The intensity σ(x, y )of message

2See also [3, p 644, footnote 3] for the abundant literature of the early 50’s.

3Although it may seem that one is back to the starting point with yet another discrete problem

to solve, the new discrete problem is simpler, each node in it has only a small number of

neighbors, and the number of nodes in the new discrete model is independent of the number

of nods in the original system.

124 E. Altman, P. Bernhard, and A. Silva

generation on Sgiven, while the intensity ρ(x, y)of signal sink on Ris not. It is only

assumed that these are consistent: the total ﬂow of messages emitted and received are

equal. On the rest Tof the boundary of Ω, no message should enter nor leave Ω.

The congestion cost per packet transmitted (say in terms of delays, or energy use) at

each point in Ωis a function c(x, y, ϕ)of the point and of the intensity ϕof the ﬂow of

messages through that point.

We wish to investigate the optimal routing policy and its relationship with a Wardrop

kind of optimality.

2.2 A Mathematical Model

Formal Equations. We shall use the notation x=(x, y )to denote a point of R2.Let

Ωbe an open domain of R2with a smooth boundary Γ,Ωbeing at every point of Γon

asinglesideofΓ, so that an exterior normal to Ω,sayn(x)is well deﬁned and smooth

on Γ.

We model the ﬂow of messages as a vector ﬁeld f:Ω→R2,andweletϕ(x)=

f(x)be its intensity. The ﬂux of messages through Sis given as a C1function σ(·):

S→R+. The consistency assumption now reads

R

ρ(x)ds=S

σ(x)ds. (1)

Let Q=S∪T and extend the function σto the whole of Qby σ(x)=0on T.We

model the conditions on the boundary as

∀x∈Q,n(x),f(x)=−σ(x)(2)

There is no source nor sink of messages in Ω, which we model as a constraint

∀x∈Ω, divf(x)=0.(3)

It follows that Γn(x),f(x)ds=0,

which sufﬁces to insure the consistency condition (1).

The congestion cost per packet cis supposed to be a strictly positive C1function

c(x,ϕ):Ω×R+→R+, increasing and convex in ϕfor each x. The total cost of

congestion will be taken as

G(f(·)) = Ω

c(x,f(x))f(x)dx.(4)

The path followed by a packet is specifed by its direction of travel eθ=(cosθ, sin θ)

along its path, according to ˙

x=eθ. The cost incurred by one packet traveling from

x0∈Sat time t0to x1∈Rreached at time t1is

J(eθ(·)) = x1

c(x,f(x))dx2+dy2=t1

c(x(t),f(x(t)))dt. (5)

Notice that this “time” tmay be a ﬁctitious time, related to physical time, say τ,bydτ=

cdtfor instance. Then cis the inverse of a speed of travel, a delay due to congestion,

and Jis the time taken by the message to go from source to destination.

The Mathematics of Routing in Massively Dense Ad-Hoc Networks 125

Regularity and Function Spaces. We shall seek f(·)in a space we call V.Wenext

discuss the choice of function spaces. A non mathematical oriented reader may skip the

description of the funcntion spaces we introduce.

We may choose V=(H1(Ω))2, but this will require σ(·)to be slightly more regular

than necessary, viz. H1/2(Γ). To keep with the classical hypothesis in ﬂuid dynamics,

we may choose V=(Hdiv(Ω))2, the space of L2functions whose divergence is in L2.

Then we my choose σ(·)in L2(Γ).

The above Sobolev spaces have been introduced by the modern theory of PDEs [7].

An extensive extensive Theory of PDEs and their numerical approximations is now

available in these spaces.

This choice of spaces allows one to have complete spaces for functions and for their

derivatives along with a scalar product of L2. The completeness is needed to have exis-

tence of minima. The scalar product allows to have duality. The completeness together

with the duality allows KKT Theorem to hold, which we make use of in this paper.

Let V0be the closure in Vof the set of C∞functions with compact support

in Ω.LetVRand V

Qbe the closures in Vof the set of C∞functions that are null

in a neighborhood of Rand Qrespectively. They are vector spaces, supersets of V0.

Let also ˜

f(·):Ω→R2be a vector ﬁeld in Vsatisfying the constraint (2) (for instance

a smooth extension of σ(x)n(x)). Let Vbe the afﬁne space ˜

f+V

We shall also need the space H1

Rof functions of H1(Ω)whose trace on Ris zero.

Finally, we let Ω0={x|f(x)=0}, or more precisely, since fis not necessarily

continuous, the largest open subset of Ωover which Ω0f(x)2dx=0.

2.3 The Case of Elastic Trafﬁc

Let’s assume that we do not have to ship the whole demand σ(x)to the destination. We

shall send less if there is congestion. The standard way to model that is ﬁrst to deﬁne a

utility u(s)for having sunits of information shipped; we take s(x)≤σ(x). The new

objective is to minimize the sum of C(f)−U(s)where U(s)is the integral of u(s(x))

over x.

One way to solve the problem is to deﬁnea new sink S. Then add an alternativeroute

from each source to S; the cost to ship funits from a source xto S

is −u(σ(x)−f). Thus instead of directly adding utilities to the optimization problem,

they appear through costs of new routes that are added. The elastic routing problem is

thus transformed into an equivalent routing problem with ﬁxed demand. This transfor-

mation is standard, see [12,16], and we shall not pursue it here.

3 Global Optimum

3.1 The Completely Differentiable Case

We seek here the vector ﬁeld f∈(L2(Ω))2satisfying the constraints (2) and (3) and

minimizing G(f).

Let C(x,ϕ)=c(x,ϕ)ϕ.Itisconvexinϕand coercive (i.e. goes to inﬁnity with

ϕ). As a consequence, f(·)→ G(f(·)) is continuous, convex and coercive. Moreover,

126 E. Altman, P. Bernhard, and A. Silva

the constraints are linear. Therefore an optimum exists, and we may apply the theorem

“KKT” (Karush, Kuhn and Tucker).

We dualize only the constraint (3) and look for fin V. Let therefore p(·)∈L2(Ω)

be the dual variable, we let

L(f,p)=ΩC(x,f(x))+p(x)divf(x)dx.

Using Green’s formula, we may also write

L(f,p)=ΩC(x,f(x))−∇p(x),f(x)dx+Γ

p(x)n(x),f(x)ds.

The optimal vector ﬁeld fshould minimize Lover V,forsomep. Therefore, 0must

belong to the subdifferential with respect to fof the restriction of Lto V.

Wherever f=0,Lis actually differentiable, so that the subdifferential contains

only the derivative. Actually, we only need the restriction of the derivative to V

Q.which

DL·g=ΩD2C(x,f(x))f(x),g(x)

f(x)−∇p(x),g(x)dx+R

p(x)n(x),g(x)ds,

should be zero for every g∈V

Q.Pickﬁrstgin V0. The last integral vanishes. It follows

that necessarily

∀x:f(x)=0,D2C(x,f(x))f(x)

f(x)=∇p(x).(6)

It follows from this equation that p(·)∈H1(Ω), and also that the ﬁrst integral in the

r.h.s. must be zero for every gin V

Q. Picking now g∈V

Q. It follows that

p(·)∈H1

R(7)

Wherever f(x)=0, a discussion arises. If D2C(x,ϕ)/ϕ remains bounded as

ϕ→0, there is nothing to add to equations (6) and (7) above. (We shall see the typical

example C(x,ϕ)=(1/2)c(x)ϕ2below.) Otherwise the situation is more complicated.

3.2 Lack of Differentiability

We investigate nowthe case where D2C(x,ϕ)/ϕ →∞as ϕ→0. This typically arises,

e.g. if D2C(x,0) =0. We shall see the typical example C(x,ϕ)=c(x)ϕbelow.

Then f→ C(x,f)is not differentiable (with respect to f) at 0. Its subdifferential

is the set

∂fC(x,0) = {q∈R2|∀g∈R2,C(x,g)−C(x,0) ≥q, g}.

Since Cis assumed differentiable and convex in its second argument, this is

equivalent to

∂fC(x,0) = {q|∀g∈R2,D2C(x,0)g≥q, g},

The Mathematics of Routing in Massively Dense Ad-Hoc Networks 127

which in turn is equivalent to q≤|D2C(x,0)|.Now,sinceCis assumed increasing

in ϕ,D2C≥0. Placing this back into the subdifferential of L,weget,forx∈Ω0,

∃q(x)such that q(x)≤D2C(x,0) and ∀g∈V

Q,Ω0

(q(x)−∇p(x))g(x)dx=0.

Combining both cases, we conclude that, for a function f(·)∈Vwith null set Ω0to

be optimal, there must exist a p(·)∈H1

Rsuch that

∀x∈Ω, ∇p(x)≤D2C(x,0) ,

∀x∈Ω−Ω0,∇p(x)=D

2C(x,f(x))1

f(x)f(x).(8)

We may notice that the ﬁrst condition above also yields

∀x:f(x)=0,∇p(x)=D2C(x,f(x)),

Overall, the problem of determining the optimum fis equivalent (if that system has a

single solution) to determining simultaneously fand psatisfying (2),(3) and (8).

This system certainly has at least one solution, since our problem is convex coercive

with afﬁne constraints, and thus has a minimum. Uniqueness on the other hand, is by

no means simple. It may be noticed that one might look for the two scalar functions ϕ

and p, satisfying

∀x:ϕ(x)=0,∇p(x)=D

2C(x,ϕ(x)) ,

∀x:ϕ(x)=0,∇p(x)≤D2C(x,0) ,

∀x∈R,p(x)=0,

and impose furthermore the constraints (2) and (3) on

f(x)= ϕ(x)

D2C(x,ϕ(x)) ∇p(x).

We shall investigate a typical case hereafter.

4 Wardrop Equilibrium

Assume the message ﬂow obeys the abovenecessary conditions. We want to investigate

whether it is optimal for a single message to follow the route prescribed by f,i.e.an

integral line of that ﬁeld, assuming that its lone deviation from that scheme would have

no effect on the overallcongestion map. (This is the so called “atomicity” assumption.)

We investigate the optimization of the criterion (5) via its Hamilton-Jacobi-Bellman

equation. Let V(x)be the return function, it must be a viscosity solution of

∀x∈Ω,minθeθ,∇V(x)+c(x,f(x))=0,

∀x∈R,V(x)=0.

hence ∀x∈Ω,−∇V(x)+c(x,f(x))=0,

∀x∈R,V(x)=0.(9)

And the optimal direction of travel is opposite to ∇V(x),i.e.eθ=−∇V(x)/∇V(x).

128 E. Altman, P. Bernhard, and A. Silva

Clearly, this is the same system of equations as previously, upon replacing p(x)

by −V(x),andD2C(x,ϕ)by c(x,ϕ). We thus conclude that the Wardrop equilibrium

can be obtained by solving the globally optimal problem in which the cost density is

replaced by ϕ

0c(x,ϕ)dϕ. This is the continuous version of the potential function ap-

proach of Beckmann et al. [4]. This transformation has been frequently used in the road

trafﬁc context but only for one particular cost structure [23,24,25,26] the equivalence

was shown to hold in [23,25].

Monomial cost. In the case where c(x,ϕ)=c(x)ϕα,thenC(x,ϕ)=αc(x,ϕ),and

therefore the two systems of equations coincide, or more precisely, they coincide in the

domain {x|f(x)=0}. We shall show that for a given ϕ(·),pis uniquely deﬁned.

We therefore have the following property :

Proposition 1. For a monomial cost, any global equilibrium where Ω0=∅is a Wardrop

equilibrium.

5 Two Examples

5.1 Linear Congestion Cost

We investigate here the simple typical case, where the cost of congestion is linear :

c(x,ϕ)=1

2c(x)ϕ,sothat

C(x,ϕ)=1

2c(x)ϕ2.

Then, Lis differentiable everywhere, and the necessary condition of optimality is just

that there should exist p:Ω→R2such that ∇p(x)=c(x)f(x). Placing this into (3)

and (2), we see that we end up with a simple elliptic equation with mixed Dirichlet -

(non-homogeneous) Neuman boundary conditions :

∀x∈Ω, div( 1

c(x)∇p(x)) = 0 ,

∀x∈Q,∂p

∂n(x)=c(x)σ(x),

∀x∈R,p(x)=0,

⎫

⎪

⎬

⎪

⎭(10)

for which we easily get existence and uniqueness of the solution.

A more or less explicit solution can then be given in terms of the Green function

G(x,ξ)of the domain

f(x)=Q

c(x)∇1G(x,ξ)σ(ξ)ds(ξ).

If he Green function is not available, according to a classical approach, we may derive

a ﬁnite element method from the variational form : Find p∈H1

Rsuch that, for any

q∈H1

R,Ω

c(x)∇p(x),∇q(x)dx−Q

σ(x)q(x)ds=0.

The Mathematics of Routing in Massively Dense Ad-Hoc Networks 129

This can be read as DK(p)=0where K:H1

R→Ris given by

K(p)=1

2Ω

c(x)∇p(x)2−Q

σ(x)p(x)ds.

Thanks to Poincar´e’s inequality, it is convex coercive. We therefore obtain:

Proposition 2. Equations (10) have a unique solution p∈H1

5.2 Uncongested Network

An Algorithm. We consider now a situation where the network operates far from con-

gestion. The “cost” c(x)may be regarded as a delay, then the cost of any trajectory is

just the time it takes, or an energy expenditure. In any case, it is related to the state

of the infrastructure, not to its load. Then, cis independent of f(x), and we get

C(x,ϕ)=c(x)ϕ. Then, (8) simpliﬁes into

∀x∈Ω, ∇p(x)≤c(x),

∀x:f(x)=0,∇p(x)=c(x)f(x)

f(x).

Let

ϕ(x)=f(x),ψ(x)= ϕ(x)

c(x).

The above system yields

∀x∈Ω, ψ(x)≥0,∇p(x)≤c(x),ψ(x)[∇p(x)−c(x)] = 0 ,(11)

and also f(x)=ψ(x)∇p(x), which placed in (3) and (2) yields

∀x∈Ω, ψ(x)∆p(x)+∇ψ(x),∇p(x)=0,

∀x∈Γ, ψ(x)n(x),∇p(x)=σ(x).(12)

We do not have a satisfactory theory of this equation. If, as we noticed, existence is

guaranteed, we do not know whether that solution is unique. It should be noticed that

the uniqueness proof given for a very similar equation in [3] does nor carry over here,

because it relies critically on the strict convexity of the cost in f.

As an attempt, we provide here an iterative algorithm which, if it converges, con-

verges toward a solution of the system. It provides us with a uniqueness result under

a strong hypothesis. We suspect that a more general result is true, and also that the

algorithm converges even without that hypothesis.

We seek ψin H1(Ω),andpin H1

Using the classical variational trick, we may reformulate system (12) as ∀q∈VR,

Ω

[ψ(x)∆p(x)+∇ψ(x),∇p(x)]q(x)dx−

Q

[ψ(x)n(x),∇p(x)−σ(x)]q(x)ds=0 .

130 E. Altman, P. Bernhard, and A. Silva

Using Green’s formula for q∈H1(Ω):

Ω

[ψ(x)∆p(x)+∇ψ(x),∇p(x)]q(x)dx=

−Ω

ψ(x)∇p(x),∇q(x)dx+Γ

ψ(x)n(x),∇p(x)q(x)ds,

system (12) can therefore be stated as:

∀q∈VR,Ω

ψ(x)∇p(x),∇q(x)dx−Q

σ(x)q(x)ds=0.(13)

This equality may also be interpreted as D1J(p, ψ)q=0where J:VR→Ris

deﬁned by

J(p, ψ)= 1

2Ω

ψ(x)∇p(x)2dx−Q

σ(x)p(x)ds.

Poincar´e’s inequality states that there exists C>0such that,

∀p∈VR,p2≤C∇p2.(14)

Thus the functional Jabove is coercive and has a single minimum.

One may guess the following algorithm: ﬁx ψ0(x)(say =1). Given ψn, minimize

Jwith respect to p, say solving the ﬁnite element equations corresponding to (13). Call

pnthe solution, and do

ψn+1(x)=max{0,ψ

n(x)+θ(∇pn(x)2−c(x)2)}(15)

for some positive θ. We shall prove the following theorem :

Proposition 3. If there exists a solutin of equations (11)(12) such that fis essen-

tially bounded away from 0 in Ω, it is unique and for θsmall enough algorithm (15)

converges toward that solution.

Analysis of the Algorithm. Let ψ,pbe a soltion of our system of equations. Notice

ﬁrst that indeed, for any θ>0,

∀x∈Ω, ψ

(x)=max{0,ψ

(x)+θ(∇p(x)2−c(x)2)}(16)

And any limit of he above algorithm has to satisfy this equation, which says that

∇p(x)=c(x)for every xwhere ψ(x)=0. Together with the condition that p

minimizes Jfor ψ, this is exactly the conditions (11) and (12).

Substract (16) from (15). It results that

|ψn+1(x)−ψ(x)|≤|ψn(x)−ψ(x)+θ(∇pn(x)2−∇p(x)2)|.

Take the square, and integrate over Ω:

Ω|ψn+1(x)−ψ(x)|2dx≤Ω|ψn(x)−ψ(x)|2dx

+2θΩ

(ψn(x)−ψ(x))(∇pn(x)2−∇p(x))2)dx

+θ2Ω

(∇pn(x)2−∇p(x)2)2dx.

(17)

The Mathematics of Routing in Massively Dense Ad-Hoc Networks 131

Using Cauchy-Schwarz inequality, the last term is bounded from above by

Ω

(∇pn(x)2−∇p(x)2)2dx≤

Ω∇(pn(x)−p(x))2dxΩ∇(pn(x)+p(x))2dx.

Hence, assuming Ω∇pn(x)2dxremains bounded, there exists a>0such that

Ω

(∇pn(x)2−∇p(x)2)2dx≤aΩ∇(pn(x)−p(x))2dx.(18)

Concerning the second term of the r.h.s. of (17), write

∇p2=∇pn+∇(p−pn)2=∇pn2+2∇pn,∇(p−pn)+∇(p−pn)2.

Thus (using short notations for convenience)

2Ω

ψn∇p2dx−Q

σpds

2Ω

ψn∇pn2dx−Q

σpnds+1

2Ω

ψn∇(p−pn)2dx

+Ω

ψn∇pn,∇(p−pn)dx−Q

σ(p−pn)ds.

By the deﬁnition of pnas solving equation (13), the second line above is zero, leaving

the ﬁrst line alone. In a symmetric fashion, we also get

2Ω

ψ∇pn2−Q

σpn=1

2Ω

ψ∇p2−Q

σp+1

2Ω

ψ∇(pn−p)2.

Summing the last two equalities (and multiplying by two), we obtain

Ω

(ψn−ψ)(∇pn2−∇p2)=−Ω

(ψn+ψ)∇(pn−p)2.

Placing this and (18) in (17), we may summarize the above calculations as

Ω|ψn+1(x)−ψ(x)|2dx≤Ω|ψn(x)−ψ(x)|2dx

−2θΩ

(ψn(x)+ψ(x))∇(pn(x)−p(x))2dx

+aθ2Ω∇(pn(x)−p(x))2dx.

(19)

Assume that, for almost all x∈Ω,ψ(x)≥b>0. It follows that

Ω

(ψn(x)+ψ(x))∇(pn(x)−p(x))2dx≥bΩ∇(pn(x)−p(x))2dx,

132 E. Altman, P. Bernhard, and A. Silva

and therefore that for any θ≤b/a,

Ω|ψn+1(x)−ψ(x)|2dx≤Ω|ψn(x)−ψ(x)|2dx−bθ

Ω∇(pn(x)−p(x))2dx.

Summing these inequalities, it follows that the series of the L2norms ∇pn∇p2

converges, and according to Poincar ´es inequality again, pn→pin H1(Ω). The ﬁeld of

optimal directions converges as well, and assuming it is regular enough for the integral

curves to be unique, the optimal ﬁeld converges as well.

The algorithm is independent from the choice of pand ψwho are therefore

uniquely deﬁned.

6 Concluding Comments

We present a brief comparison of our treatment with [3], called hereafter M.B..InM.B.,

one introduces both the density u(x)of commodity to be moved, and the speed v(x)of

this motion, which is a data. And the cost of transportation is assumed to be a function

of ualone. The decision variable in M.B. is the vector ﬁeld ϕof transportation where

the direction of ϕis that of the transportation, and ϕits density u. Hence M.B.’s vϕ

is our f. And his equation (11) is our equation (6).

In M.B. there is an area source or sink of matter to be transported. It did not seem

necessary in our context, but technically, it would be trivially done just adding a nonzero

r.h.s. to equation (3) and its various forms, the ﬁrst equation of (10) and of (12).

Now, since the early 50’s, the theory of PDE’s has been considerably developed,

using the tools of Sobolev spaces and the variational theory of J-L. Lions, P. Lax, and

others. Thus our derivation is not formal any more, and we are able to give existence

and uniqueness theorems impossible to derive in 1952. Notice that our example with

no congestion, where our uniqueness theorem is not very satisfactory, does not satisfy

the hypotheses of the uniqueness theorem of M.B., because that paper requires that the

cost function be strictly convex.

Finally, we solve for the concept of Wardrop equilibrium, and we are therefore able

to compare the global optimum to the Wardrop equilibrium, which was not available to

Beckmann in 1952.

By casting the routing problem in dense Ad-hoc networks in the context of the road

trafﬁc framework of Beckmann, we are able to formulateand solve various optimization

problems and study various cost functions, which was not the case with the physics-

inspired paradigms that had been used beforeto study massively densead-hoc networks.

Acknowledgement

This work was partly supported by the INRIA grant (ARC) for promoting cooperation

on Population, Game Theory and Evolution. The work of the ﬁrst and third authors was

partly supported by the BIONETS European contract.

The Mathematics of Routing in Massively Dense Ad-Hoc Networks 133

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Localized Spanner Construction for Ad Hoc

Networks with Variable Transmission Range

David Pelegand Liam Roditty

Department of Computer Science and Applied Mathematics, The Weizmann Institute

of Science, Rehovot 76100, Israel

Abstract. This paper presents an algorithm for constructing a span-

ner for ad hoc networks whose nodes have variable transmission range.

Almost all previous spanner constructions for ad hoc networks assumed

that all nodes in the network have the same transmission range. This

allowed a succinct representation of the network as a unit disk graph,

serving as the basis for the construction. In contrast, when nodes have

variable transmission range, the ad hoc network must be modeled by a

general disk graph. Whereas unit disk graphs are undirected, general disk

graphs are directed. This complicates the construction of a spanner for

the network, since currently there are no eﬃcient constructions of low-

stretch spanners for general directed graphs. Nevertheless, in this paper

it is shown that the class of disk graphs enjoys (eﬃciently constructible)

spanners of quality similar to that of unit disk graph spanners. Moreover,

it is shown that the new construction can be done in a localized fashion.

1 Introduction

A wireless ad hoc network is composed of a collection Sof nnodes distributed

in the two dimensional plane. The nodes can communicate with each other using

wireless connections. As opposed to cellular networks, there is no wire infrastruc-

ture and the connections between the nodes are restricted by their transmission

energy. As nodes often receive their energy from a battery, reducing energy

consumption is one of the most fundamental problems in the design of ad hoc

networks. A popular approach for coping with the challenge of designing an eﬃ-

cient ad hoc network is to ﬁnd a topology in which only a linear number of links

need to be maintained, while the degradation of paths that connect any pair of

nodes is restricted.

In the common wireless network model, the power needed to transmit from

pto qis |pq|α,where|pq|is the Euclidean distance between pand qand α

is a constant that varies between 2 and 4. The basic assumption adopted in

most of the literature on ad hoc networks is that all the nodes have the same

transmission range. Consequently, the ad hoc network can be represented using

aunit disk graph, that is, a graph in which two nodes share an edge if their

Supported in part by grants from the Minerva Foundation and the Israel Ministry

of Science.

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 135–147, 2008.

Springer-Verlag Berlin Heidelberg 2008

136 D. Peleg and L. Roditty

Euclidean distance is at most 1. The size (in edges) of the unit disk graph can

be as large as O(n2).

One fundamental object used in the design of ad hoc network topologies is a

spanner [16,18,19]. A graph His a t-spanner of a graph G if δH(u, v)≤t·δG(u, v )

for every two nodes uand v,whereδG(u, v) denotes the shortest path distance

between uand vin the graph Gand His a subgraph of G. The parameter tis

referred to as the stretch factor of the spanner.

There is an extensive body of literature on spanners in both the geometric

setting and the ad hoc setting. In the geometric setting, the graph Gto be

spanned is the complete graph over a set Sof npoints, where the weight of each

edge of Gis the distance between its endpoints in Rd. Yao in [26] , Vaidya [23],

Salowe [21] and Callahan and Kosaraju [3] showed how to compute a geometric

(1+ )-spanner with O(n/d)edgesinO(nlog n) time. In [11], Gao et. al. showed

how to maintain a (1 + )-spanner in a distributed manner in a mobile setting,

i.e., when points can move.

In the ad hoc settings, where the graph to be spanned is a unit disk graph,

the most popular constructions that are used as underlying network topologies

for routing are the relative neighborhood graph (RNG) and Gabriel graph (GG)

which are planar subgraphs (see [2,12]). These graphs might suﬀer a very high

stretch in the worst-case. Subsequent work by Gao et. al. [10], Wang and Yang-

Li [24] and Yang-Li et. al. [14] considered the restricted Delaunay graph, whose

worst-case stretch is constant (larger than 1 + ). In [25], Wang and Yang-Li

showed how to construct a spanner of bounded degree which is also planar.

That spanner too has constant stretch.

Spanners in ad hoc networks have crucial role. Not only do they preserve the

connectivity of the network but they also guarantee that the distance between

every pair of nodes is within some constant factor from the shortest possible

distance. Moreover, the size of the spanner is only linear. These properties made

the use of spanners an attractive approach for ad hoc networks. To learn more on

the tight connection between topology control in ad hoc networks and spanners

see [20].

Common to all the papers mentioned above in the ad hoc setting is the as-

sumption that the ad hoc network is represented by a unit disk graph, that

is, every node of the network is assumed to have the same transmission range.

This model is of signiﬁcant theoretical appeal, but its accuracy is limited due

to the fact that coverage areas are assumed to be disk of equal radius, implying

in particular that transmission coverage must be symmetric. The focus on the

restricted model of unit disk graph is partially explained by the lack of methods

for dealing with more general models on one hand and the attractive proper-

ties of unit disk graphs on the other hand. There are few papers which studied

more general models than the unit disk graph, such as the Quasi-unit disk graph

in [13] and [17], however, these models are still limited. Li, Song and Wang [15]

considered a model similar to ours, in which every node has a diﬀerent trans-

mission range. In their model an edge connects uand vin the communication

Localized Spanner Construction for Ad Hoc Networks 137

graph only if ucan transmit to vand vcan transmit to u. Thus, the resulting

graph is still undirected.

The current paper considers a more general and sometimes more natural case

in which any node has a diﬀerent transmission range, taken from the range

[1,M], and an edge is placed from uto vif ucan transmit to v. This yields an

intermediate model between the geometric setting and the usual ad hoc setting,

as the transmission graph induced in this case is no longer a unit disk graph but

a general disk graph. In such graphs, edges have a direction, since the fact that p

can transmit to qdoes not necessarily imply that qcan transmit to p.Thus,the

resulting graph is directed and the transmission coverage is no longer assumed

to be symmetric. In this respect, our work canbeviewedasanintermediatestep

towards more general coverage models.

The main result of the current paper (in Section 2) is an algorithm for con-

structinga(1+)-spanner for a given disk graph with O(n/−dlog M)edges.

The algorithm can be implemented in O(mlog n) time, where mis the number

of edges in the disk graph.

Our result is also of theoretical signiﬁcance. Finding good spanners for di-

rected graphs is a diﬃcult problem. A general bound, similar to the one avail-

able for undirected graphs, cannot exist for the directed case, as indicated by

considering the example of a directed bipartite graph in which all the edges are

directed from one side to the other; clearly, any spanner for such a graph must

contain every edge. In that sense, our spanner construction yields the ﬁrst result

establishing the existence of a directed spanner for a non-trivial class of directed

graphs.

Many routing protocols for ad hoc network use only the local information

which is stored with every node. In such algorithms a packet is routed out from

a node by considering only its neighbors in the topology. See [1,2,12,22] for

more information. As our topology is constructed on top of a directed network

our result opens a new direction for localized routing algorithms.

In addition, the paper also presents (in Section 3) an algorithm for construct-

ing a linear size (O(n/−d)edges)(1+)-spanner for a given unit disk graph.

In particular, we show that any geometric (1 + )-spanner can be turned into a

(1 + )-spanner for a unit disk graph by applying a simple process.

2 Spanners for General Disk Graphs

Let Sbe a set of points in Rdand assume that any point p∈Shas a transmission

radius r(p), taken from the range [1,M]. The transmission graph of Sis a disk

graph I(S, E), whose vertices are the points of Sand whose edge set includes an

edge from pto qif pcan transmit to q. Obviously, the resulting graph is directed,

as it might happen that pcan transmit to qwhile qcannot transmit to p.Inthis

section we show how to compute a (1 + )-spanner with O(n/−dlog M)edges

for a given disk graph.

The construction of the spanner is based on hierarchal partition of the points

of Sthat takes into account the variable transmission radii.

138 D. Peleg and L. Roditty

Let be an arbitrarily small positive constant and let αand βbe two small

constants depending on , to be ﬁxed later on. Assume that the transmission

radii are scaled so that the smallest edge in the disk graph is of weight 1. Let

ibe an integer from the range [0,log1+αM]andletMi=M/(1 + α)i.Let

E(Mi+1,M

i)={(x, y)|Mi+1 ≤|xy|≤Mi}.Let(x, y) be the level of the edge

(x, y), that is, if (x, y)∈E(Mi+1 ,M

i)then(x, y)=i.Letpbe a point with a

transmission radius r(p)∈[Mi+1,M

i]. It follows that level iis the ﬁrst level in

which pcan have outgoing edges. We denote this level with (p).

The spanner construction algorithm receives as input a (directed) disk graph

I(S, E) and a desired approximation factor . It constructs the set of span-

ner edges EDIR

SP and returns the graph HDIR(S, E DIR

SP ). The construction is as

follows. The edges of I(S, E) are partitioned into classes E(Mi+1 ,M

i)fori∈

[0,log1+αM]. Assume that in each class the edges are sorted by their weight.

For ever y i∈[0,log1+αM], starting from i= 0, the edges of the class

E(Mi+1,M

i) are considered in a non-decreasing order. On each stage of the

construction we maintain a set of pivots Pi.Letx∈Sand let NN(x, Pi)be

the nearest neighbor of xamong the points of Pi. For a pivot p∈Pi, deﬁne

Γi(p)={x|x∈S, N N(x, Pi)=p, r(x)≥|xp|},thatis,allthepointswhose

nearest neighbor from Piis pwhich can transmit to p.

When considering the edge (x, y), the algorithm acts according to the fol-

lowing rule: If NN(x, Pi)>βM

i+1 then xis added to Piand the edge (x, y)

is added to EDIR

SP .IfNN(x, Pi)≤βMi+1 and there is no edge (x,y)∈EDIR

such that x∈Γi(NN(x, Pi)) then the edge (x, y) is added to EDIR

SP .When

ireaches log1+αM, the algorithm handles all the edges that belong to

E(Mlog1+αM+1,M

log1+αM). This includes also edges whose weight is 1, the

minimal possible weight.

The spanner construction algorithm is given in Figure 1. The algorithm re-

turns the directed graph HDIR (S, EDIR

SP ). In what follows we prove that HDIR

(S, EDIR

SP )isa(1+)-spanner with O(n/−dlog M) edges of the directed graph

I(S, E).

2.1 The Stretch of the Spanner

We start by showing that the stretch of the graph HDIR(S, EDIR

SP ) returned by

the algorithm is 1 + .

Lemma 1 (Stretch). Let >0and let HDIR (S, EDIR

SP )be the graph returned by

Algorithm disk-spanner.If(x, y)∈Ethen δG(x, y)≤(1 + )|xy|.

Proof. Assume that the transmission ranges are scaled such that the shortest

edge is of weight 1. Set α=β</6. We prove that every directed edge of an

arbitrary node x∈Sis approximated with 1 + stretch. Let i∈[0,log1+αM].

The proof is by induction on i. For a given node x, the base of the induction

is the maximal value of iin which xhas an edge in E(Mi+1 ,M

i). Let jbe

this value for x,thatis,thesetE(Mj+1 ,M

j) contains the shortest edge that

touches x. Every other node is at distance at least Mj+1 away from x, hence x

Localized Spanner Construction for Ad Hoc Networks 139

Algorithm disk-spanner (I(S, E),)

EDIR

SP ←φ

P0←φ

for i←0tolog1+αM

for each (x, y)∈E(Mi+1 ,M

i)do

if |NN(x, Pi)x|>βM

i+1 then

Pi←Pi∪{x}

if (x,y)∈EDIR

SP s.t. x∈Γi(NN(x, Pi))

EDIR

SP ←EDIR

SP ∪{(x, y)}

Pi+1 ←Pi

return HDIR(S, E DIR

SP )

Fig. 1. A high level implementation of the spanner construction algorithm for general

disk graphs

is a pivot at this stage and every edge that touches xfrom the set E(Mj+1 ,M

is added to EDIR

SP .

We now turn to prove the induction hypothesis. Let (x, y)∈E(Mi+1,M

i)for

some i<jand let p=NN(x, Pi). If the edge (x, y ) is not in the spanner, then

there must be an edge (ˆx, y)∈EDIR

SP ,whereˆx∈Γi(p). The crucial observation is

that xhas a transmission range of at least Mi+1. It follows from the algorithm

that |ˆxp|≤βMi+1 and |xp|≤βMi+1.

By the choice of β, it follows that 2βMi+1 <M

i+1 and (x, ˆx)∈E.Thus,there

is a (directed) path from xto yof the form x, ˆx, ywhose length is 2βMi+1 +Mi.

However,onlytheedge(ˆx, y)isinEDIR

SP . By the inductive hypothesis, the edge

(x, ˆx) whose weight is 2βMi+1 is approximated with 1 + stretch. Thus, there

is a path in the spanner from xto ywhose length is at most (1 + )|xˆx|+Mi,

and this can be bounded by

(1 + )2βMi+1 +Mi= ((1 + )2β+(1+α))Mi+1.

As the edge (x, y)∈E(Mi+1,M

i)itfollowsthat|xy|≥Mi+1.Itremainsto

prove that 1 + 2β +2β+α≤1+, which follows directly from the choice of α

and β.

2.2 The Size of the Spanner

We now prove that the size of the spanner HDIR(S, E DIR

SP )isO(n/dlog M). As

a ﬁrst step, we state the following well-known lemma, cf. [9].

Lemma 2. [Packing Lemma] If all points in a set U∈Rdare at least rapart

from each other, then there are at most (2R/r +1)

dpoints in Uwithin any ball

Xof radius R.

The next lemma establishes a bound on the number of incoming spanner edges

that a point may be assigned on stage i∈[0,log1+αM] of the algorithm.

140 D. Peleg and L. Roditty

Lemma 3. Let i∈[0,log1+αM]and let y∈S. The total number of incoming

edges of ythat were added to the spanner on stage iis O(−d).

Proof. Let (x, y ) be a spanner edge and let NN(x, Pi)=p. We associate (x, y)

to p. From the spanner construction algorithm it follows that this is the only

incoming edge of ywhose source is in Γi(p). Thus, this is the only incoming

edge of ywhich is associated to p. Now consider all the incoming edges of yon

stage i. The source of each of these edges is associated to a unique pivot within

distance of at most Mi+βMi+1 away from yand any two pivots are βMi+1 apart

from each other. Using Lemma 2, we get that the number of edges entering yis

(Mi+βMi+1

βMi+1 +1)

d= ((1 + α)/β +2)

d=O(−d).

It follows from the above lemma that the total number of edges that were added

to EDIR

SP inthemainloopisO(n/dlog M).

2.3 The Construction Time

We now describe how to eﬃciently implement the algorithm. Let nbe the number

of vertices and let mbe the number of edges in the disk graph I(S, E).

First, the algorithm has to partition the set Einto the sets E(Mlog1+αM+1,

Mlog1+αM),...,E(M1,M

0).ThiscanbedoneinO(m) time. The algorithm

also preforms nearest neighbor queries. It is easy to see that at most O(m)such

queries are processed. To obtain an eﬃcient implementation we maintain the set

Piusing the dynamic nearest neighbor data structure of Cole and Gottlieb [6].

Every operation is supported in O(log n) time. However, their data structure is

only capable of answering -approximate nearest neighbor queries. Luckily, it is

enough for our purpose. The only eﬀect of using an approximation is that the

separation between any two pivots becomes (1 + )βMi+1 for some arbitrarily

small >0, instead of βMi+1, which has a negligible eﬀect on our bounds.

Any new pivot is inserted into the data structure in O(log n) time. The set of

pivots on the (i+ 1)st stage is initiated with the set of pivots of the ith stage.

Thus, any point is inserted exactly once into that data structure.

By the above discussion it follows that the total cost of the construction

algorithm is O(mlog n).

2.4 A Localized Algorithm

We now turn to describe a localized implementation of the algorithm. We assume

a synchronous model in which a unique id is assigned to every node and that

any node knows the id’s of its outgoing neighbors (i.e., the nodes it can reach).

Similarly to the centralized algorithm, the localized algorithm of every node u

has a main loop and in each iteration of the main loop the pivots of the current

level are chosen by a simple adaption of the standard distributed algorithm for

ﬁnding a maximal independent set (cf. Peleg [18]; chapter 8). More speciﬁcally,

let Ni(u) be the set of nodes at distance at most βMi+1 from uwhose transmis-

sion radius is at least Mi+1,whereuis the node currently running the algorithm.

Localized Spanner Construction for Ad Hoc Networks 141

Algorithm local-disk-spanner (code for node u)

for i←0tolog1+αM

v←extract-min(Ni(u))

if id(v)>id(u)

EDIR

SP ←φ

obtain Ev(Mi+1,M

i) from every v∈Ni(u)

let ˆ

E←(∪v∈Ni(u)Ev(Mi+1,M

i)) ∪Eu(Mi+1,M

for every (x, y )∈ˆ

Edo

if (x,y)∈EDIR

SP s.t. x∈Ni(u)

EDIR

SP ←EDIR

SP ∪{(x, y )}

send (x, y)tox

Fig. 2. A localized spanner construction algorithm for general disk graphs

If the graph was undirected then this set could be obtained easily. However, in

the directed case umay have neighbors whose transmission range it too small,

and thus should not be in Ni(u). By a simple procedure we can overcome this

problem without adding any additional assumption to our model. Notice that

every node in Ni(u) can transmit to u,thus,ucan broadcast a message within

its transmission range and every neighbor that gets the message returns an ac-

knowledgment to uif uis within its transmission range. By this procedure, u

can ﬁnd its neighbors that can transmit to it and this is the only information

that is needed in order to form the set Ni(u).

The pivot selection is done as follows. The node vwith minimal id in Ni(u)is

extracted from Ni(u)andifu’s id is smaller than v’s then umarks itself as a pivot

in level i.Ifuis not a pivot then nothing further is done. However, if uis a pivot

then it performs a centralized computation of the spanner edges emanating from

nodes of Ni(u), and informs these nodes. For a node v,letEv(Mi+1,M

i) denotes

the set of edges of E(Mi+1 ,M

i) emanating from v. The edges that emanate from

uand from the nodes of Ni(u) are scanned in a non-decreasing order of length

andanedge(x, y) is added to the spanner if and only if it is the ﬁrst edge from

avertexof{u}∪Ni(u)toy. The algorithm is formally given in Figure 2. Next,

we show that the message complexity is linear in the number of edges of the disk

graph.

Lemma 4. The message complexity of the localized algorithm is O(m+n/d).

Proof. In the i-th iteration every node vsends its edge set Ev(Mi+1 ,M

i)to

every pivot uwhere v∈Ni(u). From packing arguments it follows that there is

a constant number of pivots that have vin their close neighbor set. Thus, every

edge of Ev(Mi+1,M

i) is passed to a constant number of pivots and in total

vgenerates O(deg(v)) messages. When a pivot computes the spanner edges it

sends messages only to points that have to maintain a link that corresponds

to a spanner edge. The total number of such messages is simply the number of

spanner edges which is O(n/d).

142 D. Peleg and L. Roditty

Table 1. Stretch 2

Region Max Radius Points Edges Removed Edges Required Stretch Savings

10 ×10 16 50 1565 343 2 0.22

15 ×15 20 100 5769 1878 2 0.33

25 ×25 25 200 18145 6999 2 0.39

30 ×30 35 500 133752 81916 2 0.61

2.5 Topology Updates

A fundamental question in topology control is what will happen when the under-

lined communication graph is being changed. For example, points are removed

from the network or new points are added.

In our case it is easy to see that a deletion or an insertion of one point may

remove or add many links which are essential to the connectivity of the network

and thus must be in the spanner without considering the distances. As a result of

that at the worse-case it may take Ω(n) time to update the spanner. Deleting and

inserting the point ucauses to update cost which is proportional to the number

of points with small transmission range that are within the transmission range

of u.

2.6 Simulations

We have implemented our spanner construction algorithm and tested it on ran-

domly generated disk graphs. The graphs are generated by picking random points

in a region of predeﬁned size. Each point is also assigned a random transmission

range from a predeﬁned interval. A disk graph is then created by adding an

edge from a point pto qif qis within the transmission radius of p.Wehave

constructed spanners with required stretch factors of 2 and 3. Given a region

size and a maximal radius, 100 diﬀerent graphs were generated and the results

Table 2. Stretch 3

Region Max Radius Points Edges Removed Edges Required Stretch Savings

10 ×10 16 50 1553 697 3 0.45

15 ×15 20 100 5813 3336 3 0.57

25 ×25 25 200 18304 11725 3 0.64

30 ×30 35 500 134203 108331 3 0.81

Localized Spanner Construction for Ad Hoc Networks 143

were averaged over all these graphs. The results are summarized in Table 1 and

Table 2. A careful look at the spanner construction reveals that the average

degree of a node in the spanner is at most 25 log M. As the results indicate

(and as one may expect), when the random disk graph becomes denser, then

the spanner obtains a better compression rate. The average degree of a node in

the random disk graph is reduced by half or more in most of the cases and the

resulted spanner has an average degree which is less than 25 log M. It implies

that there are many natural instances on which better bounds then the worse

case bound can be obtained by our spanner construction algorithm.

3A(1+)-Spanner for Unit Disk Graphs

In this section we show how to compute a (1 + )-spanner for a unit disk graph.

More speciﬁcally, we show that given a set of points Sany (1 + )geometric

spanner of Scan be turned into (1 + )-spanner of the unit disk graph of S.

Let H(S, ESP) be a geometric (1 + )-spanner of Sand let I(S, E ) be the unit

disk graph of S. The following lemma shows that the distances induced by the

graph I(S, E) are approximated with a stretch factor of 1 + in H(S, ESP ).

Lemma 5. Let Sbe a set of points and let H(S, ESP)be any (1 + )-spanner of

S.IfI(S, E )is the unit disk graph of Sthen δH(p, q)≤(1 + )δI(p, q)for every

pair of points p, q ∈S.

Proof. Let p, q ∈Sand let p=x1,x

2,...,x

=qbe the vertices on a shortest

path between pand qin I(S, E). By the deﬁnition of H,δH(xi,x

i+1)≤(1 +

)|xixi+1|.Thus,δH(p, q)≤(1 + )−1

i=1 |xixi+1|=(1+)δI(p, q).

The above lemma states that for any pair of points there exists a path

in Hthat approximates the shortest path between them in the unit disk

graph I. However, His not necessarily a spanner of I,asitmighthaveedgesthat

are not included in I, while a spanner must be a subgraph of the original graph.

At ﬁrst glance it might seem that a possible solution to this problem is to remove

every edge whose length is strictly greater than 1 from H. Indeed, by doing so we

ensure that the resulting graph is a subgraph of I. However, it might no longer

be a (1 + )-spanner for I. In particular, consider two points pand qsuch that

|pq|= 1. It might so happen that the path σthat approximates this distance in G

is composed of two edges, (p, r)and(r, q), where |pr|=1+/2and|rq|=/2.

In such a situation, if all edges whose weight is greater than 1 are removed

from H, then the path σis disconnected.

Our solution to this problem is as follows. Starting from a (1 + )geometric

spanner H(S, ESP)ofS, every edge whose length is in the range (1,1+]is

removed from ESP. In compensation, for any removed edge we add, if possible,

at most three replacement edges. Each of these three new edges belongs to the

unit disk graph and their total length is at most 1 + 2.

Speciﬁcally, let (x, y) be an edge whose weight is in the range (1,1+]. We look

for a pair of points uand vsuch that |xu|≤,|vy|≤and (u, v)∈E.Ifsuch

144 D. Peleg and L. Roditty

Algorithm unit-disk-spanner (I(S, E ),)

H(S, ESP)←geom-spanner(S, )

EUDG

SP ←ESP

for every (x, y)∈EUDG

SP do

if |xy|>1then

EUDG

SP ←EUDG

SP \{(x, y)}

if |xy|∈(1,1+]then

if ∃(u, v)∈Es.t. |xu|≤∧|vy|≤

EUDG

SP ←EUDG

SP ∪{(x, u),(u, v),(v, y)}

return HUDG(S, EUDG

SP )

Fig. 3. A high level implementation of the spanner construction algorithm for unit

disk graphs

a pair of points exists, we add the edges (x, u), (u, v)and(v, y) to the spanner

instead of the edge (x, y).SuchasituationisdepictedinFigure4.Noticethat

it might be that u=xor v=y. If no such pair of points uand vis found, then

nothing is done. Denote the resulting spanner by HUDG(S, EUDG

SP ). The algorithm

is given in Figure 3.

3.1 The Properties of the Spanner

In this section we show that the unit disk graph spanner constructed by our

algorithm has the same properties as a regular geometric spanner.

Lemma 6. The graph HUDG(S, E UDG

SP )constructed by unit-disk-spanner Algo-

rithm is a (1 + )-spanner of I(S, E)with O(n/d)edges.

Proof. It is easy to see that EUDG

SP ⊆E, as every edge of EUDG

SP is of weight at

most 1. From Lemma 5 it follows that every edge of I(S, E) is approximated by

the geometric spanner. The removal of an edge whose weight is strictly greater

than 1+has no eﬀect on the approximation of edges of the unit disk graph, since

these edges are of weight 1 or less, so edges of weight greater than 1 + do not

participate in approximating them. When an edge whose weight is in the range

(1,1+] is replaced with a path of length at most 1 + 2, only the approximation

factor is aﬀected, increasing from 1 + to at most (1 + )(1 + 2)≤1+5.It

remains to show that if a removed edge whose weight is from the range (1,1+]

has no replacement path, then its removal is harmless, i.e., there is no edge in

the unit disk graph whose approximation is aﬀected. Consider such a removed

edge (x, y), and assume that there is no edge (u, v)∈Esuch that |xu|≤and

|vy|≤. It follows that for every edge in the unit disk graph, at least one of

its endpoints is at distance strictly greater than from both xand y.Thus,the

edge (x, y) cannot be used in the approximation of any edge of the unit disk

graph and it can be removed without eﬀecting the approximation factor.

Localized Spanner Construction for Ad Hoc Networks 145

1+ε

εv

Fig. 4. A geometric spanner edge and its possible replacement path

The size of EUDG

SP remains O(n/d), as at most three edges are added for any

removed edge.

3.2 The Construction Time

In this section we explain how to eﬃciently implement the algorithm when the

set of points is in the plane. For every edge of the geometric spanner whose

weight is in the range (1,1+], we need to check whether a replacement path

exists. For every p∈S, we create a nearest neighbor data structure for the points

within a radius of around p(including the point itself). The cost for that is at

most O(deg(p) log deg(p)), where deg(p) is the degree of pin I(S, E ) (See, [8,5]).

Queries can be answered in O(log deg(p)) time. Given an edge (x, y)∈EUDG

whose weight is in the range (1,1+], we scan all the edges of length at most 

that touch xin I(S, E). For each such edge (x, u), the algorithm queries the data

structure of yto ﬁnd the closest point to uamong the points within distance

from y. If the closest point is at distance 1 or less, then we have found the

replacement path. If not, then we proceed to the next edge of x.Thecostofthis

search is O(deg(x)logdeg(y)). This is done for every geometric spanner edge

whose weight is in the range (1,1+]. A problem may arise if a point with

large degree in I(S, E) also has many spanner edges. To avoid that, we use a

geometric spanner of bounded degree [4,7], that is, one where every point has

O(−d) spanner edges. Hence every point will take part in O(−d)tests,eachof

cost proportional to its degree. The total running time is thus O(mlog n).

The next theorem summarizes the above arguments.

Theorem 1. Let Sbe a set of npoints in the plane. Let I(S, E)be the unit

disk graph that corresponds to S,where|E|=m.Thereexistsa(1 + )spanner

of I(S, E)with O(n/)edges that can be constru cted in O(mlog n)time.

4 Concluding Remarks

We have presented in this paper two constructions. The ﬁrst and most important

is the ﬁrst construction ever of spanners for disk graphs. This result raises many

other questions, both practical and theoretical. From the perspective of routing

it is interesting to use this construction as a topology for greedy based routing

algorithms in ad-hoc networks. Our spanner construction allows routing in ad-

hoc networks with variable transmission radii. It is also interesting to consider

the question of whether eﬃcient compact routing schemes exhibiting a tradeoﬀ

between the space usage of each node and the stretch of the paths exist for the

model of disk graphs. From a theoretical perspective it is interesting to explore

which other natural classes of directed graphs have good spanners.

146 D. Peleg and L. Roditty

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Geographic Routing with Early Obstacles

Detection and Avoidance in Dense Wireless

Sensor Networks

Luminita Moraru1,, Pierre Leone1, Sotiris Nikoletseas2, and Jose Rolim1

1Computer Science Department

University of Geneva

1211 Geneva 4, Switzerland

2University of Patras and CTI

26500 Patras, Greece

Abstract. Existing geographic routing algorithms for sensor networks

are mainly concerned with ﬁnding a path toward a destination, without

explicitly addressing the impact of obstacles on the routing performance.

When the size of the communication voids is increased, they might not

scale well with respect to the quality of paths, measured in terms of hop

count and path length.

This paper introduces a routing algorithm with early obstacle detec-

tion and avoidance. The routing decisions are based on path optimality

evaluation, made at the node level, gradually over time. We implement

our algorithm and evaluate diﬀerent aspects: message delivery perfor-

mance, topology control overhead and algorithm convergence time. The

simulation ﬁndings demonstrate that our algorithm manages to improve

signiﬁcantly and quite fast the path quality while keeping the compu-

tational complexity and message overhead low. The algorithm is fully

distributed, and uses only limited local network knowledge.

1 Introduction

Geographic routing algorithms represent one of the most suitable solution for

routing within sensor networks, mainly due to their stateless nature. The path

is built only with information about the one hop neighbors and of the destination,

thus they require negligible memory at sensor nodes - a direct consequence is

network scalability - no additional topology control traﬃc is needed when the

network changes.

The simplest geographic routing strategy, greedy, chooses for forwarding the

neighbor closest to the destination [3],[13],[17]. But it has a main drawback,

called the local maximum phenomenon: when the current node has no neighbor

closer to the destination then itself, the delivery of the message fails. This is

often the case if there is an obstacle or a void in the network, or in low density

network areas.

Research partially funded by the Seventh Framework Project FRONTS (contract

number 215270) of the Prevasive Adaptation Proactive Initiative of IST/FET.

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 148–161, 2008.

Springer-Verlag Berlin Heidelberg 2008

Geographic Routing with Early Obstacles Detection and Avoidance 149

Fig. 1. Communication Voids

The solution to this problem is a recovery mode, an alternative routing method

with guaranteed delivery, used when greedy fails. Several classes of algorithms

have been proposed for this purpose. Further we will discuss the class of memo-

ryless recovery mechanisms, perimeter routing, based on planar graph traversal

techniques. The algorithms in this class work only on planar graphs, thus before

entering this mode, a planar subgraph of the initial graph must be available. The

basic idea behind this algorithms is as follows: a message is forwarded clockwise

along a face of a planar graph. When it reaches a link that intersects the line

between the source and the destination, it switches to the adjoining face. A

message will leave the perimeter mode when it will ﬁnd a node closer to the

destination than the perimeter entry point.

Geographic routing algorithms scale well with respect to eﬀectiveness of the path

when the size of the communication voids is varied. But these paths are not opti-

mal in terms of length, and in fact they might be quite long, thus ineﬃcient. This

is due mainly to the nature of the protocol used during the rescue mode: perimeter

routing. It will choose sometimes relays that are further away from the destination

than the current node. Additionally, it requires graph planarity, and the planariza-

tion process preserves the shortest links, thus increasing the hop count.

The complexity of obstacle avoidance problem is inﬂuenced as well by the

shape of the obstacles. Diﬃculties appear mainly in avoiding concave obstacles

(see Fig 1(a)). Even if we consider only the case of convex obstacles (see Fig 1(b)),

an important constraint remains: nodes should exploit only local information.

In this paper we consider the behavior of geographic routing algorithms within

network conﬁgurations with obstacles and local irregularities. Our contribution

is to identify the presence of the object early on the routing path and redirect the

messages on a shorter path as soon as possible. The strategy we are proposing is

as follows: during message forwarding, each node evaluates the optimality of the

paths that go through it. The node tags itself based on the outcome of the node

optimality evaluation method - the evaluation is positive if a node has at least

one neighbor tagged as optimal closer to the destination then itself. If a node

is non-optimal, than we consider that any path toward the destination using it

will be as well non-optimal.

Subsequent message forwarding decisions will analyse ﬁrst the suitability of

optimal nodes when choosing the relays. If no optimal node is suitable (e.g. no

150 L. Moraru et al.

neighbor closer to the destination than the current node is optimal), then a non

optimal node is used.

When obstacles are present, the consequences of our method are the

tagging of the nodes in the vicinity of the object as non optimal, and the early

redirection of the message toward the edge of the object, resulting in a signiﬁcant

decrease of the path length. The cost is a small overhead, depending on obstacle

size and shape, (independent of the network size) and paid only once.

2 State of the Art and Comparison

We address the problem of early detection and avoidance of obstacles in geo-

graphic routing algorithms. Although several geographic routing with obstacles

avoidance techniques were proposed so far, most of them are concerned mainly

in guaranteeing the delivery: ﬁnding some path when greedy forwarding is not

possible. Moreover, there are situations where the constraints like the stateless

nature (i.e. the low memory needed) of geographic routing, are in contrast to

the quantity of data they need to make a decision. Further we will introduce

the techniques with guaranteed data delivery, outlining their characteristics and

drawbacks. The solutions are divided in the following categories, as described

in [4]: planar graph based, geometric obstacle detection, cost based, ﬂood based,

and hybrid.

Planar graph based obstacle avoidance techniques, [1],[6],[9],[11], are used since

they were proved to guarantee delivery if a path exists. In the initial stage,

these strategies use greedy. When a node has no neighbor closer to the desti-

nation, greedy is replaced by one of existing planar graph traversal algorithms

[13],[14],[15],[19],[22]. Since the representation of the network is not always a

planar graph, this class of strategies uses a distributed planarization algorithm,

like those proposed in[8],[12],[21]. The performances of these strategies depend

on two factors: the graph traversal and the distributed planarization algorithms.

Nevertheless, most of the algorithms are concerned with improving the planar

graph traversal algorithms while ignoring the optimality of the path. Still, the

gain in path length (compared with the optimal path) becomes signiﬁcant when

obstacles are present and it is proportional with their size.

An optimality evaluation method is described in [18]. It can be built on top of

any method based on planar graph traversal. Each node keeps track of the ratio

between greedy decisions and the total number of routing decisions. If the ratio

is higher than a speciﬁc threshold, then the node is considered as being optimal.

The main drawback of this method, is that the optimality of the path does not

depend on the network topology only, this way failing to correctly evaluate some

of the nodes.

Geometric obstacle detection is proposed in [7]. It uses the geometric proper-

ties of a node to determine if a message can be stuck at that node. An algorithm

is developed to ﬁnd holes in the network, deﬁned as areas of the network bounded

by the stuck nodes. The disadvantage of this technique is the high complexity

Geographic Routing with Early Obstacles Detection and Avoidance 151

of the detection of the holes. Additionally, it does not guarantee delivery when

the destination is inside the hole.

Cost based approach [5] consists in assigning a cost to each node, propor-

tional to the distance to the destination. When greedy forwarding fails, a node

will forward a packet to a neighbor with a lower cost than itself. Although the

complexity and the overhead of the algorithm is rather medium, it does not

choose optimal paths. Floodin g based techniques [20],[10] are using broadcast to

forward the message, once a packet is stuck. Although the complexity is low, the

overhead is high. They guarantee delivery, but path optimality is not a concern.

Multipath techniques, like [16], [2], explore several paths toward the destination,

to trade-oﬀ eﬃciency with fault tolerance. Similar with the case of ﬂooding tech-

niques, the overhead may be high. Hybrid techniques use at least a combination

of two obstacle avoidance methods. The motivation is the improved eﬃciency

of the path and the guaranteed delivery of the message. They are used when

only one of the two techniques is not enough to achieve these requirements. The

disadvantage is the increased overall complexity.

The methods described above are mainly concerned with guaranteeing deliv-

ery. In contrast, we aim at providing high quality paths, by keeping track of

previous evaluations in a distributed manner. Additionally, our technique pre-

serves the properties of the network, like scalability and low complexity since

it works only with local information about the direct neighbors of the node

currently propagating data.

3 Non Optimality Evaluation Methods

The algorithm presented in this paper is part of a class of algorithms based on

non optimal nodes detection. It will be presented in parallel with the previous

work in the same area. In each case we propose a diﬀerent method for the

detection of non-optimal nodes. We deﬁne a node as non optimal if any message

using the node as a relay will eventually use rescue mode to reach the destination.

Anon optimal path between a source and the destination is a path containing

at least one non optimal node.

3.1 Behavior Based Tagging (BBT)

In [18], the optimality of a node is evaluated as follows: if a node uses greedy

forwarding, then a positive counter is incremented, if perimeter mode is used,

then a negative counter is incremented. A node is considered on an optimal path

if the ratio between the greedy decisions and the total number of decisions is

higher than a speciﬁed threshold.

The routing algorithm will consider the result of the evaluation of the nodes

while selecting the relays for a message. When a message is routed in the greedy

mode, the node will ﬁrst search for neighbors closer to the destination and

marked as optimal. If no neighbor is found, it will switch to perimeter. When a

message is routed in the perimeter mode, the current relay will switch back to

152 L. Moraru et al.

greedy if it ﬁnds a node closer to the destination than the perimeter entry point,

otherwise it will continue in the perimeter mode.

The behavior of this method is shown in the examples in Fig 2(a), 3(a), 4(a),

and it will be discussed in the next subsection. The drawback of this approach is

the wrong evaluation of some nodes as non optimal, due to the inﬂuence of the

position of the perimeter entry point on the routing mode used at each node (this

behaviour will be explained in more details in the next subsection). Therefore,

a more precise evaluation method is needed.

3.2 Neighborhood Based Tagging (NBT)

The evaluation method is as follows: a node will mark itself as non-optimal

toward a certain direction if it does not have optimal neighbors (or does not

have neighbors at all) toward that direction. The impact of this method on the

network is the apparition of a marked convex region along some of the faces of

the object. Further, we will give a formal deﬁnition of non optimal nodes.

Let G=(N,E) be a graph representation of the network, where Nrepresents

the set of nodes and Ethe set of links. We select nk∈Na random node in the

network and dthe sink receiving all the messages. Let Sk={ni|(nk,n

i)∈E}be

the set of one hop neighbors and S

k={ni|ni∈Sk∧dist(ni,d)<dist(nk,d)}.

If M⊂Nis the set of non optimal nodes in the network, then nk∈Mif

S

k∩M=S

Algorithm 1. Optimality Evaluation Method

this.setProperty(optimality,’NON-OPTIMAL’)

for all niinS do

if this.closer(D, ni)and ni.getP roperty(optimality)==

OP T IM ALthen

this.setProperty(optimality,’OPTIMAL’)

break

end if

end for

The pseudocode of the algorithm is presented herein. Algorithm 1 describes

the optimality evaluation method. this refers to the node making the evaluation.

Algorithm 2 describes the routing strategy that includes non optimality of the

nodes for path evaluation.

We deﬁne the marked area as the area in the vicinity of the ob ject containing

nodes tagged as non optimal. The unmarked area is represented by the rest of

the network. The inﬂuence of optimality tag on routing decisions is as follows:

–Unmarked area: the behaviour of the routing protocol remains unchanged.

Once a node in the marked area, it will use greedy to get to the destination.

Once there are no closer neighbors, the node uses perimeter.

–Border: The routing protocol tries to avoid the entry into the marked area.

Therefore, for a message in the greedy mode, a node will search ﬁrst a neigh-

bor, closer to the destination than itself, between the optimal nodes. If it

Geographic Routing with Early Obstacles Detection and Avoidance 153

fails, it will start a new search considering the set of non optimal nodes,

closer to the destination than itself.

–Marked area: similar with the unmarked area.

Algorithm 2. Optimality based Routing Strategy

if routing mode is ”perimeter”then

next ←get next hop(”perimeter”,neighbors)

else

selected neighs ←filter by property(neighbor s, optimality,OP T I M AL)

next ←get next hop(”greedy”, selected neighs)

if !∃next then

next ←get next hop(”greedy”,neighbors\selected neighs)

if !∃next then

next ←get next hop(”perimeter”,neighbors)

end if

evaluate optimality

Our algorithmic design is aiming at the following improvements:

–Smaller marked area - there are nodes which have greedy neighbors toward

the destination, but they are using perimeter routing since they are not

closer to the destination than the perimeter entry point. The tagging method

based on neighborhood will mark them as optimal, while the method based

on behavior would have marked them as non optimal.

–Shorter paths - since greedy tries to route around the marked area, reducing

this area will result in reducing the length of the path.

–More accurate evaluation of the optimality, since the dependence of the

perimeter entry point and the position of the source is eliminated.

3.3 Example

An example of the behavior of the algorithm is presented in Fig 2, 3, 4. They

show both the evaluation (tagging) and routing path chosen by the network

during three transmitted messages. The evaluation is made progressively, during

the routing tasks: each time a node has to make a routing decision, it checks the

status of its neighbors.

Figure 2(a) shows the transmission of the ﬁrst message. The message is orig-

inated at node n1. Each node from n1ton4 has a greedy neighbour toward the

destination. Node n6 has no greedy node toward the destination, therefore the

algorithm switches to rescue mode, with n6 as the perimeter entry point. Since

none of the nodes n7−n10 is closer to the destination than n6, all these nodes

will use perimeter mode. All the nodes n6−n10 will increase their negative

counter and will be evaluated as non-optimal. n11 is closer to the destination

than n6, therefore the routing mode will be switched to greedy. Greedy mode

154 L. Moraru et al.

n2 n3

n10

n11

n12

n13

n14

n2 n3

n10

n11

n12

n13

n14

(a) Behavior based tagging

n2 n3

n10

n11

n12

n13

n14

n2 n3

n10

n11

n12

n13

n14

(b) Neighborhood based tagging

Fig. 2. The path of the ﬁrst message

will be kept until the destination since all the remaining nodes on the path have

neighbours closer to the destination than themselves.

Figure 2(b) shows the path of the same node when neighborhood based tag-

ging is used. Nodes n1−n4 have a neighbor closer to the destination than them-

selves. Therefore they are marked as optimal. Nodes n6−n8havenoneighbor

closer to the destination than themselves, therefore they are marked as non op-

timal. Starting from n9, the nodes are optimal again. Similar with Fig. 2(a), n6

is the perimeter entry point, and n10 is the perimeter exit point. At this step,

neighborhood based tagging has no inﬂuence on the routing method.

Figure 3 shows the path of the second message between the same source and

destination. In both cases, n4 will choose the neighbor tagged as optimal and

closer to the destination - n5. In Fig. 3(a), n5 will have no optimal neighbor

closer to the destination, therefore it will start perimeter mode and increase

the negative counter, becoming non optimal. In Fig. 3(b), n5 has no optimal

neighbour closer to the destination and will tag itself as non optimal.

In Fig. 4 we will see the path of a message after a few other retransmissions.

NBT ﬁnds an optimal path around the obstacle, while BBT will have some

nodes marked as non-optimal on a path that could use only greedy forwarding

towards the destination.

n2 n3

n10

n11

n12

n13

n14

n2 n3

n10

n11

n12

n13

n14

(a) Behaviour based tagging

n2 n3

n10

n11

n12

n13

n14

n2 n3

n10

n11

n12

n13

n14

(b) Neighborhood based tagging

Fig. 3. The path of the second message

Geographic Routing with Early Obstacles Detection and Avoidance 155

n2 n3

n10

n11

n12

n13

n14

n2 n3

n10

n11

n12

n13

n14

(a) Behavior based tagging

n2 n3

n10

n11

n12

n13

n14

n2 n3

n10

n11

n12

n13

n14

(b) Neighborhood based tagging

Fig. 4. The path of the n-th message

4 Algorithm Analysis

Each node makes routing decisions based on the optimality of the neighbors.

Therefore each node has to inform its neighbors about its current state. There

are several options for transferring this information. First is by piggybacking it

on the network control messages - periodic beacon messages, advertising their

current status and position. This solution is suitable for the case of frequent

state changes (i.e. behavior based routing).

The second option is to send an status update to the neighbors each time a

node changes its state. This is suitable for a small number of node state changes,

such is the case for neighborhood based routing. We will further show that for a

static network, the state of node can switch at most once. Therefore, this option

is more suitable for our case. We propose ﬁrst a separation of nodes into layers,

as follows:

–Layer 0: Nodes that have no greedy neighbors toward the destination: L0=

{ni|S

i=∅}

–Layer 1: Nodes that have greedy neighbors toward the destination only nodes

of Layer 0: L1={ni|∀nk∈S

i,n

k∈L0}.

–Layer n: Nodes that have greedy neighbors toward the destination only nodes

of Layers 0..n-1: Ln={ni|S

i={nk|nk∈L0∪L1...∪Ln−1}}.

Proposition 1. The Neighborhood Based Tagging Algorithm is stable: the tag

of a node is switched only once.

Proof. The status of a node ni∈L0depends only on the network topology. If it

is static, then the status of nionce tagged as non-optimal, remains unchanged.

The status of a node ni∈L1depends only on its neighbors nk∈S

i, but

∀nk∈S

i,n

k∈L0, therefore, once evaluated, their state will not change either.

Similarly, the state of a node ni∈Lndepend only on nk∈L0∪L1...∪Ln−1,

which are stable, therefore the nodes ni∈Lnare stable as well.

Another issue is the size of the tagged area. The total number of non optimal

nodes depends only on the density and the topology of the network (the rela-

tive position of destination toward the object, and the size of the object). We

156 L. Moraru et al.

deﬁne the smallest density for which the the number of tagged nodes is both

limited and proportional with the size of the marked area as the critical density.

Experimentally, we found a critical density around 10.

For densities higher than critical density, the messages coming from sources

for which exists a greedy path toward the destination, will generate the detection

of a limited number of non optimal nodes before ﬁnding this greedy path that

they will use afterwords, as shown in Fig. 4(b). Further we will prove that the

algorithm preserves the greedy paths.

Theorem 1. If there is a path P=n0,n

1, ..., nibetween a sou rce sand a des-

tination d, such that

dist(ni,d)>dist(ni−1,d)...dist(n2,d)>dist(n1,d)>dist(n0,d)

then no node nk∈Pis tagged as non-optimal.

Proof. We proof the theorem by induction. The node n0is directly connected

to the destination d, therefore it is optimal. The node n1has a neighbor closer

to the destination, the node n0, therefore it is optimal. We assume that the

node ni−1is optimal. Then nihas an optimal neighbor toward the destination,

therefore it is optimal.

Corollary 1. If we can enclose the obstacle in a region such that for all the

nodes outside this region it exists a greedy path toward the destination, then the

marked region cannot exceed this region around the obstacle.

In order to extend the suitability of the algorithm for any network

conﬁguration - nodes density smaller than the critical density, we redeﬁne our

algorithm by considering a new parameter during the optimality evaluation: the

layer to which a node belongs, as deﬁned at the begining of this section. We will

shouw that the size of a layer is ﬁnite and if we limit the number of layers of

marked nodes, then the algorithm is convergent to a stable state.

Proposition 2. The size of a layer is ﬁnite.

Proof. By induction on i.

Basis i=1 The size of Layer 0 is proportional with the object, therefore ﬁnite.

A node in Layer 1 must have at least one greedy neighbor in Layer 0, it has to

be in the transmission range of a node in Layer 0. Therefore the size of the Layer

1 is proportional with the size of Layer 0 and ﬁnite.

Inductive step. Suppose the size of Layers 0,1,2.. n-1 is ﬁnite. The nodes in Layer

n have only greedy neighbors in one of the lower ranked layers. Therefore the

size of the Layer n is ﬁnite.

The algorithm is convergent if the number of layers is ﬁnite. We can limit the

number of layers by introducing a new parameter, a layer threshold. If a non

optimal node is detected in a layer above this limit, then it will not switch its

state. This will limit the evaluation to the nodes in the vicinity of the obstacle.

Geographic Routing with Early Obstacles Detection and Avoidance 157

10.020815.0492 19.8762 25.1292 30.3765

Hop count

Network density

(a) GFG

9.963815.0755 19.995824.9044 30.5982

Hop count

Network density

(b) Behavior based tagging

9.91 15.1205 20.1735 25.0917 30.457

Hop count

Network density

Fig. 5. Number of hops

5 Simulation Results

In this section we numerically validate the expected behavior and performance

of our algorithms. The simulations we present compare our geographic routing

algorithm and the well known greedy face greedy (GFG) algorithm which is

considered a reference algorithm in the state of the art. Additionally we compare

with a similar tagging based class of heuristic algorithms, described in [18].

To make the comparison, the criteria we are interested in are (a) whether the

tagging algorithm is convergent: whether the number of tagged nodes becomes

constant after some time, (b) the total number of tagged nodes and (c) the

performance in terms of path length and hop counts. The numerical experiments

show that our algorithm competes well with the GFG and behavior based routing

evaluation in terms of the total number of nodes on the routing paths, while

reducing the number tagged nodes, thus the topology control traﬃc.

5.1 Details on the Experiments and the Representation of Results

The experiments are made with a network of nodes randomly distributed on a

200x200 units area. The size of the object (rectangulary shaped) is 30x50 units

and the position of the upper left corner is 70x110. The transmission range of

the nodes is constant, equal to 7 units, The total number of nodes varies between

2800 and 7900 such as to obtain diﬀerent densities between 10 and 30.

For each step of the simulation, a new message is sent from a random source

to a single destination (110,85), such that all the trajectories will intersect the

object. The initial network setup is similar with Fig. 2. Within a step, a node

that acts as a relay reads all the messages sent by its neighbors in the previous

step and schedules them for retransmission within this step.

Each experiment is repeated 100 times with a diﬀerent network topology, and

the outcomes are presented in a box plot graphic. Box plots are composed of

a box with the lower line being the lower quartile, the middle one the median

and the upper one being the upper quartile of the sample. The dashed lines

extending above and below the box show the span of the other samples. The

plus sign represents outliers.

158 L. Moraru et al.

10.020815.0492 19.8762 25.1292 30.3765

Path Length

Network density

(a) GFG

9.963815.0755 19.995824.9044 30.5982

Path Length

Network density

(b) Behavior based tagging

9.91 15.1205 20.1735 25.0917 30.457

Path Length

Network density

Fig. 6. Path length

5.2 Performance Evaluation

The performances in terms of path length for the three algorithms are presented

in Fig 6. We are evaluating the path stretch - deﬁned as the ratio between the

total path length of a message and the minimum euclidian distance between

the source and the destination, while taking into account the presence of the

obstacle.

For the smallest two densities considered, BBT has a major drawback: it per-

formes worse than GFG. The reason is the inﬂuence of voids on the routing mode.

Nodes are using perimeter routing due to the presence of the voids, therefore the

size of the marked area will be increased by the lack of nodes, having as a con-

sequence an increase of path lengths. For these densities, our protocol reduces

with 50% the path stretch obtained by BBT. Therefore, we extend the suitablity

of the early obstacle avoidance to a broader range of densities. It reduces for all

densities the path stretch obtained by GFG with 30%. We extend the suitablity

of the early obstacle avoidance to a broader range of densities. Still, BBT has

slightly better performances for the highest densities: it has a decrease of 10%

of the path stretch of NBT (but with 4 times more nodes marked).

Figure 5 shows the hops stretch of a message sent from a source to a des-

tination. It is measured as the ratio between the number of hops of a message

between the source and the destination, and the ideal number of hops (measured

as the ratio between the euclidian path length described above and the trans-

mission radius). The simulations show that for the lowest density NBT improves

with 30% the performances of BBT and with 20% the performance of GFG.

We note that the overhead in our algorithm is independent of the network

size. Thus our method scales well. Furthermore, additional messages are sent

only once, i.e. the overhead is independent of the number of events generated

in the network, while all messages routed around the obstacle beneﬁt of smaller

paths. Overall, the overhead impossed by tagging nodes is much less compared

to the saving in routing messages. As an example, for routing 10 messages, we

save 10 times the path gain (in this case 20 hops per message) i.e a total of 200

transmissions, while we spend only 50 messages for tagging. The convergence

time for the two strategies is compared in Fig. 7. The variations are small,

although the evaluation methods are diﬀerent. Let the convergence time be the

Geographic Routing with Early Obstacles Detection and Avoidance 159

10.0066 15.0215 20.0299 25.047 30.4254

100

200

300

400

500

600

700

800

900

1000

Convergence time

Network density

(a) Behavior based tagging

9.9983 15.0337 20.0322 25.0417 30.4278

100

200

300

400

500

600

700

800

900

1000

Convergence time

Network density

(b) Neighbors based tagging

Fig. 7. Convergence time

time when the number of tagged nodes remained unchanged for the last 300

steps. Therefore we consider that the algorithm is fast convergent.

A signiﬁcant diﬀerence can be noticed with respect to the number of tagged

nodes (Fig. 8): NBT will mark only 1/4 of the nodes marked by BBT.Another

important observation is that the number of tagged nodes does not increase for

higher densities. The reason is that the geometrical surface covered by tagged

nodes decreases as well with the increase in density. The probability that a node

has greedy neighbors toward the destination is direct proportional to the density.

Since only tagged nodes transmit overhead messages, and since this is done only

once, reducing the number of tagged nodes leads to a smaller overhead.

10.0066 15.0215 20.0299 25.047 30.4254

100

200

300

400

500

600

700

Non optimal nodes

Network density

(a) Behavior based tagging

9.9983 15.0337 20.0322 25.0417 30.4278

100

200

300

400

500

600

700

Non optimal nodes

Network density

(b) Neighbors based tagging

Fig. 8. Number of tagged nodes

6 Conclusions

This paper presented an algorithm for early detection and avoidance of obsta-

cles, by progressive evaluation of the nodes making routing decisions.We proved

several properties of the algorithm: stability, convergence and we showed that it

preserves previous properties of the geographic routing algorithms.

The simulations show the performances of the proposed algorithm, better

then those of the state of the art algorithms. At the same time, the algorithm

is lightweight, it needs only 1 bit of information piggybacked on the topology

160 L. Moraru et al.

maintenance messages, or sent reactively, and only one extra bit of storage for

each neighbor.

The complexity is low - for a ﬁxed destination the overhead introduced de-

pends only on the obstacle size and shape, while it is independent of the network

size. Furthermore, this overhead is paid only once, independently of the load of

the network, while all messages beneﬁt of reduced path length. Additionally, the

algorithm is ﬂexible, it can be used on top of a large class of routing and pla-

narisation algorithms. At the same time it is independent on the physical layer

model used.

Future work will consider diﬀerent assumptions for network topology: multiple

base stations and mobile base station.

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DIN: An Ad-Hoc Algorithm to Estimate

Distances in Wireless Sensor Networks

Freddy L´opez Villafuerte and Jochen Schiller

Fre i e U n i v ersit¨at Berlin, Institut f¨ur Informatik

Takustr. 9, 14195 Berlin, Germany

{lopez,schiller}@inf.fu-berlin.de

Abstract. A current challenge in wireless sensor networks is the

positioning of sensor nodes for indoor environments without dedicated

hardware. Especially in this domain, many applications rely on spatial

information to relate collected data to the location of its origin. First of

all, an estimation of the distance between two nodes is necessary to de-

termine their positions. So far, the majority of approaches have explored

physical properties of signals such as the strength of a received signal

or its arrival time. However, this has been problematic since either the

complexity on the software or on the hardware side is not adequate for

embedded systems, or the approaches lack the required accuracy. In this

paper we present the DIN algorithm (Distance by Intersection of Neigh-

borhoods) to determine the distance between two nodes in an Ad-hoc

manner, relying solely on the investigation of local node densities. To

evaluate the accuracy of this algorithm, we conducted extensive simula-

tions and experimented with diﬀerent testbed setups using real sensor

nodes. We were able to assure competitive values for the measured error.

Keywords: Localization, Neighborhood, Network Density.

1 Introduction

Wireless Sensor Networks (WSN) [1] store and partially process the sensed data

either within the same sensor nodes which take the local samples or transmit the

sensed data to a remote central computer where the data will receive a bigger

and more complex handling process. To have a record of the place of study it is

very important to correlate the collected measurements sensed by the nodes to

a speciﬁc location. Furthermore, the position of the nodes opens up new ways

to detect special events track an object of interest and improve the network

coordination by executing geographic routing algorithms. The location problem

is especially crucial in WSN, because it is necessary to ﬁnd methods that work

in ad-hoc fashion and without additional specialized hardware to save scarce

resources since the positioning indoors is not possible with GPS.

The ﬁrst step into this direction is to estimate the distance between nodes. To

obtain this information there is a variety of techniques that exploit physical phe-

nomena such as the time of arrival of sound signals [2], the time diﬀerence of ar-

rival between radio and ultrasonic signals [3,4], the use of interferometry [5], radio

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 162–175, 2008.

Springer-Verlag Berlin Heidelberg 2008

DIN: An Ad-Hoc Algorithm to Estimate Distances 163

signal strength indicator (RSSI) [6], or the use of camera pictures with a previ-

ous scene analysis [7]. In this paper we focus on the problem of GPS-less, ad-hoc

and low cost localization for WSN. We propose a method to estimate distances

based only on the analysis of local node densities called Distance by Intersection

of Neighborhoods (DIN). This algorithm estimates distances between nodes which

share a communication link using the number of nodes that are positioned in the

union and intersection area of their communication ranges. We evaluated our al-

gorithm for indoor usage using simulations and real hardware experiments.

The structure of the paper is as follows: First we motivate the need for a

new, ﬂexible and ad hoc technique to estimate distances applicable for indoor

usage. Through diﬀerent network setups and a thorough calibration of real sensor

nodes, we present the results of a RSSI-based distance estimation in section 2.

We propose a new alternative to develop a similar range-free system using the

DIN algorithm in section 3.

The mathematical model relating the number of nodes in the union and inter-

section area with the distances between them will be described in this section as

a foundation of our proposed algorithm. Making use of the ns-2 simulator, we

look at the behavior of the DIN algorithm in uniform and near-uniform nodes

distribution with diﬀerent node densities. We verify the quality of our algorithm

not only with the results of these simulations but also putting into practice the

proposed technique on real sensor nodes with diﬀerent network conﬁgurations.

The evaluation of the distance errors of the RSSI-based system, the ns-2

simulations and the implementations of the DIN algorithm on real hardware in

section 3 is presented. Section 4 discusses the related work and other approaches

for distance estimations. Finally, we give an outlook on future work in section 5

and summarize our ﬁndings in the conclusions in section 6.

2 RSSI as Statement of the Problem

The Determination of the distance between sensor nodes that are close to one

another (within the range of tens of centimeters up to a few meters) is usually

carried out with the help of Time of Arrival (TOA) or Time Diﬀerence of Arrival

(TDOA) systems. The accuracy that these systems are able to provide comes at

the cost of a high synchronization overhead, thus high energy expenses at runtime

and the need for dedicated hardware on the sensor nodes [3]. In contrast, range-

free algorithms rely solely on conventional hardware of sensor nodes, with the

preferred present technique to conclude the distance of the receiving node from

the sender by means of mapping the measured RSSI value to a distance. This

mapping has to be justiﬁed by previous measurements, but has the advantage

that it imposes no additional cost on a node since it is provided by the transceiver

practically for free.

To understand the distribution of RSSI values in an indoor setup, we measured

these values with our MSB sensor nodes, (see section 2.1) at regular points and

created maps, two of which are depictedinFigures1aand1b.Thesemaps

vizualize very well the problem that arises when utilizing a simple mapping:

164 F. L´opez Villafuerte and J. Schiller

0.25

0.5

0.75

1.25

1.5

1.75

2.25

2.5

2.75

3.25

3.5

3.75

4.25

4.5

4.75

0.25

0.5

0.75

1.25

1.5

1.75

2.25

2.5

2.75

3.25

3.5

3.75

4.25

4.5

4.75

meter

(a)

RSSI Value

30-35

25-30

20-25

15-20

10-15

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.75 5

0.25

0.5

0.75

1.25

1.5

1.75

2.25

2.5

2.75

3.25

3.5

3.75

4.25

4.5

4.75

meter

(b)

Fig. 1. (a) Received signal strength of a sending node placed at the lower right corner

within an indoor testbed, (b) Received signal strength of a sending node placed in the

middle of the network within an indoor testbed

As can be seen in map 1 a the transmission range is far from being regular,

nodes may be far away from the sender and still receive a high RSSI value while

others are closer and exposed to lower values, and thus will miscalculate their

distance. Fluctuation of the received signal imposes a major challenge on current

range-free algorithms. Also, Figure 1b indicates that the determination of a small

distance in the range of tens of centimeters is not possible, since the resolution

of RSSI does not allow for such an accuracy. Even worse, the distribution of

RSSI values is inﬂuenced by spatial, temporal and environmental parameters, the

orientation of the antenna and the choice of transceiver, making the calibration

an almost unaccomplishable challenge. First at all, we implemented an RSSI-

based distance estimation experiment to obtain the idea of its performance with

real hardware using the Scatterweb nodes described in the next subsection. The

main purpose is to know the quality of this range free technique for indoor

environments using WSN.

2.1 ScatterWeb Sensor Network Platform

The hardware used to test the DIN algorithm was the ScatterWeb Modular

Sensor Boards (MSB) [8]. These MSB feature the 16-bit microcontroller MSP430

from Texas Instruments equipped with 55 KB of ﬂash memory and 5 KB RAM.

In order to communicate to other nodes, each board with a Chipcon CC1020

transceiver uses the ISM band at 869 MHz. This transceiver allows monitoring

the received signal strength (RSSI) at reception, the transmit power can be set

manually by the developer. A number of additional sensors can be plugged to the

core board, such as temperature, humidity or light sensors, in order to expand

the standard functionalities of the node.

DIN: An Ad-Hoc Algorithm to Estimate Distances 165

2.2 Communication Range Calibration

The primary goal has been to test the behaviour of distance estimation based

on RSSI values with the best hardware conﬁguration possible. Furthermore, it

is also necessary for the implementation of our proposed algorithm (see section

3) to construct an experimental indoor set up where not all the nodes were

within each others transmission range. The ﬁrst problem that we encountered

was that even with the smallest value for setting the transmit power, every node

in the network could establish a radio communication link in the place where the

nodes where deployed. To solve this problem, we use an RSSI value to artiﬁcially

limit the transmission range by ﬁltering signals below a certain value. Although

at ﬁrst glance this solution may seem to be a testbed workaround, the results

obtained will still be valid in a larger multi-hop environment since the ﬁlter will

be equally used here, thus no diﬀerence in the behaviour of our algorithm will

be observed.

The next calibration for an approximation of a circular transmission range

was obtained by mapping the radiation pattern of the MSB nodes on an indoor

environment. For this purpose a sending node was located on three diﬀerent

positions of a 5x5 square area (upper-left corner, central position, and lower-

right corner) in a seminar room of our institute. Two of the created maps are

shown in the Figure 1a and 1b. The RSSI measurements were taken every 25

cm from an emitter node until a complete sweep of the setup area was ﬁnished.

Both nodes where positioned over cleared desk height in order to provide a

good transmission scenario. As we expected these ﬁgures have conﬁrmed that

the transmission is far from being circular but strongly irregular and without

homogeneity. The nodes can be far away from the transmitter node and still

receive high RSSI values while others are closer and exposed to lower values.

The process to determine a standard radio range for the DIN algorithm was

done by analyzing every transmission pattern map previously produced and

evaluating the quality of the transmission range in terms of ﬂuctuations of the

RSSI values of the area covered by the signal. From the measurements we reason

that with an RSSI threshold of 33(-42.5 dBm) an artiﬁcially limit transmission

range could be implemented. To determine a standard radio range for our system,

it was necessary to analyze every transmission pattern map previously produced

and to evaluate the quality of the transmission range in terms of ﬂuctuations of

the RSSI values of the area covered by signal. Taking as a reference the position

of the sender node, we create diﬀerent circular transmission range in steps of 0.25

cm until it covered the complete setup area. In order to ﬁnd the best circular

transmission range that ﬁt better with the RSSI threshold, we evaluate every

disc communication range with the help of the variable called radio weigh (RW)

deﬁned as follow:

RW=RI−RO−NRI(1)

In the matemathical expression of RWfrom Equation 1 the number RIis deﬁned

as the number of regular points inside the ﬁctitious radio scope within the range

of the artiﬁcially RSSI limit value (33). ROis the variable that counts the RSSI

166 F. L´opez Villafuerte and J. Schiller

-300

-250

-200

-150

-100

-50

100

150

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Fictitious Radio Range Range [meter]

Radio Weigh (Rw)

LowerRight

TopLeft

Center

Average

(a) (b)

Fig. 2. (a) Radio Weigh curves to determine a general approximation of the radio

communication range, (b) Approximation of the distance between nodes based on RSSI

for indoor scenario at a transmission power of 0x01

values in range but outside a given radio range and ﬁnally NRIit is the number

of points that are inside the disc communication range but that have an RSSI

value lower than 33. Averaging all the RWvalues of all the received signal

strength measurements over the diﬀerent scenarios we obtained the average curve

of the Figure 2 a. We can observe the curve reaches its maximum value in 3 m.

Thus, we decided to consider a radio transmission range equal to 3 m using an

RSSI threshold value of 33 with a transmit power of 0x01 from the CC1020 radio

transceiver.

2.3 RSSI-Based Distance Estimation

In order to determine distances from RSSI values, we interweave the correspond-

ing RSSI data to each sender-receiver distances of diﬀerent radiation pattern

maps such as Figure 1 a and 1 b. Using Matlab, we construct a polynomial

function as depicted in Figure 2 b. This approximation curve

fx=−0.0127x2+0.3697x+2.2688 (2)

is constrained to the measurement area since extrapolation instantly leads to in-

tolerable errors, a fact that once again emphasises the need for careful calibration

when relying solely on RSSI values. The protocol used to determine distances

in the network was developed as follows: Every node in the network has the

opportunity to broadcast its id. The receptor nodes register the signal strength

of this packet and compute its distance to the sender node by substituting the

value of the signal strength for x in Equation 2 and solving for fx.Twodiﬀerent

testbed layouts with 36 MSB nodes were used to test the RSSI-based distance

estimation, see Figure 3 a and 3 b.

The results of our experiment are shown in Figure 3 c. We chose to use

interquartile diagrams since it is possible to judge the value dispersions of the

DIN: An Ad-Hoc Algorithm to Estimate Distances 167

78910 11

1617181920

24 25 26 27

34 35

(a)

0.5

5 m 1m

1 m

7 8 9 10111213141516

2122

31 32

(b)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Horseshoe Uniform

RSSI Normalized Distance Error [d/R]

Interquartile 1

Interquartile 2

Interquartile 3

Average

(c)

Fig. 3. (a) Uniform node distribution, (b) Horseshoe distribution, (c) Averaged nor-

malized errors per interquartiles in horseshoe and uniform distribution derived from

RSSI distance estimation

distance errors. It can be observed that the errors are artiﬁcially normalized

after the collection of data, it means that every error value its divided by 3 m

(the ﬁctitious radius). This was applied to ﬁnd an easier form to compare the

results with the obtained on the next sections.

Although the normalization on the RSSI results was applied, the artiﬁcial

radio transmission range was not used in this case. That means, every node

in the network has been able to communicate and estimate its distances to

each other. The data on RSSI-distance estimation shown in Figure 3 c, reveals

an average misplacement of 1.88 and 1.89 m for an uniform and near-uniform

distributed network respectively. As we expected, the RSSI measurements lack

the required accuracy to determine distances between adjacent nodes.

3 Distance by Intersection of Neighborhoods

We introduce the Distance by Intersection of Neighborhoods algortihm as a pro-

posal to increment the accuracy and ﬂexibility of the range-free techniques such

as the RSSI-based distance estimation. The essence of the approach is to deter-

mine distances between nodes through the analysis of the local density that they

ﬁnd to each other. To obtain a distance from the local density survey and put

into practice our proposed algorithm, we began with a mathematical expression

of the distance between two nodes in term of the union and intersection areas of

their communication radii. We verify our mathematical model using the help of

the ns-2 simulator with diﬀerent nodes distribution. Finally we put into prac-

tice the DIN algorithm with real sensor nodes in uniformly and near-uniformly

distributed networks.

3.1 Relating Distance to the Union and Intersection Communication

Areas

An important consideration in our mathematical foundations is that we based

the DIN algorithm on an idealized radio model. Although we are aware that

168 F. L´opez Villafuerte and J. Schiller

assumption is not valid in reality, as we have shown in section 2, we use it

because it was simple and easy to reason about mathematically. Three main

assumptions were taken into consideration:

1. Unit disc graph radio transmission range.

2. Identical transmission ranges for all the nodes in the network.

3. Uniform distribution of nodes in the network.

Considering two neighbouring nodes which share a radio link communication, we

can obtain the mathematical expression by geometrical analysis of their Circle-

Circle Intersection. We deﬁned the function H(dn) as the relationship between

the intersection area (Ai) and the union area (Au) of the overlapping transmis-

sion ranges depicted as circles:

H(dn)= Ai

=4cos

−1(dn

2)−dn4−d2

4π−4cos

−1(dn

2)+dn4−d2

(3)

Since we are interested in ﬁnding an expression for the distance between two

neighbour nodes, we have to solve equation 3 for dn,wherednis the distance

between the communicated nodes normalized by the circular radio range R. For

the expression H(dn), we relate Ai

Au≈ki

ku.Wherekiis the number of nodes in

the intersection area Aiand kudenote the number of nodes that are in the union

area Au. Using MatLab, we obtained a polynomial approximation of degree 3 to

determine the normalized distance between nodes.

dn≈ −2.73H3

n+5.66H2

n−4.88Hn+1.88 ki=ku

ki−1ki=ku(4)

Equation 4 is limited by H(dn) values between 1 and 4cos

−1(1

2)−√3

4π−4cos

−1(1

2)+√3.Those

values assure a shared link communication between two adjacent nodes.

3.2 Simulation Results of the DIN Algorithm with ns-2

An important issue to examine with the help of ns-2 has been to determine

the behaviour of DIN under variable network settings. The simulation results

are obtained with a ﬁxed number of 100 nodes. In order to examine the eﬀect

of node density variability, the network size was increased until the density of

nodes become too sparse, thus the network disconnected. Another way to get

the density variability is changing the transmission range of nodes accordingly.

Using the DIN algorithm, every node in the network is able to compute its

relative distances to those nodes that are in its transmission range. To measure

the performance of DIN independent of variable radio communication ranges

we use the normalized error as can been seen in Figure 4 a and Figure 4 b.

The corresponding normalized error is simply the absolute value of the actual

distance between nodes and the calculated distance divided by the radius of

thenodetransmissionrange.Tobeable to compare the accuracy of the DIN

algorithm with diﬀerent network sizes, we deﬁne the Space-Range Ratio (SRR)

DIN: An Ad-Hoc Algorithm to Estimate Distances 169

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0769 0.0833 0.0909 0.1000 0.1111 0.1250 0.1428 0.1666 0.2000 0.2500 0.3333 0.5000 1.0000

Space-Range Rates [R/L]

Normalized Distance Error [d/R]

Interquartile 1

Interquartile 2

Interquartile 3

Average

(a)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0769 0.0833 0.0909 0.1000 0.1111 0.1250 0.1428 0.1666 0.2000 0.2500 0.3333 0.5000 1.0000

Space-Range Rates [R/L]

Normalized Distance Error [d/R]

Interquartile 1

Interquartile 2

Interquartile 3

Average

(b)

Fig. 4. (a) Absolute normalized errors in distance estimation versus covered radio

range in a uniformly distributed network, (b) Absolute normalized errors in distance

estimation versus Space-Range Rates in a Horseshoe setup

as the relationship between the radio communication scope of the idealized node

over the Length (L) of the square side where the nodes are deployed. Although

the nature of DIN was yielded for uniform distributions, a set of simulations

with a near-uniform distribution using ns-2 was implemented. This second step

is in order to test the accuracy of the DIN algorithm on a diﬀerent set up.

Figure 4 a shows that the best performance of the DIN algorithm is produced

with an SRR value of 0.1666, where the 25% of the estimations have normalized

error values less than 0.0532R. Comparing to our previous work, we discover that

the DIN algorithm yields better performance than WDNI [9] algorithm, where

the smallest normalized error reported was with a value of 0.16R. Although the

absolute normalized distance error in Figure 4 a shows the trend to decrease

with increasing node densities. Unlike WDNI, the DIN algorithm uses solely

the number of local nodes without the help of a weighting function, thus it is

not compensated for high node densities. We can denote that the duty zone of

DIN is between SRR values of 0.0769 and 0.5. Those values represent deployed

spaces with Lvalues from 2 Rto 13Rrespectively. In this interval, we can see

that the normalized distance error for the 75% of the estimations is less than

0.39R, see Interquartile 3. For bigger deployed areas than SRR values of 0.0769,

the average normalized distance error increase smoothly. This is due to the

connections in the network star to break, so the interquartiles begin to reach

the maximum normalized error. In Figure 4 b, we can observe that for SRR

values between 0.0625 and 0.5 the normalized average error and the 75% of

the error values in every case is lower than 0.37R. For this conﬁguration, DIN

has better performance than in the uniform distribution, that means, for values

of SRR smaller to 0.0769 it continues displaying smaller error under to 0.37R.

Unlike to the uniform distribution, the errors in horseshoe set up grow up in a

smooth way. That is due to the deployed area in this conﬁguration is smaller

compared to the uniform distribution, in such a way that the network remains

connected longer but producing higher errors for bigger deployed spaces.

170 F. L´opez Villafuerte and J. Schiller

Table 1 . Minimal and maximal normalized error values in simulations of the Uniform

and Horseshoe distributions

Uniform Distribution

1st Interquartile 2nd Interquartile 3rd Interquartile Average

Value SRR Value SRR Value SRR Value SRR

Min. Norm. Error 0.0532 0.1666 0.1061 0.1666 0.186 0.1666 0.127 0.25

Max. Norm. Error 0.0966 0.0833 0.1968 0.0769 0.387 0.0769 0.3118 0.0769

Horseshoe Distribution

1st Interquartile 2nd Interquartile 3rd Interquartile Average

Value SRR Value SRR Value SRR Value SRR

Min. Norm. Error 0.0627 0.1111 0.1283 0.1111 0.2195 0.1111 0.1618 0.1428

Max. Norm. Error 0.1046 0.5 0.2 0.5 0.36 0.0625 0.2832 0.0625

Looking at the normalized error of interquartile one, we realize that the best

25% of the errors is presented for a SRR value of 0.1111 showing error values less

to 0.0627. Once again, we can observe an operation area in terms of SRR values,

for high node densities (SRR=1) the distance estimations have less accuracy.

They assume to be uniformly distributed causing high error rates in the distance

estimations. On the other hand, DIN loses precision for networks with low node

densities due to the lack of nodes producing less available information.

Table 1 show the minimum and maximum values over all the experiments

obtained with the diﬀerent network distribution using the ns-2 simulator. In

this section, we conﬁrm that a node which uses the DIN can estimate distances

between their neighbours as long as the transmission range is set to a value that

enables most of the nodes to experience a neighbourhood close to a uniform dis-

tribution. The second step to test the accuracy of our algorithm is implementing

DIN using real hardware; the results of this new test are presented in the next

section.

In this section, we saw that DIN will work very well compared to the error

value of the uniform distribution, see table 1 . We conﬁrm once again that our

algorithm works as long as the transmission range is set to a value that enables

most of the nodes to experience a neighbourhood close to a uniform distribution.

3.3 Experimental Evaluation of DNI

Simplifying assumptions about radio propagation, network coverage and node

distributions are common in network research. The core idea of DIN is to use

a circular transmission range of nodes to ﬁnd a relationship between distances

and local nodes densities. Since the results of simulations were very promising

and trying to validate a comparison with the RSSI-based distance estimation, we

decided to implement DIN with the same testbed settings including the physical

setup of the sensor nodes with the same transceiver settings. We measure the

impact of a real environment on the performance of our algorithm using the ap-

proximation of the circular radio transmission scope limited by an RSSI threshold

presented in section 2.2. First of all, we replace the computation of Equation 4

DIN: An Ad-Hoc Algorithm to Estimate Distances 171

with a density-to-distance lookup table. Depending on the number of nodes in

common Kiand the local node density Ku, a node can derive its distance from a

neighbouring node. The protocol of DIN proceeds in three phases. In phase one,

every node in the network broadcast a HELLO packet to discover neighbouring

nodes within its communication range. It is important to take into consideration

that signals received with an RSSI value below 33 will be dropped automatically

to preserve the artiﬁcially constructed transmission range. To avoid collisions

on the medium, we implemented a delay timer depending on the node ID. The

information obtained in the ﬁrst phase is a neighbor table with a single entry for

each discovered neighbour.The second step on the DIN protocol is the exchange

of neighbour tables. This process allows ﬁnding how many nodes are in the union

and intersection transmission area of two neighbour nodes in the network. With

this information, every node is able to compute the distance to an adjacent node

looking to its density-to-distance table. The main problem to exchange neigh-

bour tables in the network was the communication link asymmetries. Here, a

sensor node can receive signals of another node perfectly but communications in

the other direction fail. To prevent retransmission of neighbour table’s request,

the expiration of an internal timer limits the overall waiting time. When a node

in the network experiments an asymmetric link, the DIN set the estimation

distance to the maximum value.

The protocol of DIN can be naturally integrated into any routing overhead.

The exchange of neighbourhood information and HELLO packets are subject

to most routing schemes, thus may also be utilized by DIN when available.

Additional information such as the local view on the network of each node can

be piggybacked on regular data packets to minimize the overhead for the distance

estimation. Therefore, DIN can be implemented on top of existing sensor network

software at very low additional communication costs. As we mentioned before,

we used the same two network conﬁgurations shown in section 2.3 to experiment

with the DIN algorithm. To assure a best comparison between our algorithm and

the results of the RSSI-based distance estimation, the same nodes were deployed

on the same seminar room over cleared desk height. The room was big enough

to save a distance at least 1 meter between border nodes and the walls.

The main results are depicted in Figure 5 a. Here, the average normalized

distance error per interquartile with the DIN is plotted, as well as the disper-

sion of obtained error values with the help of the interquartile diagrams. Once

again, DIN works best for uniformly distributed network. The average, normal-

ized miscalculation of the nodes of 0.325Rin this setting equals to 0.975 m,

with the best 25% of the distance calculations having an error below 0.118Ror

0.354 m, a value that provides a good accuracy for indoor usage. In 75% of all

cases, the error remains at a value of 0.443Ror a maximal oﬀset of 1.3 m within

acceptable bounds. On the other hand, the horseshoe distribution remains be-

low a threshold of 0.15Rwhich is equivalent to 0.45 m in interquartile 1, and

features an average error of roughly 1 m at the most, an observation that shows

the validity of applying the DIN to near-uniform network distributions despite

its initial design for uniform distributions.

172 F. L´opez Villafuerte and J. Schiller

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Horseshoe Uniform

DIN Testbed:Normalized Average Distance Error [d/R]

Interquartile 1

Interquartile 2

Interquartile 3

Average

(a)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

ID Border Nodes ID Inner Nodes

Normalized Average Distance Error [d/R]

(b)

Fig. 5. (a) Normalized distance errors per interquartile in horseshoe and uniform dis-

tribution derived from the DIN testbed, (b) Average normalized errors in uniform node

distribution for border and inner nodes in the experimental setup

An interesting question that we wanted to examine has been the inﬂuence

of the node placement, more precisely the membership of nodes to the border

or inner portion of the network on the distance estimation. The bars of nodes

1 to 20 in Figure 5 b represent the error of nodes placed at the border of the

network, while nodes 21 to 36 denote the inner sensor nodes. In the portion of

the inner nodes the best estimation of the network is presented with a value

of 0.17R. The 94% of the estimations in this section is lower than 0.30R. The

border nodes made distance estimations with a value lower than 0.4R for the

65% of the total cases. Making a closer analysis over the network, we found that

the border nodes distance estimations are worse than the inner nodes due to a

poor neighbour table quality. Asymmetric links and packet collisions led to a

neighbour table with far less entries than usual.

Two interesting points in the graphical are the normalized average distance es-

timations of the nodes 6 and 11 which present distance estimations far from be-

ing acceptable. Both nodes were placed on the top corners of our experimental

testbed. Analyzing its information obtained during run time, we realized that they

could set a communication link with nodes that were outside of the artiﬁcial radio

communication scope. Thus they underestimate the real distance to these nodes.

However there are border nodes like the node number 3 that presents good dis-

tance estimations. This is because to each calculated distance estimation has been

exceptionally good. Overall, we can conclude that the node placement does seem

to have an inﬂuence on the distance calculation but more and larger scenarios have

to be evaluated to add statistically signiﬁcant evidence to such a proposition.

4 Evaluation of DIN

The good results observed in the interquartile diagrams by testing the DIN al-

gorithm on the ns-2 simulator, are conﬁrmed by the test run conducted by

the Scatterweb sensor nodes. Looking on the interquartile 1 and 2 for uni-

form and horseshoe node distributions, we realize that the average normalized

DIN: An Ad-Hoc Algorithm to Estimate Distances 173

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 5 10 15 20 25 30 35 40

Node ID

Normalized Average Distance Error [d/R]

RSSI Uniform

RSSI Horseshoe

DIN Uniform

DIN Horseshoe

Fig. 6. Average normalized errors per node in horseshoe and uniform distribution with

the RSSI and the DIN distance estimation

errors are slightly lower in a simulation environment than in an implementa-

tion on real hardware. Keep in mind that the SRR value for the experimen-

tal setup correspond to a simulative value between 0.5 and 1 which has to

be considered when comparing the overall averages of testbed and simulations

results.

Taking as a reference the interquaertiles with an SRR value of 0.5 for the

cases of horseshoe and uniform nodes distribution on simulation diagrams, we

can see that the interquartile 3 of these both distributions in our testbed add

to higher values due to an increase number of miscalculation. We consider that

this behaviour is due to external inﬂuences such as fading, interference or asym-

metric links. However the discrepancies on the average normalized errors be-

tween real and simulation environments is not higher than 0.14Rwhich it is

an acceptable behaviour for the practical usage. The data on RSSI distance

estimation as shown in Figure 3 c reveals the weaknesses of relying solely on

RSSI readings. In average RSSI distance estimation errors are almost twice as

high for all tested scenarios compared with the ones provide by the DIN algo-

rithm using real hardware. The average misplacement using the RSSI distance

estimations is of 1.88m in a uniformly distributed network. A view on the nor-

malized average error per node, see Figure 6, nicely illustrates the superior-

ity of the DIN in the diﬀerent node distributions, a result that conﬁrms our

expectations.

As we see in Figure 6, the approximation of the distances based on RSSI values

lacks simply the required ﬂexibility to cope with the problem of asymmetries,

interferences and ﬂuctuations that are typical of the received strength maps

Table 2 . Testbed Comparisons

DIN Real RSSI DIN Simulation

Uniform Horseshoe Uniform Horseshoe Uniform Horseshoe

Min.Norm.Error 0.00047 0.003833 0.003957 0.00766 4.52E-5 9.99E-6

Max.Norm.Error 1.3132 1.1574 2.1666 2.089 0.602477 0.7145

174 F. L´opez Villafuerte and J. Schiller

shown in section 2. With the help of the DIN algorithm it is at least partially

solved with the knowledge of the local node densities. The best and worst error

values for the distance estimations in the diﬀerent scenarios and implementations

are depicted in table 2.

5 Future Work

First of all, it is necessary to evaluate in a rough manner the impact of the

ﬁctitious variable radio transmission range in the DIN algorithm using diﬀerent

transmission power into diﬀerent setup conﬁgurations. Another important point

is to conﬁrm the accuracy of DIN in larger testbeds for variable node densities.

On one hand, we have to make an analysis of the behaviour of the distance

estimations in multi-hops environment using our algorithm. On the other hand,

it will be especially interesting to ﬁnd out whether a lower bound for the number

of neighbouring nodes and a given accuracy can be derived for multi-hop, low,

medium and high density networks. Finally, the main goal will be the use of

the DIN algorithm in the localization context. Therefore, we plan to simulate

and develop with real hardware the position through our algorithm. Quality

comparisons with other localization approaches such as DVHop or APIT [10]

will be included in future work.

6Conclusion

In this paper we presented DIN, an algorithm to estimate distances between two

adjacent nodes based solely on local neighbourhood information. As a founda-

tion, the area of intersection of two overlapping transmission ranges has been

related to the number of local density of the nodes involved to determine their

distances. In simulations, we can observe that the duty zone of DIN is between

SRR values of 0.0769 and 0.5 for uniformly distribution networks and between

SRR values between 0.0625 and 0.5 for near-uniform distribution networks with

the majority of normalized error values below 0.39R. Here, the best average,

normalized distance error has been 0.127Rfor a uniform distribution of sensor

nodes. The good results obtained putting into practice the DIN algorithm with

diﬀerent testbed layouts, reﬂect the ﬁndings of the simulations, although we

were only able to analyse a fraction of the simulation cases. Finally, we conﬁrm

the better accuracy on distance estimation of our approach comparing the real

hardware tesbed results with the obtained using solely RSSI-values. With this

work, we demonstrated that DIN yields competitive error values for distance es-

timation. The advantage of this approach is that neither the usage of specialized

hardware, nor the measurements of physical properties that are inaccurate or

unreliable are necessary for this estimation. The DIN is a completely Ad-hoc

algorithm that it keeps the overhead in communication and calculation at min-

imum. We therefore believe that the knowledge about local node densities can

be used as a new parameter to solve the localization problem.

DIN: An Ad-Hoc Algorithm to Estimate Distances 175

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D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 176–188, 2008.

Cheating on the CW and RTS/CTS Mechanisms in

Single-Hop IEEE 802.11e Networks

Szymon Szott, Marek Natkaniec, and Andrzej R. Pach

AGH University of Science and Technology,

Department of Telecommunications,

Kraków, Poland

{szott,natkanie,pach}@kt.agh.edu.pl

Abstract. This paper presents a work in progress which deals with the problem

of node misbehaviour in ad-hoc networks. A realistic approach is used to de-

termine the impact of contention window manipulation and RTS/CTS cheating.

It is explained why IEEE 802.11e ad-hoc networks are more prone to misbehav-

iour. The paper presents simulation results related to the mentioned types of

misbehaviour. The analysis is performed for several distinct scenarios, which

yields novel results. It is shown under which conditions a misbehaving node can

gain a significant advantage over well-behaving nodes. The limitations of the

IEEE 802.11e standard in providing QoS in the presence of misbehaving nodes

is also presented.

Keywords: Ad-hoc networks, IEEE 802.11e, misbehaviour.

1 Introduction

With the increasing popularity of wireless connectivity in mobile devices (laptops,

PDAs, cell phones, etc.) there is a need for interconnecting these devices in a sponta-

neous manner. Mobile ad-hoc networks (MANETs) are networks built without infra-

structure in which every node acts as both terminal and router. Thus, they rely on the

cooperation of nodes to ensure the proper functioning of the network. A problem

arises if a node decides not to cooperate with others. We call such actions misbehav-

iour. A node may decide to misbehave in order to gain certain measurable profits

(such as higher throughput, increased battery life). Misbehaviour is always done at the

cost of the well-behaving nodes in the network. Therefore, it would be beneficial if

such actions were, if not made impossible, then at least discouraged.

The problem of node misbehaviour is strengthened by the fact that the current

WLAN standards (the IEEE 802.11 family) do not contain any incentives for nodes to

behave accordingly. The 802.11 standards are all based on the notion that each node

will strictly adhere to them. However, new wireless drivers [8] enable easy modifica-

tion of MAC layer parameters. Section 2 describes the 802.11 standard (in particular

the QoS extension – 802.11e) and shows to what forms of misbehaviour the standard

is prone to.

The focus of this paper is put on two types of misbehaviour in ad-hoc networks.

One of them is contention window (CW) cheating. This means modifying the

Cheating on the CW and RTS/CTS Mechanisms 177

parameters introduced in the 802.11 standard (CWmin and CWmax), which are respon-

sible for channel access. This, and other different aspects of misbehaviour in

MANETs, has already been addressed in the literature (Section 3). However, the pro-

posed solutions do not take many aspects into account. One particular aspect is the

RTS/CTS mechanism (normally used to avoid the hidden node problem) and its influ-

ence on network performance in the presence of misbehaving nodes. This is related to

the second type of misbehaviour discussed in this paper – cheating on the RTS/CTS

mechanism. A node may decide on not using this mechanism, even though other

nodes in the network do.

In this paper we show the results from several simulation scenarios (Sections 4

and 5). We try to answer the following questions: How does CW cheating impact

network performance (throughput, delay, and fairness) when RTS/CTS is used? Is this

affected by the network size? Is cheating on the RTS/CTS mechanism beneficial for

the misbehaving user? Should it be used alone or together with CW cheating? How do

these two types of misbehaviour impact the QoS provisioning mechanisms of

802.11e? The authors of the paper prove that a rational misbehaving node will choose

the lowest possible CW parameters as they are the most beneficial. The most innova-

tive contribution of this paper is the study of RTS/CTS cheating. To the authors' best

knowledge, this has not been done before.

2 Misbehaviour in the 802.11 Standard

The IEEE 802.11 standard [3] defines a distributed access method for wireless net-

works – DCF (Distributed Coordination Function). This is the basic access method in

ad-hoc mode. It is based on CSMA/CA (Carrier Sense Multiple Access/Collision

Avoidance).

In the context of DCF, the 802.11 MAC protocol distinguishes two important time

periods: SIFS and DIFS (Short- and DCF- Inter Frame Space), the latter is longer.

The lengths of both of these times are defined in the standard. When stations sense

that the medium is free, they begin to measure these periods in order to estimate when

they can begin their own transmission. The choice of the time period depends on the

frame type.

The contention window algorithm works as follows. Each node, ready to transmit,

senses the medium to determine whether it is idle. If so, it begins to transmit. Other-

wise, since the channel is busy, the node waits for the current transmission to finish

and then waits until the medium is free for one DIFS period. Afterwards, it randomly

chooses a backoff value from the range [0, CW]. The chosen value denotes the time

slot in which the node will begin its transmission. This decreases the probability that

two nodes will transmit simultaneously and thus cause a collision. The countdown of

the backoff value is paused when the channel is busy. When the backoff reaches zero,

the node may transmit. At the beginning, the parameter CW is equal to a predefined

value CWmin. After each collision, CW is doubled until it reaches another predefined

value – CWmax. A successful transmission resets CW to the value of CWmin.

The IEEE 802.11e standard [4] introduces EDCA (Enhanced Distributed Channel

Access) as the new distributed channel access mechanism. Traffic is divided into four

access categories (AC) to provide appropriate QoS. These categories are, from the

178 S. Szott, M. Natkaniec, and A.R. Pach

highest priority: Voice (Vo), Video (Vi), Best effort (BE), and Background (BK). Each

category has its own set of access parameters: AIFS (Arbitration InterFrame Space),

TXOP (Transmission Opportunity), and, in particular, CWmin and CWmax (Table 1).

These parameters are responsible for traffic differentiation.

Table 1. Values of CW parameters in 802.11e

AC CWmin CWmax

Voice 7 15

Video 15 31

Best effort 31 1023

Background 31 1023

The medium contention rules for EDCA are similar to 802.11 DCF. The difference

in channel access prioritization is shown in Fig. 1 and Fig. 2. Each frame arriving at

the MAC layer is mapped, according to its priority, to an appropriate AC. There are

four transmission queues; one for each AC. AIFS[AC] is the parameter which re-

places the DIFS of DCF. An internal collision resolution mechanism (virtual colli-

sion) is used to determine which frame can be sent. A physical collision can still

occur, when two or more nodes start their transmissions simultaneously.

Fig. 1. Mapping to access categories [4]

Fig. 2. Channel access prioritization [4]

Cheating on the CW and RTS/CTS Mechanisms 179

In 802.11 the data exchange is made by the default simple DATA-ACK. This

means that the sender sends a DATA frame and the receiver acknowledges it with an

ACK frame. However, this leads to the hidden node problem. To counter this prob-

lem, the data exchange can be switched to RTS-CTS-DATA-ACK. The RTS/CTS

mechanism uses two small frames (Request/Clear to Send) sent prior to the actual

data exchange to inform neighbouring nodes about planned transmissions. This con-

sumes bandwidth, but is necessary to avoid collisions caused by hidden nodes.

The IEEE 802.11 family of standards contain no incentive for nodes to adhere to

the specified parameter values. Since new drivers allow manipulating these parame-

ters it is possible that users will want to cheat to maximize their network performance.

Based on the described characteristics of 802.11, several types of misbehaviour can

be considered. In this paper we concentrate on two of those: cheating on the conten-

tion window parameters and the RTS/CTS mechanism. Both these mechanisms result

in a decrease in channel access time. The former is done by choosing lower CW val-

ues and the latter by refusing to send the RTS/CTS frames.

3 State-of-the-Art

One of the first papers dealing with the problem of contention window misbehaviour

was [6] (later extended in [7]). The authors take into account several misbehaviour

strategies, such as selecting a smaller backoff (from the range [0, CW/4]), having a

fixed backoff (1 slot) or not doubling the CW. It was the first paper to report degraded

throughput in 802.11 infrastructure networks. The authors proposed an algorithm to

solve this problem, under the assumption that the receiver (802.11 Access Point) is

well-behaved. In their approach, it is the receiver, not the sender which chooses the

random backoff value. This value is transferred to the sender in either a CTS or ACK

frame. Misbehaviour occurs when the sender deviates from that backoff. The penalty

assigned by the receiver is a higher backoff value in subsequent transmissions. The

problem with this approach, other than requiring changes to the 802.11 standard, is

that it is unsuitable for ad-hoc networks, where the receiver cannot be trusted. Hidden

nodes also cause a problem in terms of determining the correct backoff.

Several works in the field were written by Baras et al.: [1], [2], and [9]. In [1], an

algorithm (named ERA-802.11) for ensuring randomness in ad-hoc networks is pro-

posed. It is based on the negotiation of CW parameters by sender and receiver (in-

spired by a protocol for flipping coins over the telephone). This assures a truly

random backoff. The detection system developed in [6] is used to monitor nodes. In

the case of misbehaviour, a report is sent to an external reputation management sys-

tem. ERA-802.11 introduces extra messages so it is not compatible with the 802.11

standard.

The problem of trying to detect CW cheating is how to correctly observe the cho-

sen backoff of another node. Observations are hindered by such factors as: interfer-

ence from other transmissions, unsynchronized clocks, and non-deterministic medium

access. It is also necessary to determine when to stop the observation and make a

decision. This problem is discussed in [9]. The authors take into account an adaptive

attacker and prove that a particular decision rule, the sequential probability ratio test

180 S. Szott, M. Natkaniec, and A.R. Pach

(SPRT), is the optimal approach to minimizing the number of needed observations.

Similar work was done in [11].

Paper [10] presents DOMINO, an advanced software application designed to protect

hotspots from greedy users. It monitors traffic, collects traces and analyzes them to

find anomalies. DOMINO can detect many types of malicious and greedy behaviour,

including backoff manipulation techniques. Anomaly detection is based on throughput

(instead of observed backoff), which the authors acknowledge is not an optimal detec-

tion metric. The application can be seamlessly integrated with access points and it

complies with standards. However, it cannot be directly used in ad-hoc networks.

To summarize, research efforts have so far been mostly focused on detecting nodes

cheating on backoff in 802.11 infrastructure scenarios. Ad-hoc networks pose a chal-

lenge because they are distributed and have no centralized authority. Thus, there have

not been that many papers discussing contention window cheating in MANETs. In

papers [12] and [13] the authors show how modifying the CW values can degrade the

performance of an 802.11e ad-hoc network. However, to the authors' knowledge, no

papers have considered cheating on the RTS/CTS mechanism. Therefore, the subse-

quent sections address this issue.

4 Simulation Scenarios

The purpose of the simulation study was to determine how misbehaviour impacts ad-

hoc network performance. The actions taken into consideration were manipulating

CW parameters and cheating on the RTS/CTS mechanism.

The simulation analysis was performed with the use of the ns2 simulator with a

modified version of the TKN EDCA model [14]. This model implements the 802.11e

standard in ns2. The modification of the TKN EDCA model involved correcting the

RTS/CTS implementation. The following scenario was considered. The number of

homogenous nodes in the ad-hoc network was set to 5, 25, and 100 to represent small,

average and large network sizes, respectively. All stations were within hearing range

of each other (i.e., it was a single-hop network). The per-station offered load changed

from 64 kb/s to 8 Mb/s.

Table 2. Simulation parameters

Parameter Value

WLAN Standards 802.11b + 802.11e

Data rate 11 Mb/s

Routing protocol None

Transport protocol UDP

Node distribution Random

Traffic generator CBR

Packet size 1000 B

Packet exchange DATA-ACK and

RTS-CTS-DATA-ACK

Cheating on the CW and RTS/CTS Mechanisms 181

Table 2 presents the various simulation parameters used. The node distribution was

random and the traffic pattern – circular (with each node sending and receiving ex-

actly one traffic stream). An example topology, for 5 nodes, can be seen in Fig. 3.

Fig. 3. Network topology

In each scenario, there was one misbehaving node (e.g., the encircled node in

Fig. 3). All nodes used the Best effort priority to send their traffic. The well behaving

(good) nodes had unaltered contention window parameters: CWmin = 31,

CWmax=1023. The misbehaving (bad) node had these parameters significantly de-

creased: CWmin = 1, CWmax = 5. It seems realistic that the misbehaving node would

choose such low (or even lower) parameters to maximize its gain. The effect of

choosing other CW values and their impact on the use of the RTS/CTS mechanism is

studied further on.

5 Results

The results of the uplink simulations are presented in the following figures. The plots

present the curves, where the error of each simulation point for a 95% confidence

interval does not exceed 2% (this is too small for graphical representation).

Fig. 4 presents the simulation results for the small network size (5 nodes). The fig-

ure shows the achieved uplink throughput as a function of offered load. The through-

put is given for the well-behaving good nodes (on average) and for the bad node

which cheats on the CW. The difference in the throughput of the good nodes was

insignificant, that is why only the average is shown. In the first case RTS/CTS is off

and in the second it is on. In the next case misbehaviour is turned off and RTS/CTS is

either on or off. Finally, in the last case, the misbehaving node cheats both on CW and

the RTS/CTS mechanism.

The black dashed lines are the reference values and represent the situation in

which there is no misbehaviour. Turning on RTS/CTS lowers the saturation

throughput. The solid lines represent the situation in which one node misbehaves

(cheats on the CW) with RTS/CTS turned off. The misbehaving node dominates the

182 S. Szott, M. Natkaniec, and A.R. Pach

network (this has been shown in [12]). If RTS/CTS is turned on in such a network

the throughput, of course, decreases: for the misbehaving node by 30 % and for the

good nodes by 40 %.

Another case has been considered – when the misbehaving node decides not to use

RTS/CTS despite the fact that the other nodes are using this mode of transmission.

The gain is obvious – the misbehaving node's throughput almost reaches the through-

put it had when RTS/CTS was not used in the network. This is obviously at the cost

of the good nodes' throughput. Therefore, there is a strong incentive for the misbehav-

ing node to turn off RTS/CTS whenever possible.

Similar results regarding obtained throughput occur for medium and large network

sizes (Fig. 5 and Fig. 6). The difference is in the throughput achieved by the misbe-

having node when the network is saturated because it decreases with network size.

There are two characteristic points in the figures which present throughput. The

first occurs once the network reaches congestion. In other words, it is the point

where if the network consisted only of well-behaving nodes it would become satu-

rated. Until that point the bad node's presence is not harmful. After reaching the con-

gestion point, the bad node increases its throughput at the cost of the good nodes. This

occurs until the second characteristic point is reached. After this, the network is in

saturation and the bad node has much more throughput than the average good node.

These two characteristic points can be perhaps most clearly seen in Fig. 4. The first

one appears for an offered load a bit higher than 1 Mbit/s, the second one – at ap-

proximately 7 Mbit/s. The conclusion is that analysis of misbehaviour should be lim-

ited to congestion scenarios. In non-congested networks the misbehaving node does

not impact network performance.

100

200

300

400

500

600

700

800

900

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Offered Load [Kb/s]

Throughput [KB/s]

RTS: OFF, Bad node RTS: OFF, Good node

RTS: ON, Bad node RTS: ON, Good node

RTS: ON, no misbehaviourRTS: OFF, no misbehaviour

RTS misbehaviour, Bad node RTS misbehaviour, Good nodes

Fig. 4. Throughput vs. offered load (total no. of nodes: 5)

Cheating on the CW and RTS/CTS Mechanisms 183

100

200

300

400

500

600

700

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Offered Load [Kb/s]

Throughput [KB/s]

RTS: OFF, Bad node RTS: OFF, Good node

RTS: ON, Bad node RTS: ON, Good node

RTS: ON, no misbehaviourRTS: OFF, no misbehaviour

RTS misbehaviour, Bad node RTS misbehaviour, Good nodes

Fig. 5. Throughput vs. offered load (total no. of nodes: 25)

100

150

200

250

300

350

400

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Offered Load [Kb/s]

Throughput [KB/s]

RTS: OFF, Bad node RTS: OFF, Good node

RTS: ON, Bad node RTS: ON, Good node

RTS: ON, no misbehaviourRTS: OFF, no m isbehaviour

RTS misbehaviour, Bad node RTS misbehaviour, Good nodes

Fig. 6. Throughput vs. offered load (total no. of nodes: 100)

presents the average frame delay of the misbehaving and well-behaving nodes in the

small network scenario. The delay of the good nodes suffers greatly in the presence of

misbehaviour. It quickly rises very sharply in all cases. The delay of the bad node is

at an acceptable level for much higher offered loads. With the RTS/CTS mechanism

turned on, the delay is low until 4 Mbit/s. If it is turned off (intentionally

184 S. Szott, M. Natkaniec, and A.R. Pach

100

150

200

250

300

350

400

450

500

0 1000 2000 3000 4000 5000 6000 7000 8000

Offered Load [Kb/s]

Delay [ms]

RTS: ON, Bad node RTS: ON, Good node

RTS: OFF, Bad node RTS: OFF, Good node

RTS misbehaviour, Bad node RTS misbehaviour, Good node

Fig. 7. Packet delay vs. offered load (total no. of nodes: 5)

or maliciously), it is at a low level until 6 Mbit/s. These observations confirm the con-

clusions presented above: cheating on the RTS/CTS mechanism "restores" the achieved

delay to the value as when the network was not using RTS/CTS. Furthermore, it can be

once again noted that in non-congested networks the misbehaving node does not impact

network performance (in this case: delay). The measured delay was similar for larger

simulated networks, therefore only this figure is being presented.

Two types of cheating have been discussed: manipulating the CW parameters and

disabling RTS/CTS in a network which uses this mechanism. The following question

arises: is the misbehaviour gain different when these actions are performed alone and

together? The answer can be seen in Fig. 8, which shows the throughput gain of the

misbehaving node in absolute values. In this case, simulations were performed for a

network of 5 nodes (the rest of the simulation parameters remained unchanged) in

which RTS/CTS was always enabled. Three cases were considered: the misbehaving

node used either CW cheating, RTS/CTS cheating or a combination of both. The

achieved throughput was compared with the average node throughput in a network with

no misbehaviour. The result is that cheating only on the RTS/CTS mechanism does not

give almost any benefits. This is obvious because when there are no hidden stations, the

RTS/CTS mechanism only introduces a delay in the medium access. However, if this is

combined with CW cheating the gain is much larger than when cheating only on the

CW mechanism. There is a synergy between low contention window parameters and

refusing to use RTS/CTS. When a node accesses the channel more often (through low

CW parameters) the gain from not using RTS/CTS is greater.

In the previously mentioned simulations, the CW parameters of the misbehaving

node were set to CWmin = 1 and CWmax = 5. In order to determine the exact impact of

the CW values the following simulation study was performed. The network of 5

nodes (Fig. 3) was in saturation – all nodes were sending UDP traffic of an offered

Cheating on the CW and RTS/CTS Mechanisms 185

100

200

300

400

500

600

700

800

0 2000 4000 6000 8000

Offered Load [Kb/s]

Misbehaviour Gain [KB/s]

CW Cheating RTS/CTS Cheating CW+RTS/CTS Cheating

Fig. 8. Misbehaviour gain for different forms of cheating

100

200

300

400

500

600

700

800

900

020406080100

CWmin = CWmax

Throughput [KB/s]

RTS: off, Bad node RTS: off, Good nodes (avg)

RTS: on, Bad node RTS: on, Good nodes (avg)

Fig. 9. Throughput comparison for different CW parameters

load of 7 Mbit/s. The RTS/CTS mechanism was either off or on. The misbehaving

node varied it CW parameters (CWmin = CWmax) from 1 to 100 (Fig. 9). The highest

throughput it achieved was for the smallest CW parameters and for RTS/CTS turned

off. The bad node's throughput decreases in an exponential manner with the increase

of the contention window size. The point where the bad node's throughput is

186 S. Szott, M. Natkaniec, and A.R. Pach

approximately equal to the average throughput of the good nodes occurs for CWmin =

CWmax = 40. Since the 802.11 standard does not include any incentives for coopera-

tion, a misbehaving user is free to chose the most profitable CW parameters (i.e.,

equal to 1).

When dealing with the 802.11e standard it is important to determine the impact of

misbehaving in one AC on the performance of a higher priority AC. Simulations were

performed, likewise, for a 5 node scenario. The RTS/CTS mechanism was turned on.

The well-behaving nodes were using Voice priority to send their traffic (CWmin = 7,

CWmax = 15). The misbehaving node continued to use Best effort traffic (with misbehav-

iour parameters CWmin = 1 and CWmax = 5). The results are presented in Fig. 10. In the

first case, with no misbehaviour, the achieved throughput rates are in line with the

802.11e standard. When the bad node cheated on the CW, it was able to dramatically

increase its throughput at the cost of the good nodes. Surprisingly, when the bad node

cheated on both the CW and RTS/CTS mechanisms, an increase in throughput was

observed for all nodes (even the good ones). This result can only be explained by the

fact that the RTS/CTS mechanism introduces overhead which consumes a small portion

of bandwidth. Since one node (the bad one) did not use RTS/CTS frames, the total

available throughput in the network increased. Therefore, even the good nodes could

use a small share of this newly available throughput to slightly increase their perform-

ance. Had the network consisted of more nodes, the increase in throughput of the well-

behaving nodes would be even less significant. If the network was multihop and hidden

nodes were present, the gain would depend on how the stations (especially the hidden

ones) were placed. In particular it can be assumed, based on [5], that if the misbehaving

node was a hidden one in a simple star topology, it would benefit neither from CW

manipulation, nor from RTS/CTS cheating.

100

120

140

160

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Offered Load [Kb/s]

Throughput [KB/s]

No misbehavior, Bad node No misbehavior, Good nodes (avg)

CW cheating, Bad node CW cheating, Good nodes (avg)

CW+RTS/CTS cheating, Bad node CW+RTS/CTS cheating, Good nodes (avg)

Fig. 10. Throughput vs. offered load for BE vs. Vo priority scenario

Cheating on the CW and RTS/CTS Mechanisms 187

6 Conclusions

This paper presented the impact that cheating on the contention window and

RTS/CTS mechanism has on single-hop ad-hoc networks. Several simulation scenar-

ios were analyzed. Throughput, delay and fairness were considered for networks of

different sizes. A rational misbehaviour model was assumed, i.e., the malicious user

would perform simple actions to obtain significant gains.

The first conclusion is that the use of modified CW parameters allows a misbehav-

ing node to jeopardize network performance. The throughput and delay of such a

node is significantly better than well-behaving nodes. This occurs regardless of net-

work size and whether the RTS/CTS mechanism is used.

Secondly, a node can cheat on the RTS/CTS mechanism, i.e., refuse to turn in on,

even though the whole network is using it. It has been shown that while such behav-

iour does not provide gains, it is especially beneficial when joined with CW misbe-

haviour. When used together, these two types of misbehaviour can give greater

advantages than when used alone.

Furthermore, a simulation analysis was performed for different CW values of the

bad node. Assuming that the misbehaving user is rational, and taking into considera-

tion the fact that 802.11 has no mechanisms to encourage proper behaviour, it is obvi-

ous that the lowest possible CW values should be chosen.

In non-congested networks, a node’s misbehaviour, though theoretically observable,

has no influences on its neighbours and is therefore harmless. Therefore, future studies

should be focused on congested networks. In real-world ad-hoc networks saturation

can be a common situation because of multimedia and peer-to-peer applications.

Finally, it was shown that 802.11e fails to provide QoS in the face of CW and

RTS/CTS cheating. A misbehaving node can easily manipulate MAC layer parame-

ters and thus gain an advantage over other nodes. Low priority traffic can be assigned

such parameters, with which it can outperform high priority traffic.

Future work will take an even more realistic approach. Studies will focus on multi-

hop ad-hoc networks, which suffer from the hidden node problem. Cheating on other

EDCA parameters (AIFS, TXOP) will be taken into account. Furthermore, more

complex traffic patterns and networks with more misbehaving nodes will be consid-

ered. It is important that misbehaviour is simple, straightforward and advantageous so

that it can be performed by any casual user, not just an expert hacker. An analytical

model will be derived to support the findings.

Acknowledgments. This work has been carried out under the Polish Ministry of Sci-

ence and Higher Education grant no. N51739133.

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Adapting BitTorrent to Wireless Ad Hoc

Networks

Mohamed Karim Sbai, Chadi Barakat, Jaeyoung Choi,

Anwar Al Hamra, and Thierry Turletti

Project-Team Plan`ete, INRIA Sophia Antipolis, France

{mksbai,cbarakat,jchoi,aalhamra,turletti}@sophia.inria.fr

Abstract. BitTorrent is one of the Internet’s most eﬃcient content dis-

tribution protocols. It is known to perform very well over the wired

Internet where end-to-end performance is almost guaranteed. However,

in wireless ad hoc networks, many constraints appear as the scarcity of

resources and their shared nature, which make running BitTorrent with

its default conﬁguration not lead to best performances. To these con-

straints it adds the fact that peers are both routers and end-users and

that TCP-performance drops seriously with the number of hops. We show

in this work that the neighbor selection mechanism in BitTorrent plays

an important role in determining the performance of the protocol when

deployed over a wireless ad hoc network. It is no longer eﬃcient to choose

and treat with peers independently of their location. A ﬁrst solution is to

limit the scope of the neighborhood. In this case, TCP connections are

fast but there is no more diversity of pieces in the network: pieces propa-

gate in a unique direction from the seed to distant peers. This prohibits

peers from reciprocating data and leads to low sharing ratios and subopti-

mal utilization of network resources. To recover from these impairments,

we propose an enhancement to BitTorrent which aims to minimize the

time to download the content and at the same time to enforce cooper-

ation among peers. Our solution considers a restricted neighborhood to

reduce routing overhead and to improve throughput, while establishing

few connections to remote peers to improve diversity of pieces. With the

help of extensive NS-2 simulations, we show that these enhancements

to BitTorrent signiﬁcantly improve the ﬁle completion time while fully

proﬁting from the incentives implemented in BitTorrent to enforce fair

sharing.

Keywords: BitTorrent, wireless ad hoc networks, neighbor selection,

piece selection, completion time, fair sharing.

1 Introduction

Wireless ad hoc networks and P2P ﬁle sharing applications are two emerging

technologies based on the same paradigm: the P2P paradigm. This paradigm

This work was supported by the Expeshare (Experience Sharing in Mobile Peer

Communities) Project of the Eureka ITEA programme.

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 189–203, 2008.

Springer-Verlag Berlin Heidelberg 2008

190 M.K. Sbai et al.

aims to establish large scale distributed services without the need for any infras-

tructure. Within this paradigm, users have symmetric roles. The global service is

ensured thanks to their collaboration. In the case of a wireless ad hoc network,

the network is a set of wireless nodes with no central administration or base

station. Nodes in such a network operate both as routers and hosts. Multi-hop

routing approaches are used to ensure connection between distant nodes. For

P2P ﬁle sharing applications, peers collaborate in downloading data and mul-

timedia content. Each peer shares some of its upload capacity by serving other

peers. The global capacity of the system grows then exponentially with the num-

ber of peers. Gnutella [5] and BitTorrent [1] are two examples of P2P content

sharing applications in the Internet.

Both P2P ﬁle sharing applications and wireless ad hoc networks are mature

ﬁelds of research. They have been studied heavily but separately in the literature.

Only few works try to study how they perform together (e.g., [10] [11] [12]). These

works focus on the content lookup problem in wireless ad hoc networks without

studying the eﬃciency of the content sharing itself. Studying the performance

of ﬁle sharing applications over wireless ad hoc networks is challenging because

of the diverse constraints imposed by the use of wireless channels. Indeed, as

nodes are both routers and end-users, the routing overhead must be taken into

consideration. Furthermore, the performance of transport protocols such as TCP

drops seriously when multi-hop paths are used. That is why current topology-

unaware P2P ﬁle sharing applications are not expected to perform well when

deployed over wireless ad hoc networks. Designing eﬃcient ﬁle sharing solutions

for such networks is an important area of research. Indeed, a P2P solution for

ﬁle sharing has diverse advantages over other data dissemination techniques like

multicast in general and this applies to wireless ad hoc networks in particular.

For instance, in case of multicast, the construction and update of the virtual

topology (tree or mesh) is costly in terms of bandwidth consumption namely

in dynamic scenarios. Moreover, the data replication in multicast follows the

virtual topology and so nodes like leaves of a tree only receive data and do not

spend resources to provide it to other nodes. Thus, no fair cooperation is ensured

when using multicast unless constructing a diﬀerent virtual topology (or tree)

per piece of data, which is technically unfeasible.

In this work, we investigate how well a P2P ﬁle sharing solution developed for

the wired Internet performs over a wireless ad hoc network. Our aim is to come up

with a solution that minimizes the content download time while at the same time

improving collaboration by enforcing fair sharing among peers. As eﬃcient and

fair content sharing is targeted, we choose to adapt BitTorrent [1] as a ﬁle sharing

protocol given its large usage and its known close to optimal performances in the

wired Internet [13]. When data is distributed using BitTorrent, interested peers

supply pieces of the data to other peers, reducing the burden on any individual

peer, providing redundancy in the network, and reducing dependency on the

original seed. In addition, BitTorrent implements incentives that encourage peers

to collaborate in downloading the content, which is not the case of multicast-tree

based solutions.

Adapting BitTorrent to Wireless Ad Hoc Networks 191

In a ﬁrst eﬀort to understand this problem, we consider the particular case

when every ad hoc node is interested in downloading the content. In this case,

the underlying topology has a big impact on the performance of BitTorrent. In-

deed, any piece sent over a suboptimal route will cause resource consumption in

all intermediate nodes. When all nodes are peers, this will aﬀect all peers located

on these nodes by stealing bandwidth from them without being able to proﬁt from

this transmission since it happens at the routing layer. However, if intermediate

nodes are not peers interested in the same content, this suboptimal piece trans-

mission will have less impact on the torrent itself since it does not directly steal

bandwidth from peers (it will steal bandwidth from other applications however).

Add to this the fact that when all nodes are peers, the traﬃc generated by the

torrent is maximal and an optimization is further required. We aim at well un-

derstanding this case and proposing an eﬃcient solution for it before moving into

less loaded scenarios in future work namely the scenario where only a part of the

nodes are peers. The performance evaluation is done through extensive NS-2 sim-

ulations using regular modules for the ad hoc routing and wireless medium and

our implementation of BitTorrent in NS-21.Our main contributions can be sum-

marized as follows. Ordinary BitTorrent establishes TCP connections with neigh-

bors independently of their location. This choice of neighbors can lead to slow

TCP connections due to long multi-hop paths and routing overhead. Sharing can

also be bad when using large pieces since complete pieces cannot be sent too far

to be reused later by other peers. A ﬁrst solution is to limit the scope of the neigh-

borhood. In this case, we noticed shorter download times but poor sharing since

there is no diversity of pieces in the network. To recover from these impairments,

we propose an enhanced variant of BitTorrent, tuned to ad hoc networks, which

considers a restricted neighborhood to diminish routing overhead and to improve

throughput, while establishing few connections to remote peers to improve di-

versity of pieces. To implement this, we modify the choking algorithm and add

a new piece selection strategy. The simulations show that these enhancements to

BitTorrent considerably improve the ﬁle completion time while fully beneﬁting

from the incentives implemented in BitTorrent to enforce fair sharing.

Section 2 of this paper presents an overview of the state of the art in de-

ploying P2P solutions over wireless ad hoc networks. Section 3 describes brieﬂy

the BitTorrent protocol. The framework of the study is discussed in Section 4.

Section 5 shows the importance of the piece size in determining the performance

of BitTorrent. Section 6 studies the impact of the scope of the neighborhood.

Section 7 presents our enhanced variant of BitTorrent. Section 8 summarizes the

work and gives some ideas on our future work.

2 State of the Art

In this section, we present an overview of the state of the art of P2P ﬁle sharing

applications and their diﬀerent implementations in wireless ad hoc networks.

1NS-2 code and scripts at: http://planete.inria.fr/personnel/

Mohamed Karim.Sbai/BitTorrent/AdaptedBitTorrent.htm

192 M.K. Sbai et al.

P2P applications in the Internet: There are several design approaches for

the construction of P2P overlays over the Internet. One can distinguish be-

tween structured and non-structured overlays. This classiﬁcation is done from

the standpoint of resources lookup. In non-structured overlays like Gnutella [5],

there is no control on the structure of the overlay. Peers discover each other by

ﬂooding the network and by learning from previous sessions. The P2P applica-

tion in this case is not conscious of the topological location of the other peers.

In case of structured overlays, an overlay routing algorithm is introduced to lo-

cate the content in the network. Several structured overlay networks have been

proposed like CAN [6], Chord [7], Pastry [9] and Tapestry [8]. All of them use

Distributed Hash Tables (DHT) in their routing of lookup requests. Such tables

allow the lookup to scale logarithmically with the number of nodes in the overlay.

Again most of these structured overlays are topology independent. On the other

hand, there is BitTorrent [1] that does not concentrate on the information lookup

since it uses a centralized tracker to discover neighbors. However, it concentrates

on optimal utilization of the network capacity when sharing the ﬁle between the

diﬀerent interested peers. Since we are mainly concerned in this work by the

data transfer plane, we adopt BitTorrent and we extend it to wireless ad hoc

networks. More details on BitTorrent are presented in Section 3.

P2P applications in Mobile Ad hoc NETworks: Both structured and non-

structured overlays have been implemented in MANET. Since nodes are both

end-users and routers, some cross-layer design approaches have been introduced.

These approaches suppose that P2P applications operate both at the network

layer and at the application layer. One can divide the design space into four

subspaces:

–Non-structured and layered design: Oliviera et al. study in [10] the perfor-

mance of Gnutella deployed over three ad hoc routing protocols DSR, AODV

and DSDV. Their results show that the ratio of delivered packets is lower

than those of unicast applications deployed over MANET. This is due to the

fact that Gnutella chooses neighbors independently of their locations. The

overlay construction is topology independent.

–Non-structured and cross-layer design: The work done by Klemm et al. in [11]

proposes to integrate the peer lookup mechanism of a P2P application like

Gnutella in the network layer and compares this design to the layered design

proposed by Oliviera et Al. They propose ORION that establishes connec-

tions on demand through the routing mechanism. The cross-layer lookup

implemented by ORION is shown to provide higher successful transfers ra-

tio than in the layered scenario.

–Structured and layered design: A proximity-conscious DHT (Pastry) has

been deployed over the DSR routing protocol in [12]. As it is a layered

design, there is no interaction between the DHT and the routing protocol.

This leads to an overhead in maintaining routes for both the application

layer and the network routing layer.

–Structured and cross-layer design: This design is named Ekta by Das et al.

in [12]. The functionalities of the Pastery DHT are integrated within the

Adapting BitTorrent to Wireless Ad Hoc Networks 193

routing protocol. The main idea is the mapping of the peer identiﬁers in

the same namespace than the IP addresses. Their results show that Ekta is

better than the layered design in terms of number of successfully delivered

packets.

Former studies on BitTorrent over wireless ad hoc networks: Several

works tried to adapt BitTorrent to wireless ad hoc networks (e.g. [14] and [15]).

They only focus on the tuning of the peer discovery phase without addressing

the eﬃciency of the content sharing itself. Michiardi et al. study in [4] the per-

formance of a cooperative mechanism to distribute content from one source to

a potentially large number of destinations. They propose to deploy BitTorrent

with a minor change allowing neighbor discovery and traﬃc locality. This is done

by selecting only near neighbors as eﬀective neighbors. The result is a decrease

in the total download time and energy consumption. Their work is relevant to

ours; however we go beyond by focusing not only on the download time but also

on the sharing among peers which will show to suﬀer if pieces are only exchanged

with close neighbors. The solution we propose in this work is able to improve

the sharing ratio and the completion time simultaneously.

3 BitTorrent: A Content Distribution Protocol

BitTorrent (see e.g., [1], [13]) is a scalable P2P content distribution protocol.

Each client shares some of its upload bandwidth with other peers interested in

the same content in order to increase the global system capacity. Peers coop-

erating to download the same content form a torrent. A peer discovers other

peers by contacting a central rendezvous node called tracker. The latter stores

IP addresses of all peers in the torrent and maintains statistics on uploads and

downloads per peer. To facilitate the replication of the content in the network

and to ensure multi-sourcing, a ﬁle is subdivided into a set of pieces. Each piece

is also subdivided into blocks. A peer which has all pieces of the ﬁle is called seed.

When the peer is still downloading pieces, it is called leecher. Each peer main-

tains a peer list. Neighbors are those of this list with whom the peer can open a

TCP-connection to exchange data and information. Only four simultaneous out-

going active TCP connections are allowed by the protocol. The corresponding

neighbors are called eﬀective neighbors. They are selected according to the chok-

ing algorithm of BitTorrent. This algorithm is executed periodically. Once the

choking period expires, a peer chooses to unchoke the 3 peers uploading to him

at the highest rate. It is a best slot unchoking. This strategy, called tit-for-tat,

ensures reciprocity and enforces collaboration among peers. Now to discover new

upload capacities, a peer chooses randomly a fourth peer to unchoke. This un-

choking slot is called optimistic slot. All other neighbors are left choked. When

unchoked, a peer selects a piece to download using a speciﬁc piece selection

strategy. This strategy is called local rarest ﬁrst. Indeed, each peer maintains an

update-to-date list of pieces owned by all its neighbors. When selecting a piece,

a peer chooses the piece with the least redundancy in its neighborhood. In case

194 M.K. Sbai et al.

of equality, one of the rarest pieces is chosen randomly. Rarest ﬁrst is supposed

to increase the entropy of pieces in the network which enforces collaboration and

hence improves global performance.

Here are the performance metrics relevant to BitTorrent that we will use in

our study and that are calculated at the end of the experimentation:

–Uij : Total bytes uploaded by peer ito peer j.

–Dij : Total bytes downloaded by peer ifrom peer j.(Uij =Dji)

–Rij : Ratio of sharing between peer iand peer j.

Rij =min(Uij ,D

ij )

max(Uij ,D

ij )(1)

–Ni: Number of neighbors jof peer isuch that Uij =0orDij =0.

–Ri: Sharing ratio for node i.

Ri=1

.

j|Uij =0 or Dij=0

Rij (2)

–Fi: The ﬁnish time of peer i. It is the time by which it receives all pieces of

the ﬁle.

As we are studying BitTorrent over wireless ad hoc networks where topology

matters, we consider some additional performance metrics related to topological

positions of peers. The ﬁle is supposed to exist at one seed S at the beginning

of the session. Our metrics quantify the quality of service perceived by peers as

a function of their relative positions with respect to the seed.

–Fh: Average ﬁnish time of peers (or nodes) located at hhops from seed S.

Fh=1

.

i|H(i)=h

Fi(3)

where nhis the number of peers located at hhops from seed S and H(i) a

function that gives the number of hops between any node iand the seed S.

–Rh: Average sharing ratio of peers (or nodes) located at hhops from seed S.

Rh=1

.

i|H(i)=h

Ri(4)

4 Framework of the Study

We proceed with an experimental approach using the NS-2 simulator. In this

section, we describe preliminary changes we made to BitTorrent to allow peer

discovery and the exchange of signaling over wireless ad hoc networks. Then, we

discuss the stack of protocols we use in our deployment of BitTorrent in NS-2.

Finally, we introduce the scenario used in our evaluation.

Adapting BitTorrent to Wireless Ad Hoc Networks 195

4.1 Trackerless BitTorrent

Wireless ad hoc networks are infrastructureless. It is convenient that one does

not rely on a centralized tracker when applying BitTorrent to such networks. So,

we opt in our study for a trackerless approach. Since the most important role of

a tracker in the Internet is to provide peers with the identiﬁers of other peers, we

need to introduce a peer discovery mechanism. In our evaluation framework, to

discover new peers, a peer ﬂoods periodically the network with a HELLO message

and waits for HELLO REPLY messages. HELLO messages are transmitted to

wireless neighbors with some initial TTL (Time-To-Live) to control the scope

of the ﬂood and hence the visibility of a peer. This TTL is a parameter of our

study. Receiving a HELLO message, a peer decrements the TTL and forwards

it to its wireless neighbors, and so on. The message is not forwarded when its

TTL reaches zero.

4.2 Stack of Protocols and Packets Exchanged between Peers

In BitTorrent, peers exchange two types of packets: Data packets and control

packets. We choose in our NS-2 implementation to send data packets via TCP

connections because reliability and congestion control are needed when trans-

porting blocks of ﬁle. However, control packets as for peer discovery and piece

updates contain small and urgent information that is better to transport using

UDP. Here are the diﬀerent control packets exchanged between peers:

– HELLO: see Section 4.1.

– HELLO REPLY: see Section 4.1.

–UPDATEPIECELIST: when a peer receives a new piece, it sends an

UPDATE PIECE LIST to all peers with whom it can exchange data.

– PIECE OFFER REQUEST: when a peer i unchokes a peer j, it sends

a PIECE OFFER REQUEST packet to j. This packet contains the list of

pieces that i has already downloaded.

– PIECE OFFER REPLY: receiving a PIECE OFFER REQUEST, a peer

answers with a PIECE OFFER REPLY packet. After applying the piece

selection strategy, it decides whether to accept or to reject the oﬀer. A ﬂag

included in the PIECE OFFER REPLY packet indicates this decision (AC-

CEPT or REJECT). In the case the oﬀer is accepted, the peer indicates

the number of the requested piece. During the choking period, many PIECE

OFFER REPLY packets can be sent to the oﬀering peer in order to allow

the transmission of several pieces.

4.3 The Main Scenario

We consider a network of N nodes (N=40 when not speciﬁed) distributed in a

plane following a grid topology (10 nodes per row). The distance between two

physical neighbors is set to 40 m for a range of wireless transmissions equal to

50m. This ensures connectivity while minimizing interference. At the beginning

of each simulation, node 0 located at the top left is the seed and the other nodes

196 M.K. Sbai et al.

Fig. 1. Average ﬁnish time as a function

of number of hops to seed

Fig. 2. Average sharing ratio as a func-

tion of number of hops to seed

are leechers. The ﬁle size is set equal to 10 Mbytes, which is large enough to en-

sure the convergence of the protocol to equilibrium. All peers start downloading

the ﬁle at the same time t=1500s by ﬁrst looking for each other then sharing

the pieces of the ﬁle according to the BitTorrent algorithms. This time interval

skipped at the beginning gives the network enough time to stabilize and calcu-

late its routing tables. The bitTorrent choking algorithm period is taken in our

simulations equal to 40s. A piece is subdivided into blocks of size 1KB. Con-

cerning the underlying layers, the nodes connect to each other using the 802.11

MAC Layer with the RTS/CTS-Data/ACK mechanism enabled. The data rate

is set to 1 Mb/s. For ad hoc routing, we use the DSDV proactive protocol.

5 Impact of Piece Size

We start by evaluating regular BitTorrent where the overlay is constructed with-

out considering the underlying wireless topology. We give a particular attention

to the piece size and to its impact on both the ﬁnish time of peers and their shar-

ing ratios. The reason to consider the piece size is that it decides how far pieces

can be sent over the network. The TTL of HELLO messages is set to its maxi-

mum value so that all peers are neighbors of each other. Two sizes of pieces are

used while keeping constant the size of the ﬁle. We consider respectively the val-

ues 100 blocks and 1000 blocks for small and big size of pieces. Figure 1 plots the

average ﬁnish time Fhas a function of the number of hops hto the seed for both

small and large size of pieces. Each point in this ﬁgure is an average over multiple

simulations and over all nodes located at the same number of hops to the seed.

As expected, the ﬁnish time increases as far as we move away from the source.

One can notice in the ﬁgure that for small pieces, remote peers have better ﬁn-

ish time than for large pieces. This is because the range of transmission of small

pieces is longer. A remote peer can then receive more pieces in the choking period

and share them with others, which improves the reusability of pieces and network

resources. This is conﬁrmed in Figure 2 where we plot the average sharing ratio

Rhas a function of the number of hops to the seed. It is clear that the sharing

ratio in case of small pieces is more important because distant nodes (or peers)

Adapting BitTorrent to Wireless Ad Hoc Networks 197

Fig. 3. Average ﬁnish time as a function

of number of hops to seed for diﬀerent

ﬂooding scope

Fig. 4. Average sharing ratio as a func-

tion of number of hops to seed for diﬀer-

ent ﬂooding scope

can now get quickly complete pieces and replicate them in their neighborhood.

Unfortunately, this is not the case with large pieces. Large pieces cannot be sent

far in the choking period so they propagate in the network as a wave resulting

in an under-utilization of network capacity. One can see the case of large pieces

as being the absence of sharing between distant nodes and the fact that nodes

wait for pieces to arrive to their upstream nodes before obtaining them. The use

of small pieces however make the pieces spread over the network, which reduces

the ﬁnish time and makes the sharing incentives implemented by BitTorrent work

better in wireless ad-hoc networks. Our solution supports this modiﬁcation.

6 Impact of the Scope of the Neighborhood

Another important factor in BitTorrent over wireless ad hoc networks is the

scope of the neighborhood. In this section, we study the impact of reducing

this scope on both the ﬁnish time and the sharing ratio. We run several simu-

lations on the topology described in 4.3 changing each time the ﬂooding scope

(TTL) of HELLO messages destined to peer discovery. Figure 3 compares the

ﬁnish time for TTL=max, 5, 2 and 1. Interestingly, the ﬁnish time improves

when the neighborhood scope is decreased. This is mainly due to better TCP

performance over short paths and to smaller routing overhead. Control packets,

namely PIECE UPDATE and HELLO packets, are sent only in the restricted

neighborhood. The case TTL=2 is slightly better than the case TTL=1 because

of the interference between physical neighbors. Figure 4 plots the average shar-

ing ratio Rhas a function of the number of hops to the seed for the diﬀerent

values of TTL. Unfortunately, we can see that the improvement in ﬁnish time

when reducing the neighborhood comes at the expense of a lower sharing ratio.

The diversity of pieces in the network decreases and the ﬁle propagates more or

less as a wave in a unique direction from the seed to the farthest nodes. Hence,

distant peers can not participate in the replication of pieces, they only wait for

pieces to arrive to their physical neighbors to obtain them. Clearly, this is bad

for cooperation among peers. An optimal solution should improve the ﬁnish time

while preserving large values for the sharing ratio.

198 M.K. Sbai et al.

7 BitTorrent Adapted to Wireless Ad Hoc Networks

The main objective of our variant of BitTorrent is to proﬁt from the advan-

tages of the limited neighborhood, namely the good performance of TCP on

short paths, the reduced routing overhead, and the reduced load of ﬂooding con-

trol packets. At the same time, we aim at improving the sharing ratio and the

reusability of network resources by creating diversity of pieces in the network.

Our main idea is to create few TCP connections to distant peers in addition to

those with close peers. Pieces can then spread over the network and propagate

in diﬀerent directions, which improves the sharing and the download completion

time. With this modiﬁcation, several zones of the network can be active simulta-

neously, which is not the case of the wave generated by regular BitTorrent with

limited neighborhood. To implement this idea, we tune BitTorrent to support the

distinction between remote and close peers. The new choking algorithm is aware

of the location of peers by using routing information. It distributes optimistic

unchokes between remote and close peers and adds a speciﬁc neighbor selection

mechanism to select a distant peer. It also applies a new piece selection strat-

egy when the peer oﬀering the piece is distant. Unlike BitTorrent with limited

neighborhood, this modiﬁcation requires a global knowledge about the identi-

ﬁers of peers in the network. We propose that each peer maintains two neighbor

tables: NEARBY NEIGHBORS TABLE (NNT) and FAR NEIGHBORS TA-

BLE (FNT). When discovering new peers, neighbors whose number of hops is

less than or equal to 2 are added to NNT. Other peers belong to FNT. The

PIECE UPDATE packets are sent only to neighbors in NNT. Peers do not need

to know about all pieces in the network as their piece selection strategy operates

only on their NNTs. Indeed, in wireless networks, the replication of pieces is

more eﬃcient when it is based on statistics in the close neighborhood since this

guarantees a faster local replication compared to when statistics are based on a

large neighborhood. As in BitTorrent, when the choking algorithm is executed,

three best uploaders are selected as eﬀective neighbors. These three neighbors

are chosen from both nearby and far neighbor tables. The peer then serves these

three neighbors during the next choking period. But in addition to these eﬀec-

tive neighbors, the peer selects a fourth random neighbor from one of the two

tables (optimistic slot). The table from which it selects the neighbor is decided

by a round robin policy that guarantees an optimal balance between the random

unchokes locally and the transmission of pieces to distant neighbors in order to

improve diversity. For a succession of optimistic unchokes, the peer selects a peer

one time from FNT, qtimes from NNT and so on. In our protocol, the quan-

tum qrepresents the ratio of the number of time slots spent on serving nearby

neighbors and those for serving far neighbors. It is also the number of slots that

a peer should wait before unchoking a distant neighbor again. Our simulations

indicate that the choice of this quantum is fundamental in deciding the perfor-

mance of our solution. Furthermore, the strategies of selecting pieces proposed

by distant neighbors and selecting eﬀective neighbors from FNT should diﬀer

from the ordinary strategies applied by BitTorrent because the objective of our

version of BitTorrent in unchoking far peers is mainly to improve diversity. The

Adapting BitTorrent to Wireless Ad Hoc Networks 199

next paragraphs explain the diﬀerent selection strategies we implement in our

solution. The following ones study the performance of the enhanced BitTorrent

and discuss the choice of the quantum q.

7.1 Selecting a Far Neighbor at Random

When a regular BitTorrent client decides to optimistically unchoke a peer, it

selects it at random with a uniform probability. In wireless networks however,

the gain we get from optimistic unchoking in terms of diversity increases with

the number of hops. So a peer has more interest in unchoking a farther peer than

another one closer to it. Thus, in our adapted version of BitTorrent, to select a

far peer to unchoke from FNT, the peer starts by selecting the number of hops

to that peer with a probability that increases linearly with the number of hops.

Let hmbe the maximum number of hops seen by the peer. We suppose that

FNT contains only peers at hmand hm−1 hops. These are the farthest peers

that if we send pieces to them, we are sure of having the largest gain in terms

of diversity and reutilization of network resources.2It follows that the number

of hops is ﬁrst selected using a probability function pgiven by this formula:

p(h)= h

hm+(hm−1) if h≥hm−1

0else

When the number of hops his chosen, the peer then selects, in a uniform random

way, a peer among those located at hhops from it as the peer to optimistically

unchoke.

7.2 Selecting a Nearby Neighbor at Random

When the peer needs to select a nearby neighbor, it chooses a node from NNT in

a uniform random way. A nearby neighbor is supposed to replicate the pieces it

receives in its two-hop limited neighborhood3. This replication is fast since the

TCP protocol has a good throughput over short paths.

7.3 Piece Selection Strategy When the Oﬀering Neighbor Is Far

When receiving a piece oﬀer from a P2P neighbor, the peer checks the number

of hops to the oﬀering neighbor. If it is greater than 2, it considers that it is an

oﬀer from a far node. In this case, a speciﬁc piece selection strategy is applied in

order to select the best piece to download from this node. This strategy will be

called the absent piece strategy. The peer ﬁrst computes the redundancy of the

oﬀered pieces in its close neighbors table and in its piece pool. At the opposite

2We add peers at hm−1hops to FNT in order to reduce the load on the one or few

peers located at hmhops.

3We form NNT using two-hop neighborhood because according to results in Section 6,

this leads to slightly better ﬁnish time and sharing than if limiting the neighborhood

to only one hop.

200 M.K. Sbai et al.

of BitTorrent, the candidate pieces will be those with zero redundancy (no need

to download a piece from a distant node if it exists at less than two hops). So a

piece can be accepted only if neither the peer nor one of its near neighbors has

downloaded it before. In case of multiple absent pieces, one piece among them

is chosen in a uniform random way. The absent piece can then be replicated

quickly in the near neighborhood. If no absent piece is noticed, the peer sends

a REJECT in the piece oﬀer reply packet. In summary, our solution supposes

that it is better to download a piece existing in the nearby neighborhood from a

nearby neighbor. Only absent pieces are taken from far neighbors so as to reduce

the routing overhead. This strategy is fundamental for getting good performances

with our variant of BitTorrent.

7.4 Piece Selection Strategy When the Oﬀering Neighbor Is Near

Local rarest ﬁrst is used when the peer receives a piece oﬀer from one of its nearby

neighbors. Pieces with the least number of copies in the close neighborhood are

selected. This is the normal behavior of the standard version of BitTorrent but

only applied in the two-hop neighborhood. Here the throughput of TCP is good

and the routing overhead is almost inexistent so we can allow ourselves to apply

the rarest ﬁrst policy that guarantees the fast replication of pieces.

7.5 Simulation Results

To study the performance of our solution, we run several NS-2 simulations over

the previously described topology. We vary the values of the quantum qand ob-

serve the behavior of the download ﬁnish times of peers and their sharing ratios.

Figure 5 compares ﬁnish time of ordinary BitTorrent with limited neighborhood

(TTL = 2) with our version of BitTorrent using diﬀerent values of the quantum

q(q=3, 2 and 1). Each curve presents the average ﬁnish time Fhas a function of

the number of hops to the seed. Recall that the role of qis to balance optimistic

unchokes between close and remote peers. The larger the q, the smaller the num-

ber of unchokes to remote peers. The ﬁnish time for our solution is better and

more equally distributed since far nodes can receive pieces from the beginning

of the session and can replicate them in their close neighborhoods. Our solution

limits the number of pieces sent to far nodes in order to reduce the routing

overhead. This creates parallel areas of activity in the network. Far nodes do

not need to wait for pieces to arrive to their neighborhoods to download them.

Hence, pieces propagate in the network in all directions. This observation is il-

lustrated in Figure 6 which compares sharing ratios of ordinary BitTorrent with

limited neighborhood (TTL=2) with our variant of BitTorrent using diﬀerent

values of the quantum. Each curve presents the average sharing ratio Rhas a

function of number of hops to the seed. Figure 6 shows that the strategies used

in our solution increase considerably the sharing ratios of all peers. This is due

to the diversity created by sending original pieces to distant nodes. So, sharing

incentives work well in this context and the distribution is less vulnerable to

the selﬁshness of some nodes. Our results also show that a quantum equal to 1

Adapting BitTorrent to Wireless Ad Hoc Networks 201

Fig. 5. Average ﬁnish time for our en-

hanced BitTorrent compared to ordinary

BitTorrent with limited neighborhood

Fig. 6. Average sharing for our enhanced

BitTorrent compared to BitTorrent with

limited neighborhood

gives a better ﬁnish time and a better sharing ratio in our setting. Clearly, the

performance of our solution depends on the choice of the quantum q. This choice

is treated in the next section.

7.6 Optimal Choice of the Quantum q

In this paragraph, we establish an empirical formula for qand then validate it

through simulations. Let hmbe the maximum length of a path between two

nodes in the network. Let αibe the number of pieces that can be sent during a

choking slot to a node located at ihops. The objective of our balanced optimistic

unchoking strategy is to send a copy of each piece to the end of the network and

wait for it to return to the middle of the network. Forward and backward pieces

meet then in the middle of the network, which guarantees the best gain. If there

were only one piece in the ﬁle, only one seed and the content is sent to the farthest

node, the piece will take approximately hm

2slots to return to the middle of the

network. Now when the ﬁle contains several pieces, the node should wait αhm

α1.hm

before unchoking the farthest node again. It is the number of slots needed for

the αhmpieces to return to the middle of the network hop by hop. Now, if all

peers in the network are interested in the content and if we assume nodes to

be uniformly distributed in the plane, N

2nodes at maximum can participate in

sending pieces to the farthest node. So one needs to increase the waiting time

by a factor of N

2. So, the formula approximating qwill be:

q=αhm

α1

.hm

2.N

2(5)

To validate this formula, we vary the number of nodes and observe how this

impacts the optimal choice of q. We plot optimal qas a function of the number

of nodes N. Simulations are done on grid topologies with N=20 to 100. Figure 7

plots the average ﬁnish time over all nodes as a function of the chosen quantum

qfor 40 nodes and 80 nodes (curves for all values of Nare not included for clarity

of presentation). Figure 8 plots both the computed and simulation results for

202 M.K. Sbai et al.

Fig. 7. Average ﬁnish time as a function

of the chosen quantum

Fig. 8. Best quantum as a function of the

number of nodes

best q.Thevaluesofαhmand α1are taken from simulations in both curves.

Even though our expression for qis simple and approximate; we can see a good

match between the two curves. In the ﬁgure, simulation values of the best qare

rounded integer values of theoretical ones. Thus, the above formula describes

well the behavior of the optimal qwhen number of nodes varies. One can notice

that this quantum increases with N, which means less pieces sent by each peer

to remote peers for larger networks.

8 Conclusions and Perspectives

P2P data sharing applications in wireless ad hoc networks should provide good

quality of service to their users in terms of ﬁnish time and sharing. There is

a high potential for these applications but unfortunately, the wireless nature

of the network imposes many constraints to be taken into consideration before

using regular applications tuned for the wired Internet. Solutions that reduce

neighborhood scope allow better ﬁnish time than those with random graphs

of communications. Nevertheless, limiting the neighborhood is shown, in this

paper, to be dangerous in terms of reducing sharing ratios between peers. The

solution we propose in this paper ﬁnds a good management of neighbor and piece

selection that reduces ﬁnish time and encourages sharing. A peer concentrates

on its nearby peers with few connections to far ones. When far neighbors are

selected, a special piece selection strategy named absent piece strategy comes

into eﬀect. Simulation results show a decrease in service time and a great improve

in sharing ratios. Our future work will be on adapting our solution to mobile

scenarios. High dynamicity of such networks will open the way to new interesting

problems.

References

1. BitTorrent protocol, http://wiki.theory.org/BitTorrentSpecification

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3. Ding, G., Bhargava, B.: Peer-to-Peer File-Sharing over Mobile Ad hoc Networks.

In: IEEE PERCOM-W, Orlando, USA (2004)

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4. Michiardi, P., Urvoy-Keller, G.: Performance analysis of cooperative content dis-

tribution for wireless ad hoc networks. In: WONS 2007, Obergurgl (2007)

5. The Gnutella speciﬁcation (2000),

http://dss.clip2.com/GnutellaProtocol04.pdf

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addressable networks. In: ACM SIGCOMM (2001)

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scalable peer-to-peer lookup service for internet applications. In: ACM SIGCOMM

(2001)

8. Zhao, B.Y., Kubiatowicz, J.D., Joseph, A.D.: Tapestry: an infrastructure for fault-

resilient wide-area location and routing. T.R. UCB//CSD-01-1141, U.C.Berkeley

(2001)

9. Rowstron, A., Druschel, P.: Pastry: scalable, diributed object location and routing

for large -scale peer-to-peer systems. In: Guerraoui, R. (ed.) Middleware 2001.

LNCS, vol. 2218. Springer, Heidelberg (2001)

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under a peer-to-peer application. In: WCNC (2003)

11. Klemm, A., Lindermann, C., Waldhorst, O.: A special-purpose peer-to-peer ﬁle

sharing system for mobile ad hoc networks. In: VTC (2003)

12. Das, S.M., Pucha, H., Hu, Y.C.: Ekta: an eﬃcient peer-to-peer substrate for dis-

tributed applications in mobile ad hoc networks. TR-ECE-04-04, Purdue University

(2004)

13. Legout, A., Urvoy-Keller, G., Michiardi, P.: Rarest First and Choke Algorithms

Are Enough. In: IMC 2006, Rio de Janeiro (2006)

14. Nandan, A., Das, S., Pau, G., Gerla, M.: Cooperative downloading in vehicular ad

hoc networks. In: WONS, Washington, USA (2005)

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Ad hoc Networks. In: MOBIQUITOUS, San Jose, USA (2006)

Optimal Gathering Algorithms

in Multi-hop Radio Tree-Networks ith

Interferences

Jean-Claude Bermond1, and Min-Li Yu2,

1MASCOTTE, joint project CNRS-INRIA-UNSA,

2004 Route des Lucioles, BP 93, F-06902 Sophia-Antipolis, France

bermond@sophia.inria.fr

2University College of the Fraser Valley, Department of Mathematics and Statistics,

Abbotsford, BC, Canada V2S 4N2

joseph.yu@ucfv.ca

Abstract. We study the problem of gathering information from the

nodes of a multi-hop radio network into a pre-deﬁned destination node

under the interference constraints. In such a network, a message can only

be properly received if there is no interference from another message

being simultaneously transmitted. The network is modeled as a graph,

where the vertices represent the nodes and the edges, the possible com-

munications. The interference constraint is modeled by a ﬁxed integer

dI≥1, which implies that nodes within distance dIin the graph from

one sender cannot receive messages from another node. In this paper, we

suppose that it takes one unit of time (slot) to transmit a unit-length

message. A step (or round) consists of a set of non interfering (compat-

ible) calls and uses one slot. We present optimal algorithms that give

minimum number of steps (delay) for the gathering problem with buﬀer-

ing possibility, when the network is a tree, the root is the destination

and dI= 1. In fact we study the equivalent personalized broadcasting

problem instead.

1 Introduction

1.1 Problem Statement

The problem we consider in this paper was motivated by a question asked by

France Telecom about “how to provide Internet connection to a village”

(see [6]) and is related to the following scenario. Suppose we are given a set

of communication devices placed in houses in a village (for instance, network

interfaces that connect computers to the Internet). They require access to a

Partially supported by the CRC CORSO with France Telecom,bytheEuropean

FET project AEOLUS, and by the INRIA associated team RESEAUXCOM with

S.F.U.

 Partially supported by the Natural Sciences and Engineering Research Council of

Canada and by the INRIA associated team RESEAUXCOM with S.F.U.

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 204–217, 2008.

Springer-Verlag Berlin Heidelberg 2008

Optimal Gathering Algorithms 205

gateway (for instance, a satellite antenna) to send and receive data through a

multi-hop wireless network. In this network, the devices communicate exclusively

by means of radio transmissions, referred to as calls. A call involves a message

and two devices, the sender and the receiver. The communication is subject to

the following technological constraints:

Reachability constraint: In order to be reached by a call, the receiver of this

call must be within reachability distance of the sender.

Interference constraint: A call may interfere with calls that are in the neigh-

borhood of the receiver, or a message can be properly received only if no

other senders are in the neighborhood of the receiver.

t-gathering problem: Suppose each device of the network has a piece of infor-

mation. The t-gathering consists of collecting (gathering) all these pieces of

information into a special device t, called the gathering node,bythemeansof

calls subject to the two constraints described before. The t-gathering prob-

lem is to realize such a constrained gathering without concatenating mes-

sages and with the minimum delay.

An equivalent formulation is the so-called.

s-personalized broadcast:Here a single device (the gateway in the problem

of France Telecom) called source shas a diﬀerent piece of information to

broadcast to every other device in the network by the means of calls subject

to the two constraints described before. The s-personalized broadcast is to

realize such a constrained gathering without concatenating messages and

with the minimum delay.

A slight variation of this problem has received much attention in the context

of sensor networks. In such networks, each device contains a sensor and the

gathering problem corresponds to the situation where information collected at

each sensor has to be gathered to a single central device (base station). However,

most of the articles are concerned with minimizing the energy consumption and

allow aggregation of data. The work which is most related to ours is [11], in

which reachability and interference constraints are also assumed, but most of its

results apply for the case of directional antennas.

1.2 Model and Assumptions

According to the model adopted in [2], the network described above is represented

by an undirected graph G=(V,E), where Vis the set of nodes, each of which rep-

resenting a communication device, and Eis the set of edges, representing the pairs

of nodes involved in possible calls. There is a special pre-deﬁned node scalled the

source (sink in the gathering case). Let dG(u, v) indicate the distance in G,de-

ﬁned as the length of a shortest path between uand v. We model the reachability

and the interference constraints by two positive integers, respectively dT≥1and

dI≥dT.AnimportantcaseisdT= 1, which means that a node is able to com-

municate only with its neighbors in the graph (or equivalently Gis the commu-

nication graph). The second parameter dImodels the interference constraint as

206 J.-C. Bermond and M.-L. Yu

follows: if a receiver is within distance dIfrom a sender, then this node cannot re-

ceive any other message. If usends a message mto v, then the call (u, v )interferes

with every node w∈Vsuch that dG(u, w)≤dI. Two calls are said to be com-

patible if they do not interfere with each other (otherwise, they are incompatible).

More precisely, two calls (s1,r

1)and(s2,r

2), for r1,r

2,s

1,s

2∈V,arecompati-

ble if dG(s1,r

2)>d

Iand dG(s2,r

1)>d

I. Observe that one of the consequences

of the interference constraint is that s1=r2and s2=r1, which implies that a

node is not able to send and receive messages simultaneously. A step (round)isa

set of compatible calls. We assume that every occurrence of a call takes one unit

of time (or one slot) and involves a one unit-length message.We also assume that

buﬀering is possible in intermediate nodes.

In this paper, our aim is to ﬁnd eﬃcient algorithms that give optimal solutions

for the s-personalized broadcast problem when dT=dI=1andGis a tree.

1.3 Related Work

The broadcasting and gossiping problems have been widely studied for wired

networks (see [15]), including models that assume no concatenation of messages

(see [4]). For radio networks, the case when dI= 1 is studied only for broadcast-

ing in [10,12] and gossiping in [8,9,14]. Note that broadcasting is diﬀerent from

our problem which is personalized broadcasting, as in the process of broadcast,

the same information has to be transmitted to all the other nodes and so ﬂood-

ing techniques can be used. Recently the gathering problem has gained much

attention. In [2], assuming an arbitrary size of information in each node, a pro-

tocol for general graphs with an approximation factor of at most 4 is presented.

It is also shown that the problem of ﬁnding an optimal gathering protocol does

not admit a Fully Polynomial Time Approximation Scheme if dI>d

T, unless

P=NP,andisNP-hard if dI=dT. In the case where each node has exactly one

unit of information to transmit (or to receive which is the case we consider), the

problem is NP-hard if dI>d

Tbut the complexity is unknown for dI=dT.An

extension of the problem where messages can be released over time is considered

in [7] and a 4-approximation algorithm is presented. In [5], optimal solutions are

provided for the two-dimensional square grid with dT=1.In [1]thecaseofa

path is considered for dT=1and anydI. The problem is solved when the sink

(source) is at one end of the path and only partly solved when the sink is in the

middle of the path.

As mentioned before, sensor networks have been the subject of many papers.

But, most of them deal with minimizing the energy consumption or maximizing

the life time of the sensor network. In [11] they minimize the delay but their

model is slightly diﬀerent from ours as each node is equipped with directional

antennas and no buﬀering capacity is available in the nodes. Furthermore they

only suppose that a node cannot receive and send simultaneously, and more

precisely, this corresponds to the case in our model when dT=1,interfer-

ence distance is zero and each node is not allowed to receive more than one

message at a time. Under their assumptions, they give optimal (polynomial)

gathering protocols for path and tree networks. Their work has been extended

Optimal Gathering Algorithms 207

to general graphs in [13] for unitary messages. In [3], a companion paper to

that one, the same problem as ours is considered, but no buﬀering is allowed.

Finally, another related model can be found in [16], where the authors study the

case in which steady-state ﬂow demands between each pair of nodes have to be

satisﬁed.

1.4 Main Result

In this paper, we deal with the situation when Gis a tree Twith Nvertices

and with a source (or root) sand dT=dI= 1 which can be viewed as a

generalization of the results of [11] and [13]. In their case the only constraint is

that a node cannot receive and transmit at the same time (which can be viewed

as dI= 0). They proved that the minimum number of steps is either N−1or

2n1−1wheren1is the size of the biggest subtree.

Here we need to consider not only subtrees, but also subsubtrees. Indeed, when

dI= 1, two calls in two diﬀerent branches are incompatible only if they have the

same sender. If two calls (s1,r

1)and(s2,r

2) in the same path are incompatible

and the arcs are in the order: s,...,s

1,r

1,...,s

2,r

2,...,thend(r1,s

2)≤1.

Otherwise two calls in the same path are compatible if they are separated by at

least two arcs.

Here we will have roughly three diﬀerent forms of trees. Either the tree looks

like a path with a big sub-sub-tree formed by the vertices at distance ≥2froms,

in which case we will need roughly 3 times the size of this big sub-component. Or

the tree has only a big component but inside this component the sub-components

are somewhat balanced in which case we need roughly 2 times the size of this

big component.In the remaining case (balanced tree an example being a spider

(generalized star) we need N−1steps.

To state more precisely our main result, let assume that deg(s)=m.Letr1,

r2, ..., rmbe the neighbors of s,andTibe the subtree of Twith root ri,where

1≤i≤m.ThesizeofTiis simply |Ti|=ni. Similarly let ri,j be the neighbors

of riand Ti,j be the subtree with root ri,j .ThesizeofTi,j will be denoted by

|Ti,j |=ni,j . Furthermore, we will assume that the Ti,j’s are ordered according

to their sizes. So ni,1=max ni,j

Let Mi=max{2ni−1,n

i+2ni,1−1}. For the rest of the paper, subtrees are

ordered according to the values of Mi:M1≥M2≥M3≥... ≥Mm.Incaseof

equality the order is determined by the sizes.

Theorem 1. When dT=dI=1and T is a tree, the minimum number of steps

to complete a personalized broadcasting ( or gathering) is equal to max{N−

1,M

1+},where=1 if M1=M2and 0otherwise.

Although the lower bound is easy to prove and the minimum time can be ex-

pressed in a simple formula, in order to obtain optimal algorithms many diﬀerent

situations are needed to be considered and a lot of experiments were performed

before the arrival to the ﬁnal optimal algorithms.

208 J.-C. Bermond and M.-L. Yu

2 Lower Bounds and Basic Algorithms

For the rest of the paper we will simply denote by g(T)(insteadofg(T,s,dT,d

used in [2] ) the minimum number of steps required to complete the personalized

broadcast from s (gathering to s) of one unitary message to each node of Tunder

the interference constraint deﬁned by dI=1.

2.1 Lower Bounds

Proposition 1. g(T)≥max{N−1,M

1+}.

Proof. We exhibit diﬀerent sets of incompatible calls which must be scheduled

in diﬀerent steps (or rounds).

Consider the calls on the arcs (s, ri) and they are all incompatible and there

are N−1 of them, as this is the number of messages needed to be sent by the

source. So N−1 is a lower bound for g(T).

Similarly, for each i, the nicalls on the arc (s, ri)andtheni−1arcsleavingri,

are all incompatible. Their number is 2ni−1. So 2ni−1 is a lower bound for g(T).

Consider also the following incompatible calls : those on the arc (s, ri)and

there are niof them, the ni,1calls on the arc (ri,r

i,1), and the ni,1−1onthe

arcs leaving ri,1. Altogether we have ni+2ni,1−1 incompatible calls and this

isalsoalowerboundforg(T).

Hence, Miand therefore M1is a lower bound. If M1=M2, then any algorithm

starts calling one of r1or r2only at step 2 or after, and so it needs at least M1+1

steps.

In the next subsections, we present algorithms that perform personalized broad-

casting, which will give optimal solutions when there is only one subtree and

will also be used for the general case, in particular when there are two subtrees,

by applying them to each subtree. We describe the algorithms for one subtree Ti

rooted in ri.WecallTiatype1subtreeifMi=2ni−1. Otherwise, it is called

a type 2 subtree.

2.2 CASE 1: TiIs a Subtree of Type 1

We ﬁrst present an algorithm for a type 1 subtree Ti. In this case recall that

Mi=2ni−1.

Let Xtdenote the set of vertices to which the source has sent a message before

step t(that is at the end of step t−1) and let Tt

ibe the subtree obtained from

Tiby deleting Xt. Similarly denote by Tt

i,j the component obtained from Ti,j by

deleting the vertices of Xt.Letnt

i=|Tt

i|and nt

i,j =|Tt

i,j |.

The idea of the algorithm is the following: the source sends every odd step to

ria message destinated to a leaf of a big component of Ti, in order to guarantee

that at any step there is no component having more than half of the vertices

(or nt

i,j ≤nt

i/2). Also in two consecutive odd steps, the source will send to

diﬀerent components of Tiin order to be able to do compatible calls eﬃciently

Optimal Gathering Algorithms 209

in even steps in diﬀerent components. We ﬁrst describe the algorithm, then use

an example to illustrate it and ﬁnally we prove that it is valid and takes Mi

steps (which is the lower bound as Mi≥N−1=ni−1).

Algorithm A: Personalized broadcasting for a subtree of type 1

At the beginning X1=∅and T1

i=Ti.

- During an odd step t=2k−1,k=1,2,...,n

Let Tt

i,jkbe the largest component of Tt

inot chosen at the preceding odd step

(that is jk=jk−1)andletxkbe a leaf in this component. The source ssends

the message mkfor xkon the arc (s, ri). Then we update Xt+1 =Xt∪xkand

Tt+1

i=Tt

i−xk.

During the odd steps, both riand the ri,j are inactive.

Finally any vertex at distance ≥3 from the source forwards immediately the

message received at the preceding step except when it is the destination, in which

case the message is stored (if it is mlwith destination xl, then the message is

forwarded to its neighbor on the path to xl).

-Duringanevenstept=2k,k=1,2,...,n

i−1

-risends to ri,jkthe message mkreceived at step 2k−1 with the destination

xkin Tt

i,jk.

-ri,jk−1sends the message mk−1(received at step 2k−2) to its neighbor on

the path to xk−1, except when it is the destination, the message is just stored.

- Any vertex at distance ≥3 from the source forwards immediately the mes-

sage received at the preceding step except when it is the destination, in which

case the message is stored.

Example: Table 2.2 illustrates how algorithm A works when it is applied to the

type 1 tree given in Fig. 1.

r1,3

r1,1r1,2

r1,3

r1,1r1,2

Fig. 1. Fig. 2.

Here, N=9,n1=8andn1,1=4.AsM1=15=2n1−1=n1+2n1,1−1, it

is a type 1 tree. At step 1, ssends a message destinated to a leaf in T1,1(the

largest component), for example x1=b(we could have chosen c). So m1=m(b),

the message destinated to b.Atstep2,r1sends m1to r1,1.Atstep3,ssends a

message destinated to a leaf in the largest component diﬀerent from T3

1,1,namely

210 J.-C. Bermond and M.-L. Yu

Table 1. Personalized broadcasting on the tree in Fig.1 with source susing Algorithm A

step m1m2m3m4m5m6m7m8

1s→r1

2r1→r1,1

3s→r1

4r1,1→a r1→r1,2

5a→b s →r1

6r1,2→d r1→r1,1

7s→r1

8r1,1→a r1→r1,2

9s→r1

10 r1→r1,1

11 s→r1

12 r1,1→c r1→r1,3

13 s→r1

14 r1→r1,1

15 s→r1

1,2and the only choice is x2=d.Atstep4,r1sends to r1,2m2=m(d)and

r1,1sends m1to a(its neighbor on the path to b). At step 5, ssends a message

destinated to a leaf in T5

1,1(the largest component), for example x3=a(we

could have chosen c). Also a, which is at distance 3 from s,forwardsm1to b

where it is stored. The other steps are described in table 2.2: we have x4=r1,2

(we could have chosen r1,3), x5=c,x6=r1,3,x7=r1,1and x8=r1. Therefore,

m1=m(b), m2=m(d), m3=m(a), m4=m(r1,2), m5=m(c), m6=m(r1,3),

m7=m(r1,1)andm8=m(r1).

Proposition 2. Algorithm A is valid, i.e. all the calls are compatible.

Proof. Consider a call with a sender sand it happens in an odd step. As riand

ri,j are inactive, only the source is sending among the vertices at distance at

most 2 from sand so this call is compatible with the others calls whose senders

are at distance ≥3.

Now consider a call with a sender rianditmusthappeninanevenstep.

Suppose it is a call done at step 2kfrom rito ri,jk. This call is compatible with

the other calls in the component Ti,jk, as they involve senders at distance at

least 4 from s. Indeed the preceding messages in Ti,jkhave been sent at step at

most 2k−4fromrito ri,jkandatstepatmost2k−2fromri,jktoaneighbor

and then forwarded. Therefore they either arrived at the destinations or at a

vertex with distance at least 4 from s. They are also compatible with the calls

in other components as none of them involve ri.

If two calls are in diﬀerent components Ti,j , then they are compatible as the

distance from a sender to a receiver of the other call is at least 3. Finally two calls

with senders in the same component Ti,j are compatible and this follows from

thefactthattheyaresentbyri,j within two steps diﬀering by at least 4, as the

same component cannot be chosen in two consecutive even steps. Because the

distance between two such senders is at least 4, the distance between a sender

and the other receiver is at least 3 >1=dI.

Optimal Gathering Algorithms 211

Proposition 3. At the end of the Mi=2ni−1steps of the algorithm A all

the vertices of Tihave received their own messages and so the gathering time is

Mi=2ni−1.

Proof. We ﬁrst prove that at any step there is no component Tt

i,j such that

i,j >nt

2.Indeed,itistrueatstept= 1 as indeed Tiis type 1, 2n1

i,1≤ni.

Suppose that the property is not true and let t0=2k0−1 be the ﬁrst step

at which it happens. Then there exists such a component of size strictly bigger

than nt0

2. Hence, in the two preceding odd steps, this component was the biggest

one and it should have been chosen in one of these two steps, and therefore, this

component was already of size bigger than half at step t0−2=2k0−3or

t0−4=2k0−5 contradicting the choice of k0.

Therefore at any step t=2k−1thereisanewvertexxkto which a message

can be sent. Hence, all the messages have been sent by the source at end of step

Mi=2ni−1.

Consider a message mkwhich is sent by sat step 2k−1. If k=nithis is the

last message with destination rianditarrivesatstep2ni−1=Mi.

Otherwise risends mkat step 2kto ri,jk.Ifri,jkis its destination, then it

arrives at step 2k≤2ni−2<M

i,ask<n

i.Otherwise,mkis sent by ri,jk

on the path to xkat step 2k+ 2 and then forwarded immediately till it reaches

xk.Letd(s, xk) be the distance between sand xk.Notethatd(s, xk)≥3. The

messages with destination on the path from sto xkare all sent after xk(otherwise

we would have not chosen a leaf contradicting the algorithm). Therefore k≤

ni−d(s, xk) + 1. Finally mkis received by xkat step 2k+d(s, xk)−1≤

2ni−d(s, xk)+1≤2ni−2=Mi−1asd(s, xk)≥3.

2.3 CASE 2: TiIs a Subtree of Type 2

Here Mi=ni+2ni,1−1. So there is a component Ti,1such that 2ni,1>n

i.The

idea consists in considering a set of vertices Siin this component such that the

subtree T∗

iobtained by deleting them is of type 1 and then to apply algorithm

AtoT∗

i=Ti−Si. For the vertices of Sinote that, in the formula for Mi,they

are counted for 3. So we will send the messages destinated to them each 3 steps.

A natural way will be to send to the vertices of Siduring the ﬁrst 3|Si|steps

of the algorithm: the source sends ﬁrst a message to them at steps 3h,where

0≤h≤ni−n∗

i−1 and then the message is forwarded immediately till it reaches

the destination. This algorithm can be also viewed in an inductive fashion: take

aleafuin Ti,1; at step 1, the source sends to rithe message to uand then the

message is immediately forwarded; at step 2, (risends it to ri,1and so on); at

step 4 we apply the algorithm to the tree T−uusing either induction or the

algorithm A if T−uis of type 1.

This idea works perfectly for one subtree and will be in fact used later for 3

or more subtrees in Section 4.3. But unfortunately it does not lead to a solution

in all the cases. For example suppose we have two subtrees. If T1is of type 1,

then the source will send every odd step. Assume that T2is of type 2 with

M2=M1−1; so the source should ﬁrst send to it at step 2. But then after 3

212 J.-C. Bermond and M.-L. Yu

steps, the source has to send again at step 5. however, sis in fact busy sending

to T1in this step.

So we will proceed in a diﬀerent manner by ﬁrst sending to vertices in T∗

using Algorithm A, and then use what we call a 3-step extension to send to the

rest of vertices by pushing the messages along some paths. So, messages arrive

in the leaves only at the last steps of the algorithm. In fact if one thinks in

terms of gathering (where the algorithm is the reverse of that for personalized

broadcasting) it is more natural to send ﬁrst the messages from vertices far away

that are those from Si=Ti−T∗

We develop an algorithm that proceeds in 2 phases. In the ﬁrst phase, each

vertex receives an integer label which indicates the step in which this message

will be sent by the source in the second phase. Therefore, in the second phase,

the source will use the information from the labels given in the previous phase

to send the proper message at each step. The algorithm is described below and

will then be illustrated by an example. We will prove that it is valid and takes

Misteps (which is the lower bound as Mi≥N−1=ni−1).

Algorithm B: Personalized broadcasting for a subtree of type 2

More precisely, let Sibe a set of σivertices of Ti,1such that, after deletion,

we obtain a tree T∗

i=Ti−Siwith n∗

i=ni−σi=|T∗

i|vertices. Now M∗

2n∗

i−1=n∗

i+2n∗

i,1−1wheren∗

i,1=ni,1−σi. Therefore, T∗

iis a type 1 subtree.

Phase 1: Run the algorithm A on T∗

i, except that the source sends at step

t=2k−1 just a label of value k(1 ≤k≤n∗

i) (not the message). Then the source

sends successively to each node of Sian unique label (in the range [n∗

i+1,...,n

i])

by using σitimes the following ”3-step extension” (3σimore steps). Order the

vertices of Si={sn∗

i+1+h,0≤h≤ni−n∗

i−1}such that the following property

is satisﬁed: for each h, sn∗

i+1+his connected to T∗∪{sn∗

i+1,...,s

n∗

i+h}. Hence

there exists a path from sto sn∗

i+1+h, where all the nodes except the last one

(sn∗

i+1+h) have already received a label. Let the vertices of this path be u0=

s, u1=ri,u

2=ri,1,u

3,...,u

dh=sn∗

i+1+h,wheredh=d(s, sn∗

i+1+h).

Do the following 3 steps in any order: in one step, do the compatible calls

(u3p,u

3p+1), in the next step, do the compatible calls (u3p+1,u

3p+2)andinthe

last one, do the compatible calls (u3p+2,u

3p+3).

During each call, each sender (if it is not the source) sends the label it has

stored. Therefore at the end of the ”3-step extension” each node has the label

of its predecessor on the path. The source sends to rianewlabeln∗

i+1+h.

Note that the calls in an extension are compatible with the calls of any other

extension as they are done at diﬀerent steps.

Note also that the order in which we organize the 3 steps has no importance.

However for the purpose of clarity and using in theorem 4, we do the steps in an

order such that the source is always sending at an odd step as soon as it becomes

possible. So we do the calls (u3p,u

3p+1) (including the call with the source as a

sender) at step 2n∗

i+3h+,where= 1 if h is even and 0 if h is odd. Here h

ranges from 0 to σi−1=ni−n∗

i−1. We do the calls (u3p+1,u

3p+2)atstep

Optimal Gathering Algorithms 213

Table 2 . 9 steps of 3-step extension to label u, v and w

step

16 r1→r1,1b→u

17 s→r1a→b

18 r1,1→a

19 s→r1c→v

20 r1→r1,1

21 r1,1→c

22 r1→r1,1b→u

23 s→r1a→b

24 r1,1→a u →w

2n∗

i+3h+(1−) and the calls (u3p+2,u

3p+3)atstep2n∗

i+3h+ 2. So the source

sends at steps 2n∗

i+1,2n∗

i+3,2n∗

i+7,...,2n∗

i+6q+1,2n∗

i+6q+3,... and

is inactive at steps 2n∗

i+6q+5.

At the end of the phase 1 of the algorithm, each node has received exactly one

unique integer label ranging from 1 to ni.Letxkbe the node which has received

the value k.

Phase 2: Run the same algorithm again, but in the ﬁrst part the source sends

at step t=2k−1, 1 ≤k≤n∗

i, the message mkdestinated to xk,andinthe

extensions at step 2n∗

i+3h+,where= 1 if h is even and 0 if h is odd,

the message mn∗

i+1+hto xn∗

i+1+h,where0≤h≤ni−n∗

i−1. (Another way to

describe this is that in the steps when the source ssends a message, it is m(v)

where vcontains the smallest label and m(v)hasnotbeensent.).

Example: Consider the type 2 tree given in Fig. 2 obtained by adding three

vertices u, v and wand edges (b, u), (u, w)and(c, v ) to the tree in Fig.1. Here,

n1=11,n

1,1=7andn∗

1= 8. Hence, M1=24=n1+2n1,1−1(>21 = 2n1−1).

Remember that by deleting the vertices u, v and w, the resulting tree is type 1.

Now we illustrate algorithm B by applying it to this tree.

In phase 1, ﬁrst we apply Algorithm A to the subtree obtained by deleting

vertices u, v and wfrom the given tree (the resulting tree is exactly that of

Fig.1), and send a label to each vertex in this subtree, and this takes 15 steps.

The resulting labels which are those obtained in the previous example are given

in the ﬁrst row of Table 3. Then 3-step extension is used to extend the labels to

the vertices u,vand w. Note that in this process, the labels given in the ﬁrst

part of 15 rounds will be changed. The 3-step extension is illustrated in Table 2.

For example, steps 16, 17 and 18 are used to extend the labeling to the vertex

uby moving the labels from sto ualong the path (s, r1,r

1,1,a,b,u). We need 9

Table 3 . Labels of vertices after the phase 1 of Algorithm B

r1r1,1r1,2r1,3a b c d u v w

labels after 15 steps 8 7 4 6 3 1 5 2 - - -

labels after 18 steps 9 8 4 6 7 3 5 2 1 - -

labels after 21 steps 10 9 4 6 7 3 8 2 1 5 -

labels after 24 steps 11 10 4 6 9 7 8 2 3 5 1

names of the vertices x11 x10 x4x6x9x7x8x2x3x5x1

214 J.-C. Bermond and M.-L. Yu

Table 4 . Last 9 steps of phase 2 of Algorithm B

step m1m3m5m7m8m9m10 m11

16 b→u r1→r1,1

17 a→b s →r1

18 r1,1→a

19 c→v s →r1

20 r1→r1,1

21 r1,1→c

22 b→u r1→r1,1

23 a→b s →r1

24 u→w r1,1→a

steps to complete the labeling of u,vand w, Table 3 gives the labels of vertices

at the end of each 3-step extension in the phase 1 of Algorithm B. The source

is not sending at step 21.

Once we have the labels for the vertices, we are able to determine which

messages the source should send at diﬀerent steps. Now we are ready for the

second phase of the algorithm. In phase 2, we run again the same algorithm,

except this time, instead of labels, at step t=2k−1, for 1 ≤k≤8, the source

sends the message m(v), where the label of the vertex vfrom the ﬁrst phase of

the algorithm is k. For example, ssends m1=m(w) at the ﬁrst step as x1=w

or the label of wis 1, and sends m2=m(d)atthethirdstep,asx2=dor the

label of dis 2 and so on. Then ssends at step 17 m(a)asx9=a, at step 19,

m(r1,1)asx10 =r1,1, and at step 23, m(r1)asx11 =r1. Note that the protocol

is exactly the same as that of the previous example for the ﬁrst 15 steps and so

they are omitted in the table 4. In fact, the vertices not in T1,1have received

their messages at the end of the ﬁrst 15 steps (they are the messages m2=m(d),

m4=m(r1,2)andm6=m(r1,3) that have arrived at their destinations). We

indicate in the table 4 the steps of transmission of the other messages.

Proposition 4. Algorithm B is valid and uses Misteps (so g(Ti)=Mi).

Proof. The algorithm B is valid as during each step we have only compatible

calls (that is the case for algorithm A applied to T∗

iandthenthecallsofeach

step of the extension have been designed to be compatible). At the end of the

algorithm each vertex has received its message. In fact, a vertex will receive its

message in the ﬁrst part of the algorithm (before the 3-steps extension) if it is in

Ti,j ,wherej= 1, and otherwise, in one of the 3-steps of the last extension. The

algorithm uses 2n∗

i−1 steps in the ﬁrst part and then 3σisteps for the extensions.

Therefore we have altogether 2n∗

i+3σi−1=(n∗

i+σi)+(n∗

i+2σi)−1 steps. But

n∗

i+σi=ni. By deﬁnition of T∗

i,n∗

i=2n∗

i,1=2(ni,1−σi)son∗

i+2σi=2ni,1

and so the number of steps is ni+2ni,1−1=Mi.

3 General Algorithms

We will apply basic algorithms (A or B according to the type of subtrees) ﬁrst in

the case of a single subtree and then of two subtrees. For m≥3, we will use some

Optimal Gathering Algorithms 215

other techniques and induction; however we will deal ﬁrst with some special cases.

Recall that subtrees are ordered according to the values of Mi:M1≥M2≥M3≥

...≥Mm. In case of equality the order is determined by the sizes.

3.1 Case of One Subtree

In that case we apply directly the basic algorithm to the tree and we get.

Theorem 2. In the case where T consists of one subtree T1,g(T)=M1>N−1.

3.2 Case of Two Subtrees

We apply the basic algorithm to the subtree T1. All the vertices are informed

in M1steps. We also apply simultaneously the basic algorithm to the subtree

T2, but starting at step 2 ; all the steps are translated by one and therefore all

vertices of T2are informed in M2+ 1 steps.

Theorem 3. In the case where T consists of two subtrees T1and T2,g(T)=

max{M1,M

2+1}(this value is equal to max{N−1,M

1+}where =1if

M1=M2and 0otherwise).

Proof. Let us ﬁrst prove that all the calls are compatible. The validity of Algo-

rithm A or B covers the case when two calls belong to the same subtree. That

is the case also for the calls having the source as sender; indeed both in algo-

rithm A or B the source is sending only during some odd steps. So here the

source sends to r1at some odd steps and to r2at some even steps. Finally if two

calls belong to diﬀerent subtrees and are not both sent by the source, then the

distance between one sender and the other receiver is at least 2.

Altogether the algorithm uses max{M1,M

2+1}=M1+steps. We claim

that M1+≥N−1, which will prove that the lower bound is attained in that

case. The claim is true if M1≥N−1. If M1≤N−2, then 2n1−1≤M1≤N−2

and 2n2−1≤M2≤N−2.(1)Thatimpliesn1+n2≤N−1. But N−1=n1+n2

and therefore there are equalities everywhere in (1); that is n1=n2=N−1

2and

M1=M2=N−2 and therefore M1+=N−1

3.3 General Case: m>2

Due to lack of space the proofs are omitted in this section. Complete proofs can

be acessible via the webpage of the ﬁrst author1. We ﬁrst deal with a special case

Theorem 4. Suppose T consists of at least 3 subtrees such that T1and T2are

of diﬀerent types and M1≥N−1and M2=M1−1.Theng(T)=M1.

Then, for the case m>2, when we are not in the special case of the preceding

theorem 4, we apply induction on Nand present algorithms which complete the

personalized broadcasting in the number of steps that meet the lower bound.

1http://www-sop.inria.fr/mascotte/personnel/Jean-Claude.Bermond/

216 J.-C. Bermond and M.-L. Yu

Therefore, the exact number of g(T) is determined. We will suppose that the

source sends at steps 1 and 2 to two diﬀerent subtrees. Furthermore, if M1≥

N−1andT1is of type 1, the algorithm used to send messages to T1is the

basic algorithm A (in particular the source will send to r1inalloddsteps).We

assume that N>4 otherwise it is trivial and we will distinguish 3 cases getting

the following theorems.

Theorem 5. Suppose T consists of at least 3 subtrees and N−1>M

1.Then

g(T)=N−1.

Theorem 6. Suppose T consists of at least 3 subtrees and M1≥N−1and T1

is of type 2. Then g(T)=M1+.

Theorem 7. Suppose T consists of at least 3 subtrees and M1≥N−1and T1

is of type 1. Then g(T)=M1.

4Conclusion

In this paper, we present eﬃcient algorithms that give optimal solution for the

gathering problem with buﬀering possibility, when the network is a tree with

dI= 1. It should be noted that in our algorithms, the size of our buﬀers never

exceeds 1. However with such a small buﬀer, we can in some cases decrease con-

siderably the gathering time comparing to the non buﬀering assumption con-

sidered in [3]. An extension would be to consider a non uniform distribution

of messages. Our algorithm can be easily extended to the case where a node

receives or sends w(u)>0 messages ; indeed it suﬃces to replace a vertex with

w(u) messages by w(u) vertices with one message. However if w(u) is allowed to

be 0, then the problem will become much more complicated.

It would also be interesting to investigate this problem for diﬀerent value of

dIor some other structures of networks. In particular it is still an open question

to decide if the problem is polynomial for trees in general.

Acknowledgments

We would like to thank all the persons who help us with fruitful discussions in

particular L. Gargano, A. Liestman, J. Peters and S. Perennes.

References

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ence constraints. In: Calamoneri, T., Finocchi, I., Italiano, G.F. (eds.) CIAC 2006.

LNCS, vol. 3998, pp. 115–126. Springer, Heidelberg (2006)

2. Bermond, J.-C., Galtier, J., Klasing, R., Morales, N., P´erennes, S.: Hardness

and approximation of gathering in static radio networks. Parallel Processing Let-

ters 16(2), 165–183 (2006)

Optimal Gathering Algorithms 217

3. Bermond, J.-C., Gargano, L., Rescigno, A.A.: Gathering with minimum delay in

tree sensor networks. In: Shvartsman, M.M.A.A., Felber, P. (eds.) SIROCCO 2008.

LNCS, vol. 5058. Springer, Heidelberg (2008)

4. Bermond, J.-C., Gargano, L., Rescigno, A.A., Vaccaro, U.: Fast gossiping by short

messages. SIAM Journal on Computing 27(4), 917–941 (1998)

5. Bermond, J.-C., Peters, J.: Eﬃcient Gathering in Radio Grids with Interference.

In: AlgoTel 2005, Presqu’ˆıle de Giens, pp. 103–106 (May 2005)

6. Bertin, P., Bresse, J.-F., Le Sage, B.: Acc`es haut d´ebit en zone rurale: une solution

”ad hoc”. France Telecom R&D 22, 16–18 (2005)

7. Bonifaci, V., Korteweg, P., Marchetti-Spaccamela, A., Stougie, L.: An approxima-

tion algorithm for the wireless gathering problem. In: Arge, L., Freivalds, R. (eds.)

SWAT 2006. LNCS, vol. 4059, pp. 328–338. Springer, Heidelberg (2006)

8. Christersson, M., Gasieniec, L., Lingas, A.: Gossiping with bounded size messages

in ad-hoc radio networks. In: Widmayer, P., Triguero, F., Morales, R., Hennessy,

M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 377–389.

Springer, Heidelberg (2002)

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networks. Journal of Algorithms 43(2), 177–189 (2002)

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Problem. Journal of Algorithms 52(1), 8–25 (2004)

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in sensory networks. IEEE Journal on Selected Areas in Communications 22(6),

1110–1120 (2004)

12. Gaber, I., Mansour, Y.: Centralized broadcast in multihop radio networks. Journal

of Algorithms 46(1), 1–20 (2003)

13. Gargano, L., Rescigno, A.: Optimally fast data gathering in sensor networks. In:

Kr´aloviˇc, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 399–411.

Springer, Heidelberg (2006)

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works. In: Proceedings of the IFIP 17th World Computer Congress, pp. 193–205.

Kluwer, B.V, Dordrecht (2002)

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formation in Commmunication Networks: Part I. Broadcasting, Gossiping, Leader

Election, and Fault-Tolerance. Springer Monograph. Springer, Heidelberg (2004)

16. Klasing, R., Morales, N., P´erennes, S.: Complexity of bandwidth allocation in radio

networks: the static case (to appear in Theoretical Computer Science)

Distributed Qualitative Localization for

Wireless Sensor Networks

Karel Heurtefeux and Fabrice Valois

ARES INRIA /CITI, INSA-Lyon, F-69621, France

{karel.heurtefeux,fabrice.valois}@insa-lyon.fr

Abstract. The use of localization mechanism is essential in wireless

sensor networks either for communication protocols (geographic routing

protocol) or for application (vehicle tracking). The goal of localization

mechanism is to determine either precisely or coarsely the node location

using either a global reference (GPS) or a locale one. In this work, we

introduce a new localized algorithm which classiﬁed the proximity of the

neighborhood for a node. This qualitative localization does not use any

anchor or dedicated hardware like a GPS. Each node builds a Qualitative

Distance Table according to the 2-hop neighborhood informations. Thus,

the algorithm allows to determine coarsely the location of the neighbors

which are classiﬁed as very close,close or far. The algorithm is analyzed

on a regular particular topology and then we evaluate this accuracy on a

random topologies. We apply this algorithm for a localized topology con-

trol and we show that these topology control algorithms remain eﬀective

even without GPS information.

Keywords: Localization, location, gps-free, wireless sensor networks.

1 Introduction

Many applications for wireless sensor networks, as vehicle tracking or environ-

ment monitoring, need location awareness to work successfully. Geographic or

location-based routing protocols can be used without mechanism of route re-

quest packets ﬂooded in the whole network and so, the energy is saved and

the performances are improved. Moreover, in topology control protocols, where

each sensor node needs to adjust its power transmission to minimize the energy

consumption the algorithms must be location-aware.

GPS [HWLC01] solves the localization issue in outdoor environments. How-

ever, for large sensor networks where nodes must be very small, low power and

cheap, putting a GPS chip in every device is too costly.

In this paper, we propose a localized algorithm that allows to each node of the

network to localize their neighbors using only local informations. Our objective

is to show that in a wireless sensor networks where special hardware or GPS

cannot be used for cost reasons, there is a way to obtain coarse positions of

This work is partially funded by the french ANR RNRT ARESA project and the

CARMA INRIA pro ject.

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 218–229, 2008.

Springer-Verlag Berlin Heidelberg 2008

Distributed Qualitative Localization for Wireless Sensor Networks 219

Fig. 1. Qualitative node proximity classiﬁcation

the nodes. The algorithm uses only local informations obtained by exchanging

neighborhood tables with classical hello packets to compute a proximity index

for each 1-hop neighbor. We show that, despite the measurement errors, the

algorithm is enough reliable and almost perfect on particular topologies (grid).

The ﬁgure 1 illustrates the result of the algorithm: the neighbors of the studied

node are classiﬁed in very close nodes, close one and far one.

The paper is organized as follows. In Section 2 some prior works about localiza-

tion techniques are reviewed. The qualitative localization algorithm is presented

in section 3. Next, the assumptions we made and the results we obtained are

discussed in section 4. We conclude this work with some future work directions

in section 6.

2 Related Works

Many localization techniques are proposed to allow nodes to estimate their lo-

cation. We can distinguish two types of strategies of localization: ﬁne and coarse

localizations. The ﬁne localization strategies determine precisely the coordinates

of a node in the whole network whereas the coarse localization strategies specify

a non precise area or introduce virtual coordinates, etc...

2.1 Fine Localization Strategies

The use of GPS system allows to localize a node precisely. However, it is ex-

pensive to install GPS receiver on each sensors. Some papers circumvent the

problem and propose to use several anchors which are precisely located: each

node can ﬁnd its own position using triangulation or multi-lateration. For that,

several solutions are proposed:

- The measuring from signal strength which is unrealistic because the radio

signals can be disturbed by the environment,

220 K. Heurtefeux and F. Valois

- ToA (Time of Arrival) [CHH01] allows to compute the distance between

two nodes by observing the time of propagation but this mechanism needs

a nodes synchronization.

- TDoA (Time diﬀerence of Arrival) [WAH97], [NJ07]: two signals of diﬀerent

natures are used (ultrasound and radio for example) to improve the results

of ToA.

- AoA (Angle of Arrival) [NN03], [AKBD06]: allows to determine the direction

of a radio wave propagation.

- A combination of the TDoA and AoA [ML07] is also proposed to improve

the accuracy and to adapt [CHH01] to 3D environments.

All those protocols don’t take into account the energy consumption and as-

sume that each node is able to compute the time or angle of arrival easily.

Anyway, the anchor systems do not avoid the localization problem but re-

duce it to a subset of nodes of the network. Moreover other problems appear

like the anchors placement in the network to allow a better localization of the

nodes [BOCB07], [DT07].

2.2 Coarse Localization Strategies

Another strategy consists of ﬁnding approximate coordinates. If a non precise

location of the sensor nodes is acceptable -depending on the application- several

approaches are possible:

- The Active Badge system [HHB93]: each node is tagged and transmits a

periodic hello packet every 10 seconds with a unique infra red signal which

is received by dedicated sensors placed at ﬁxed positions within a building,

and relayed to the location manager.

- Location Estimation Algorithm [HE04] provides a probabilistic distribution

of the possible node locations. According to both the prior location infor-

mation and new observations from anchor nodes, impossible locations are

ﬁltered.

- The virtual coordinates [CA06]: each node determines its distance in number

of hop to anchors and thus builds a virtual coordinates system. [WABDB07]

shows that a routing protocol can be based only on virtual coordinates.

These protocols are not adapted to the sensor networks because either they

require anchors connected to a ﬁxed architecture or they require a centralized

computation.

3 Algorithm Overview

Remember that the goal of our algorithm is to determine coarsely the loca-

tion of the neighbors of a given node using only local informations. These local

informations come from the hello packets which are exchanged between 1-hop

neighbors. The qualitative location of a neighbor can be very close,close or far.

Distributed Qualitative Localization for Wireless Sensor Networks 221

Such coarsely location can be used to construct a reliable unicast routing proto-

col in degraded wireless environment with a high level of interferences: to choose

the very close nodes allows to choose the nodes with a high C/I ratio as relays.

Applications in topology control or virtual coordinates for routing protocol are

also possible.

AnodeAcalculate proximity index with his neighbor Bin the following way:

A(B)=(|V(A)|∩|V(B)|)−max(|V(A)|,|V(B)|)

where V(A) is the neighborhood of Aand |V(A)|is the cardinality of V(A).

The main idea is to give a high proximity index (PI) to the neighbor nodes

having many common neighbors with the origin node (A) and few distinct neigh-

bors. Indeed, we take into account the ratio between the number of common

neighbors and the number of distinct neighbors. Eﬀectively, close neighbors has

a strong similar vicinity whereas distant neighbors will have much distinct neigh-

bors. Thus, the proximity index is useful to represent the nodes which are qualita-

tively close. This logical proximity index is related to the geographical proximity

in the case of dense and uniform networks. This mechanism allows to establish

three distinguish classes among the neighbors: the very close class (or 1), the

close class (or 2) and the far class (or 3) (see ﬁgure 1). We calculate the class

node in the following way:

Let PI(x) the proximity index of neighbor x:

inter =|max(PI(xi))−min(PI(xi))|

classx=⎧

⎪

⎨

⎪

⎩

1if P I(x)≥max(PI(xi)) −inter

2ifmax(PI(xi)) −inter > P I(x)

≥max(PI(xi)) −2.inter

3if P I(x)<max(PI(xi)) −2.inter

Each node of the network computes a proximity index for each of its neighbors

according to the local information received from its 1-hop neighbors. Each node

maintains a table of his 1-hop and 2-hop neighborhood but diﬀuses only the

table of its direct neighbors with periodic hello packets. Figure 2 and table 3

show an algorithm application on a particular node for a given topology. Node

27 classiﬁes its neighbors in 3 proximity classes. We can see in details values

found by the qualitative localization algorithm in Table 3. Table 3 proposes also

a comparison between the qualitative classiﬁcation of neighbors of the node 27

according to the algorithm and the real classiﬁcation based on the Euclidean

distance. Note that, on this example, the network is parse.

The protocol is inexpensive in energy because it only uses informations nec-

essary to many other protocols: self-organization (CDS-rule-k [WL99], CDS-

MIS [WAF02],...) and pro-active routing protocols (OLSR [CJ03]) deployed in

wireless sensor networks. Moreover, if the network is not very dynamic (low mo-

bility, not many birth or death of nodes in the network [HV07]) this exchange

of packets can be reduced and limited to the deployment phase of the network.

222 K. Heurtefeux and F. Valois

Fig. 2. Example of qualitative localization computed by the node 27

Neighbors nodes proximity index euclidean distance proximity class real class

18 2.050.067 very close very close

3 1.065,18 very close very close

13 0.577,01 very close close

38 −0.583,66 close far

28 −0.5103,76 close far

24 −0.566,20 close very close

10 −1.5101,18 close far

1−2.073,09 far close

20 −2.565,96 far very close

39 −3.0115,62 far far

34 −3.0115,98 far far

15 −3.568,28 far very close

12 −4.0104,40 far far

Fig. 3. Comparison of the qualitative localization applied on the node 27. The classiﬁ-

cation obtained (very close,close,far ) is compared to the classiﬁcation obtained using

a GPS with the Euclidean distance.

4 Simulation Results

All the results we provided here are computed using the simulator Java in Simu-

lation Time (JiST) and Scalable Wireless Ad hoc Network Simulator (SWANS)

[BHvR05]. The WSN topology is modeled as a Unit Disk Graph (UDG) and a

CSMA/CA-like MAC layer is also used. Each node is motionless. The network

cardinality varies between 50 and 700 nodes which are randomly and uniformly

distributed in the simulation area except when we study the grid topology. The

transmission power is used to control the average degree of network nodes. The

objective is to investigate our protocol and observe its reliability to well classify

the nodes.

Distributed Qualitative Localization for Wireless Sensor Networks 223

Fig. 4. Algorithm deployed on a grid

4.1 Qualitative Localization Protocol Behavior on a Regular

Topology

We simulated a network of 100 sensors distributed uniformly to form a grid of

10x10 (see ﬁgure 4). Then, we increased the transmission power of each sen-

sor and observe how our qualitative localization protocol reacts. Sometimes the

vicinity of a node is not representative of the regularity of the whole network. In

this case (Fig. 4, scenario b) or when the nodes are in the border area, the al-

gorithm does not achieve to distinguish correctly the ﬁrst two neighbors classes

because of some incoherencies in the neighborhood. For other topologies, the

neighbors classes can be determined without errors and the proximity index

leads to the same classiﬁcation that the euclidean distance. We can conclude

that, when the topology and the neighborhood is almost uniform and regular,

the qualitative localization is very eﬀective and relevant.

224 K. Heurtefeux and F. Valois

Fig. 5. Quadratic Distance in function of the average degree for each classes

4.2 Qualitative Localization Protocol Behavior on Random

Topologies

But the sensor networks are seldom deployed with a regular topology. In order to

measure the algorithm accuracy in more realistic environment we deployed, with

a uniform and random distribution, 100 nodes and we varied the transmission

power to increase the average degree. Then we calculated the quadratic distance

between the neighbor nodes list classiﬁed using a GPS location and the same

list classiﬁed using our algorithm.

Let two lists vand win Rnbe as follow: v=(v1,v

2, ..., vn), w=(w1,w

2, ..., wn).

The quadratic distance dq is:

dq =!



i=1

(vi−wi)2

In this study we investigate the quadratic distance of the algorithm for the classes

close and very close and all the classes (Fig 5). We observe that the quadratic

distance increases but in a much slower way than the average degree. When the

average degree increases, the number of neighbors to be located for each node

increases. If the quadratic distance remains low that means that the precision

increases. This phenomenon is explained by a higher number of informations and

thus a high reliability. The various classes evolve in the same way. Nevertheless,

we can observe a lower increase for the classes very close and close.

In the case of dense topology (700 nodes, average degree: 40), the localization

is very eﬀective. We can see the localization into three classes on the ﬁgure 6.

The yellow nodes are in the very close class, the orange ones in the close class

andtheredonesinfar the class.

Each node allocates a class to its neighbors according to its proximity index.

How evolve those classes when average degree increases? Will the very close

Distributed Qualitative Localization for Wireless Sensor Networks 225

Fig. 6. Application of the algorithm in a random topology

class increases proportionally with the number of neighbors? We saw that the

quadratic distance increased slightly when the average degree increased. How-

ever this metric is very sensitive to the length of the lists evaluated. Thus we

investigate the average percentage of nodes selected in the very close class and

in the close class (Fig. 7). We can note that, when the average degree increases,

the percentage of nodes of the very close class decreases, whereas that of the

close class increases. The far class remainder constant. This indicates that more

Fig. 7. Classes cardinality in function of the average degree

226 K. Heurtefeux and F. Valois

Fig. 8. Algorithm reliability

important is the density and more the index proximity able to distinguish the

really very close nodes.

If we use this algorithm to know at which distance is a neighbor node, we

should know if a neighbor selected as close or very close is indeed close or very

close in the real world. To answer this question, we determined the number of

neighbors belonging to the close and very close classes selected by the algorithm

being indeed in the close and very close classes in a GPS-aware classiﬁcation

(red curve in Figure 8). Then we observe the number of nodes selected by the

algorithm in these two classes and we note those which are not belonging to the

GPS-aware classiﬁcation close and very close (blue curve in Figure 8). More than

80% of nodes are well classiﬁed even for topologies with a low average degree.

5 Algorithm Application on Topology Control

In dense sensor networks it is often desirable to limit the vicinity to the closest

neighbors. Several topology control algorithms exist like:

- Gabriel Graph [GS69]: an edge between uand vis selected if disk(u, v)

contains no another node inside.

- LMST [LHS03a]: Each node knows the location of its 1-hop neighbor and

each node computes a MST in its neighborhood. The construction of the

LMST topology is based on the construction of local MST by each node.

An edge (u, v) is in the ﬁnal LMST iif vis in the LMST(u) and uis in the

LMST(v).

- RNG [Tou80]: Thanks to the position of the 1-hop neighbors, a node removes

the longest links in the following way: given two neighbor nodes uand v,if

there is a node wsuch as d(u, v)>d(u, w)andd(v, u)>d(v, w) then the

edge (u, v) is deselected.

Distributed Qualitative Localization for Wireless Sensor Networks 227

Fig. 9. a) Physical topology, b) Topology control (RNG, GPS) c) Topology control

(RNG, Qualitative location)

Fig. 10. Evolution of length of the topology links used

But those algorithms are generally based on the knowledge of the exact position

of sensors (GPS, antenna array, RSSI, etc...). We applied our qualitative location

algorithm to build a Relative Neighborhood Graph (see Figure 9, denoted as

RNG-QLoP). Thanks to the proximity index of the 1 and 2 hop neighbors, a node

removes the longest links in the following way: given two neighbor nodes uand

v,ifthereisanodewsuch as PI

u(w)>PI

u(v)andPI

v(w)>PI

v(u) then the

edge (u, v) is deselected. In Figure 10, we observe the eﬀectiveness of the logical

structure created by observing the overall length of the selected links: more the

overall length is low, more the algorithm is relevant because of the energy saved.

This analysis highlights two points: the performance of RNG-QLoP algorithm is

very close to the RNG using GPS and more the density is important and more

the performance of RNG-QLoP is important too. It is due to the information

quantity increasing when the number of neighbors increases: it leads to a better

precision.

228 K. Heurtefeux and F. Valois

6 Conclusions and Future Works

In this work we propose a qualitative localization algorithm using only local

information. Our proposition does not use GPS information or any anchor or

dedicated hardware. Based on the local informations from its neighborhood, a

node can classify its neighbors as very close or close or far nodes. We have illus-

trated the behavior of our algorithm on a regular topology and on random one. A

quadratic distance is computed to highlight the relevant classiﬁcation provided.

We apply this qualitative location algorithm for topology control (QLoP). A

Relative Neighborhood Graph is computed using QLoP: the performances are

very close the performances obtained when an absolute location (GPS) is used.

Next, we will apply this qualitative localization algorithm to provide unicast

routing protocol suited to wireless networks with interferences. Our idea is to

favor paths made up of small hops and thus, to use very close nodes as relays

because of their important signal-to-noise ratio.

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A Lower Bound on the Capacity

of Wireless Ad Hoc Networks

with Cooperating Nodes

Anthony S. Acampora and Louisa Pui Sum Ip

Department of Electrical and Computer Engineering,

University of California, San Diego,

9500 Gilman Drive,

La Jolla, California, 92093, USA

acampora@cts.com, louisa.ip@sri.com

Abstract. In this paper, we consider the eﬀects on network capacity

when the nodes of an ad hoc network are allowed to cooperate. These re-

sults are then compared to the theoretical upper bound on the capacity of

an ad hoc network without cooperation. For our cooperative model, two

or more nodes are grouped together to cooperatively transmit informa-

tion from the source node to the destination node. Here the lower bound

is presented without frequency reuse and it is found that node coopera-

tion can only help improve network capacity as the number of nodes in

cooperation increases. However, the results of our cooperative network

model show that without frequency reuse, node cooperation could not

out perform a peer-to-peer network with frequency reuse. Furthermore,

the improvement of network capacity might not be worthwhile beyond

two nodes cooperating together. The three-node cooperation yields min-

imum gain, if not negligible, compared to the two-node cooperation.

Keywords: Ad Hoc Networks, Capacity Bounds, Cooperation, Peer to

Peer Networks, Routing Algorithm, Spatial Diversity, Wireless Networks.

1 Introduction

Previously we have studied the information theoretic bounds on the capacity of

peer-to-peer wireless ad hoc networks with hop-by-hop routing. We found the

theoretical upper bound of an N x N network from the capacity matrix repre-

senting the point-to-point Shannon capacity that exists between two nodes and

a relative traﬃc matrix [1],[2]. Each element of the capacity matrix represents

the maximum rate at which information may be transferred between pair of

two nodes with no co-channel interference. For the relative traﬃc matrix, each

element represents the exogenous traﬃc between the source node and the desti-

nation node. Applying source switching entropy, we are able to bound the upper

maximum factor by which the relative traﬃc matrix may be scaled. We use the

result as a yardstick against any approach for peer-to-peer wireless networking

and other cooperative networking schemes.

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 230–240, 2008.

Springer-Verlag Berlin Heidelberg 2008

A Lower Bound on the Capacity of Wireless Ad Hoc Networks 231

The area of single node hop-by-hop and single hop routing algorithm for

wireless ad hoc networks has been well studied. These methods of transmission

oftenrequiredhightransmitpower,thuscaused an increase of interference. One

method to increase eﬃciency of the network is to increase spatial diversity by

using multiple antennas in a node. However, multiple antennas in a simple node

are often impractical and undesirable. Unlike wired infrastructures where pack-

ets may be directed to the recieving node only, packets in a wireless network are

broadcast in the wireless medium. Other nodes near the transmitting node may

receive the packets at no extra cost to the transmitting node. Therefore, another

way to provide the spatial diversity is to allow individual nodes who are within

receiving range of the transmitting node be grouped together and transmit coop-

eratively. There have been abundance of study done on the cooperation of paired

nodes transmitting to a single receiver [3],[4],[5],[6], paired nodes transmitting to

two receiver [5],[7],[8], but little attention has been placed on any higher order

number of nodes cooperating together [9],[10]. In this paper, we examined the

beneﬁts of pairing up more than two nodes for cooperation and compared the

results with paired nodes cooperation and traditional hop-by-hop networks.

The purpose of this study is to determine if there are any beneﬁts in allowing

more than two nodes to cooperatively send together and how does a simple time-

share bound of a cooperative wireless ad hoc network compare to the capacity

bound of a traditional hop-by-hop network with frequency reuse. We steered

our attention to ﬁnding the lower bound of a similar network but with node

cooperation. We ﬁrst focus on a simple model of node cooperation with time-

share bound. If this lower bound is reasonably close to our previous upper bound,

it might be worthwhile to explore further. One obvious idea is to incorporate

frequency reuse in place of our simple time share bound. On the other hand,

if this lower bound is performing much worse than our previous upper bound,

perhaps another method is needed or it could be that our previous upper bound

was too loose. Maybe node cooperation is hindering, rather than expediting the

transfer of packets.

This paper is organized in ﬁve sections. In section 2, we present the overall

network model, the capacity matrix and the relative traﬃc model. In Section 3,

we present the algorithm employed and how the optimum path is determined.

In Section 4, we present the results based on two simple cases; 9 and 25 nodes

networks. The results show that without frequency reuse, node cooperation could

not out perform peer-to-peer networks with frequency reuse as presented in our

previous paper [1]. Even though the upper bound of the traditional hop-by-

hop network capacity is much higher than what we have for lower bound with

cooperation, nevertheless, for a simple time division strategy we achieved an

order of magnitude 14.28 times at SNR equal to 5 and 5.67 times at SNR equal

to 15 better than our hop-by-hop network with no frequency reuse, for a 9-node

network with path loss, multipath fading and shadow fading. Furthermore, the

three-node cooperation yields very minimum gain, if not negligible, compared to

the two-node cooperation. Finally, in Section 5, we conclude with some numerical

results and present future direction.

232 A.S. Acampora and L.P.S. Ip

2 The Capacity Matrix and Traﬃc Matrix of the

Network Model

The model for the N-node wireless network is shown in Figure 1. Each wireless

node may send or receive information to or from another single node, paired

nodes, three nodes, or up to N−2 nodes. The constraint placed on each node is

that no node may send and receive simultaneously. For nodes with cooperation,

we assume a phase shifter is built in with the model. Each source node may

experience propagation impairments (e.g., shadow and multipath fading) that

limit the rate at which information may be sent. Whenever a source node sends

information to destination node via another single node, it behaves as a peer-

to-peer network.

Fig. 1. Possible paths taken by source node for transmitting packets to destination

node in an N-node wireless ad hoc network

The co-channel interference free capacity between a (or multiple) sending and

receiving node(s) is deﬁned as C=Wlog(1 + ρ). Wis the bandwidth available

and it is set to one here for results in per Hz. ρis the interference free signal-

to-noise ratio (SNR). For each transmitting/receiving pair, the capacity matrix

can be written as

C=⎡

⎢

⎣

C11 C12 ... C

C21 C22

.....

CN1CN2... C

⎤

⎥

⎦(1)

where Cij means node i is the transmitting node and node j is the receiving node.

Each node may not send a packet to itself, thus the diagonal of the capacity

matrix is default to zero.

A Lower Bound on the Capacity of Wireless Ad Hoc Networks 233

Our propagation model consists of path loss, ﬂat multipath fading and shadow

fading between each node. The path loss between each node is deﬁned as

r=d

R4

(2)

where Ris the relative distance between two nodes and dis the distance between

two nodes as deﬁned in the beginning of section 4. This deﬁnes the normalized

SNR ratio if the transmitting and receiving nodes are separated by a distance d.

The ﬂat multipath fading is deﬁned as an exponential distribution with ran-

dom variable X and mean one. Mathematically, multipath fading has little eﬀect

to the signal to noise ratio when paired with path loss. The shadow fading follows

a log normal distribution with standard deviation of 6 dB.

The N nodes are randomly distributed over the service area and the SNR with

propagation impairments is computed in the following fashion.

ρij =ρ∗d

R4

∗eX∗10 

10 (3)

where ρis the SNR in linear scale and is Gaussian distributed, zero mean

and standard deviation of six. ρij is the SNR from node i to node j. The actual

capacity with normalized bandwidth is then equates to

C=log(1 + ρij ).(4)

In the event where a node is sending to two or more nodes, the smaller of the

capacity elements is selected. This capacity link is deﬁned as

Cjkl

i=min{Cij ,C

ik,C

il}(5)

for the case where node iis sending to nodes j,kand l.

To simplify the problem, we assume nodes are perfectly synchronized and

allow superposition at the receiving node. Although it is important to consider

the eﬀects of an asynchronous network [8] and its performance tolerance to

noncoherent scenarios [11], it is beyond the scope of this paper.

In the case where two or more nodes are cooperatively sending to a single

node, the actual capacity would then be based on the sending nodes SNR. SNR

is deﬁned as the signal power over noise power, these two parameters are of units

watt or volt2. For example, if a link is sending with Pwatts, the volt would then

be the square root of P. After adding the two signals in volts, we take the square

of the resulting voltage to obtain watts. For example, if node jand node kare

sending cooperatively to node i,wehave

jk =vji +vki =√ρji +√ρki .(6)

The SNR of this transmission is then deﬁned as

(vi

jk)2=(

√ρji +√ρki)2.(7)

234 A.S. Acampora and L.P.S. Ip

We may express the equation in watt,

ρi

jk =(

√ρji +√ρki)2(8)

and the actual capacity is calculated as in equation (4). While we are assum-

ing perfect time synchronization, it would be worthwhile to examine how slight

imperfection of time synchronization would eﬀect the signal quality at the re-

ceiver. It would be useful to examine the receiver’s tolerance to imperfect time

synchronization.

For two or more nodes to cooperate and send to a single node, we store these

values in another capacity matrix. This pre-determined capacity table is similar

to the idea of table-driven routing protocols used to maintain up-to-date routing

information between the nodes within the network [12].

Using the same principal in which we deﬁned the capacity matrix, we can

deﬁne the Relative Traﬃc Matrix as

T=⎡

⎢

⎣

t11 t12 ... t

t21 t22

.....

tN1tN2... t

⎤

⎥

⎦(9)

where tij is the exogenous traﬃc generated due to information delivered from

node ito node jin ﬁxed length packets per second as in our previous upper bound

calculation [1]. As in the case with the capacity matrix, the diagonal elements

of the traﬃc matrix are zeros. However, it is not necessary that the matrix

is symmetric because the source and destination nodes could be of diﬀerent

equipment. We currently use a uniform traﬃc model to isolate the problem on

how cooperation eﬀect network capacity.

3 Routing Algorithm and Cost Calculation

Each element in the network may send information only when the network is

free. The network has no frequency re-use and therefore presents the time-share

bound.

The traﬃc may ﬂow in any path available with the following constraint; a

single node may transmit a packet to a pair of nodes or to another single node,

but a pair of nodes may not transmit information to another pair of nodes.

Figure 2 shows a diagram of how traﬃc elements ﬂow sequentially.

When a node is free to send information from its queue, it may send to a

conventional single node, two or more nodes. We used a simple iterative method

in ﬁnding the best optimal pairing of nodes. We allowed the ﬁrst node to be

of any node from node 1 to node N with the exception that it may not be the

source node or the destination node. We then pick the second node in the same

manner except we start the search loop from one node after the starting point

of the ﬁrst node’s search loop. This is because pairing of node 1 and node 2 is

the same as pairing of node 2 and node 1. The decision on which path to take is

A Lower Bound on the Capacity of Wireless Ad Hoc Networks 235

Fig. 2. Algorithm on how many hops is optimum for transmitting packets from source

node to destination node

based on a simple algorithm of selecting the least time required path. The source

node will send information through a node pair if and only if such transmission

requires less time than a single node transmission path.

The number of hops is also determined based on the least time required for

transmission. We deﬁned the time required to send a packet from one node or

nodes to another node as the cost for that hop. If a single hop transmission takes

the least amount of time, the source node will directly send the packet to the

destination node. However, if the source node detects that transmiting to the

destination node via another single or paired node requires less net time than

the one-hop method, the source node will take the latter path.

We deﬁne tref as the time it takes for a source node to send information

directly to the destination node. If Mbits were sent using capacity link Cij ,

tref would be the Mbits divided by the capacity link. This relationship can be

expressed as follows:

tref ∝1

Cij

.(10)

With two or more hops, we ﬁrst determine if the transmission time from one

node to another single node is less than, or more than from one node to a pair

of nodes. We take the smaller of the two,

troute =min [tsingle ,t

pair].(11)

troute is calculated from the source node to intermediate nodes and arriving at

the destination node. If a three-hop path requires less time than a two-hop path

(perhaps due to higher capacity links between intermediate nodes), troute is then

the sum of the transmission time of the three hops in which the packet traveled

236 A.S. Acampora and L.P.S. Ip

from the source to the destination node. While a single node may send to a pair

of nodes, a pair of nodes is constrained to only sending to a single node.

The time it takes for a source node transmitting information to the destina-

tion node is the smaller of tref and troute. The total time a network takes for

each node to send its information is then the sum of each node’s transmission

time, or

ttotal =



l=1

min [tref,t

route].(12)

The total capacity of the network is then

Cnetwork =N

i=1 N

j=1 tij

N

i=1 N

j=1 tij ttotal

(13)

where tij is an element from the traﬃc matrix. This is the lower bound with no

frequency reuse.

4Results

As in our previous work [1], to generate numerical results, we consider a square

service area, with each side of the square being length Land N nodes are placed

in the square service area with distance dapart in all directions. There would

be √Nnodes in each row and each column and the distance dbetween each

node is

d=L

√N−1(14)

By doing so, if the transmitting node is separated from the source node by

distance d, we may then deﬁne the SNR as the normalized signal to noise ratio

in the absence of fading and interference. Further more, our model assumes a

r)4path loss, ﬂat multipath fading and log normal shadow fading with standard

deviation of 6dB as with our previous work.

Figure 3 shows the performance for diﬀerent quantities of nodes paired up as

a group to cooperatively transmit packets they receive to another node over a

9-node network. The traﬃc matrix used here is uniformly distributed. We have

included path loss, multipath fading and shadow fading in the simulation. A

total of ten simulations were run, with each run corresponding to a diﬀerent set

of randomly distributed nodes over the service area.

It is clear that by including cooperation, the overall network performance

improved signiﬁcantly, by approximately a factor of 20 with SNR equal to 0 and

the factor decreases as the SNR increases.

The plot on the right in Figure 3 is a close-up view of the performance curve

for node cooperation with two, three, four, ﬁve and six nodes. Our results show

that the capacity gain is not signiﬁcant beyond grouping two nodes together.

The three-node cooperation yields minimum gain, if not negligible, compared to

the two-node cooperation. However, by increasing the number of nodes to be

A Lower Bound on the Capacity of Wireless Ad Hoc Networks 237

Fig. 3. Performances for a diﬀerent number of nodes per group in cooperation based on

the average of ten trials for a 9-node network, with uniform traiﬃc, path loss, multipath

fading and shadow fading. The ﬁgure on the right is a close-up look at the curves with

cooperation.

allowed to group together for cooperation, the network capacity could only be

improved because we are picking the least transmission time path.

Whenever a node is added into a group to cooperatively transmit a packet,

the complexity of transmission increases. For example, each transmitting node

must receive the packet; synchronizes its clock before transmitting the packet

out to the intended node. While performance does improve as we increase the

number of nodes cooperating with each other, the increase of complexity might

not be worthwhile for grouping more than two nodes together. Figure 4 shows

the same result as Figure 3 but with a 25-node network. From our observations,

the advantages of using node cooperation diminish as SNR increases, this is

because the eﬀects of the imperfection of the channel diminish with higher SNR.

Although the network setup with node cooperation has clearly out performed

the network without cooperation, here we are calculating a network’s time-share

bound with no frequency reuse. From previous work, where frequency reuse is

taken into consideration, our results for a peer-to-peer networks with frequency

reuse still out perform the results presented here for the network using node

cooperation and no frequency reuse.

We now compare our current results with no frequency reuse to our previous

work of peer-to-peer networks with hop-by-hop routing and frequency reuse. We

look at the case of a 25-node network with uniform traﬃc, with path loss, mul-

tipath fading and shadow fading as with ﬁgure 4. Although the new result for

25 nodes, peer-to-peer transmission resembles a linear line, but the curve tapers

oﬀ slowly at higher SNR. Our information theoretic upper bound is shown in

Figure 5 along with our current lower bounds with and without cooperation and

238 A.S. Acampora and L.P.S. Ip

Fig. 4. Performances for a diﬀerent number of nodes per group in cooperation based

on the average of ten trials for a 25-node network, with uniform traﬃc matrix, path

loss, multipath fading and shadow fading. The ﬁgure on the right is a close-up look at

the curves with cooperation.

Fig. 5. Performance comparison of diﬀerent number of nodes per group in cooperation

to traditional hop-by-hop network(top most solid line with “*”), based on the average

of ten trials for a 25-node network with uniform traﬃc matrix, path loss, multipath

fading and shadow fading

A Lower Bound on the Capacity of Wireless Ad Hoc Networks 239

no frequency reuse. We noticed that our lower bound with cooperation is far less

than our upper bound without cooperation. This tells us either our upper bound

is very lose, or there is substantial opportunity to devise a routing algorithm ca-

pable of much better performance than the simple strategy we have invoked in

this paper. Our goal for the future is to investigate both of these. We expect

cooperation would substantially out perform a network that uses simple hop-

by-hop routing. Currently, the total information theoretic network capacity is

roughly 300 times better than our current result with node cooperation at SNR

equal to zero, roughly about 85 times better at SNR equal to 15 and 60 times

better at SNR equal to 30. As SNR increases, cooperation between nodes would

become less eﬀective in improving network capacity. This is because the higher

the SNR, the less eﬀects the imperfections of the channel would cause. How-

ever, peer-to-peer transmission would never outperform two-node cooperation

transmission based on the routing algorithm we employed.

5 Conclusions

By considering node-cooperation, we can signiﬁcantly improve the performance

of the network capacity. We have used a simple case with no frequency reuse

to show the beneﬁt of cooperation. The net capacity of the network has clearly

improved over the traditional peer-to-peer network. However, even with node

cooperation, a time-based bound could not out perform a simple peer-to-peer

network if such network utilizes frequency reuse.

We have previously stated that with the upper bound found in [1], no media

access protocol and no hop-by-hop routing algorithm can possibly produce an

overall network capacity greater than this upper bound. Here, we show that with

node cooperation, even the simplest case with two nodes cooperatively transmit-

ting information, can out perform simple peer-to-peer node transmission without

frequency reuse. What might be missing to allow cooperative network to perform

better than our previous upper bond might be of the lack of frequency reuse or

the lack of receiver cooperation. From [7], it showed that transmitter and reciever

cooperation performs better than receiver cooperation or transmiter cooperation

only. With this possibility, we next plan to explore the beneﬁts oﬀered by fre-

quency reuse for our current network model with cooperation for two nodes pair.

If our future model with frequency reuse still could not out perform our infor-

mation theoretic upper bound, we might consider adding receiver cooperation

to our model.

Acknowledgments. The authors sincerely thank the three reviewers for their

constructive comments in the early stage of submission. The aurthors are also

very thankful to Bryan Chavez, senior research engineer at SRI International

and Dr. Michael Tan, for generously spending valuable time in reviewing this

paper prior to our ﬁnal submission.

240 A.S. Acampora and L.P.S. Ip

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Attacks on CKK Family of RFID Authentication

Protocols

Zbigniew Goł˛ebiewski1, Krzysztof Majcher2, and Filip Zagórski2

1Institute of Computer Science, Wrocław University

zbigniew.golebiewski@ii.uni.wroc.pl

2Institute of Mathematics and Computer Science, Wrocław University of Technology

krzysztof.majcher@pwr.wroc.pl,

filipz@im.pwr.wroc.pl

Abstract. At Pervasive 2008, Cichon, Klonowski, Kutylowski proposed a fam-

ily of shared-key authentication protocols (CKK). Small computational and com-

munication cost, together with possibility of eﬃcient hardware implementation

makes CKK attractive for low-cost devices such as RFID tags. In this paper we

present a couple of attacks on CKK protocols, both passive and active.

Keywords: lightweight cryptography, RFID, authentication, HB, HB+.

1 Introduction

A lightweight cryptography becomes important nowadays. Such kind of cryptography

is especially used in weak devices containing simple, low cost microchips. One of the

examples of such a devices are RFID Tags, which use 8-bit processors, small memory

(few hundred bits) and the possibility of low-bandwidth radio communication on short

distances. Low-cost RFID systems are introduced as the successors of widely used bar-

codes. RFID Tags are commonly used as a small data storage of the objects which they

are attached to, RFIDs allow their automatic identiﬁcation.

RFID systems consist of the radio frequency tags and radio frequency reader. A

tag usually does not have any battery and is induced by a signal sent by a reader. An

activated tag can respond to the challenge sent by a reader and thus authenticate itself.

It is easy to see that because of the simplicity of the architecture used in RFIDs,

designing secure and reliable authentication protocols is one of the main problems.

Because of very strong hardware (cost) limitations, one cannot use the battle-tested

asymmetric cryptography protocols as RSA ([10]), ElGamal ([5]) and even symmet-

ric cryptography protocols as AES ([3]) – i. e. the “smallest” implementation of AES

contains over 10000 logic gates and because of the price it cannot be used in low-cost

RFIDs.

Many recent papers describe variety of the lightweight authentications protocols ded-

icated for RFID systems. Many of them use about few hundred of logic gates. One of the

security mechanisms was proposed by Vajda and Buttyán in ([11]) and then by Stephen

This work was partially supported by EU within the 7th Framework Programme under contract

215270 (FRONTS).

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 241–250, 2008.

Springer-Verlag Berlin Heidelberg 2008

242 Z. Goł ˛ebiewski, K. Majcher, and F. Zagórski

Weis et al. in ([12]). Those security mechanisms are not suﬃcient enough (i. e. proto-

cols are too complicated or there were proposed attacks on those protocols (cf. [4])).

The milestone in the research was done by Ari Juels and Stephen Weis in ([8]), where

they have described HB and HB+authentication protocol. HB+is upgraded version of

the human-to-computer authentication protocol designed by Hopper and Blum (HB)

([7]) and it is based on the “Learning Parity with Noise” (LPN) problem which was

proved to be NP hard. The authors of HB+protocol claim that HB+is secure against

passive and active adversaries. There are few papers in which authors analysed the se-

curity of the HB+([1], [9], [6]) but all proposed there attacks are not practical in the

point of view RFID systems. The HB+protocol has also few disadvantages. The main

of them is that: if the authentication should be secure and reliable then a tag and a reader

have to send many kilobytes of data. Therefore the authentication could last too long

(even few seconds).

Another approach to the security mechanisms for RFID systems was proposed by Ci-

chon, Klonowski and Kutyłowski in ([2]) (in the rest of this paper called CKK authen-

tication protocol). They introducefew versions of a protocol that is based on pre-shared

keys represented as the hidden subsets of random sequence. It is worth to mention that

CKK tag needs few bits to be sent. For the case of the key length 128, a tag needs to

send only 158 bits, while in the case of HB+, for the same key length and noise para-

meter 0.05, number of transmittedbits is about 32000 (the higher noise parameter is the

more bits need to be transmitted).

In this paper we perform security analysis of the versions of CKKprotocol, we de-

scribe possible passive and active attacks.

Organization of the paper. In the 2 section, we describe members of CKKfamily and

introduce basic notation which is then use through the paper.

Section 3 presents passive attacks on CKK,CKK2,CKKpprotocols. While in the

Section 4, we present active attacks.

2 Protocols Description

2.1 CKK Tags Description

In ([2]) there are three RFID authentication schemes proposed:CKK,CKK2and CKKp.

In each of them, a Tag Tshares with a Reader Rsecret – vectors: s1,...,skof the length

n(in the CKKpalso a permutation σ∈Sn+k). The diﬀerences between the schemes are

in the way of a Tag responses.

For n=128 parameter kis set to 30. For the rest of the paper we assume the following

notation. x[i]isthei-th bit of the vector x.x⊕ystates for the bitwise XOR of vectors

xand y. Finally, <x|y>means the inner product of xand y. We write x∈RAfor “xis

being picked uniformly at random from the set A”. For a vector xwe write xfor a vector

with each bit being ﬂipped (from 0 to 1 and vice versa).

By an observation of a tag we mean a sequence of vectors which one can see dur-

ing tag authentication. For CKK protocol, an observation rof a tag is a par r=

(a,c)=(independent part, dependent part), for CKK2tag, observation ris a triple

r=(a,c0,c1)=(independent part, ﬁrst answer, second answer). One of the c0,c1is

Attacks on CKK Family of RFID Authentication Protocols 243

Table 1 . CKKprotocols family description

CKK protocol

Public parameters: n,k

Secret key: s1,...,sk∈{0,1}n

Tag Reader

chooses a∈R{0,1}n

computes for i=1,...,k

c[i]=<a|si>

c=(c[1],...,c[k])

r=(a,c)r

−→ check for i=1,...k

c[i]?

=<a|si>

CKK2protocol

Public parameters: n,k

Secret key: s1,...,sk∈{0,1}n

Tag Reader

chooses a∈R{0,1}n

chooses b∈R{0,1}

computes for i=1,...,k

cb[i]=<a|si>

cb=(c[1],...,c[k])

chooses c1−b∈R{0,1}k

r=(a,c0,c1)r

−→ check for i=1,...k

if c0[i]?

=<a|si>or

if c1[i]?

=<a|si>

CKKpprotocol

Public parameters: n,k

Secret keys: σ∈Sn+k,s1,...,sk∈{0,1}n

Tag Reader

←− choose j∈N

chooses a∈R{0,1}n

computes for i=1,...,kc[i]=<a|si>

c=(c[1],...,c[k]) and r=(a,c)

r=σj(r)r

−→ compute ˆr=σ−j(r)=(ˆa,ˆc)

check for i=1,...,kˆc[i]?

=<ˆa|si>

correct, the second one is a random string. In the case of CKKp, an observation is a vec-

tor of the length n+kwhere bits of the independent and dependent parts are permuted.

For CKK and CKK2protocols, with a sequence of observations of a tag O=

{r1,...,rm}we associate a set of independent parts of observations:

Oa={a1,...,am}={ai:aiis an independent part of ri∈O}

For a given set B⊂Oa, which is a basis of the {0,1}n, and a vector a∈{0,1}n,we

deﬁne a set repB(a) as a set of vectors from B, which occurs in the linear combination

of representation of a,i.e.a=b∈repB(a)b.The length of vector ain the basis Bis the

size of a set repB(a).

We say that a vector ahas short representation if |repB(a)|<k.

We say that an observation ris in type of a tag Tif it has the same length as some

observation of Tand it could be generated as correct Tauthentication.

3 Passive Attacks on the CKK Family

In the current section we describe a passive attacks on each of the CKK protocol. For

the rest of this section we use following notation.

In description of all passive attacks, we assume that a set of observations collected

by an attacker, Alice:

O={r1,...,rm}

contains m>ntuples. All passive attacks presented are linear of the length of n,butall

of them require at least m≥n+1 to be collected.

244 Z. Goł ˛ebiewski, K. Majcher, and F. Zagórski

3.1 Passive Attack on CKK

Let us assume that an attacker, Alice, have listened to m≥nexecutions of the CKK pro-

tocol performed by a Tag T, thus collecting a set of observations:

O={r1,...,rm}={(a1,c1),...,(am,cm)}.

Then with high probability (for m=n=128 the probability equals to p=0.28; for

m=n+1itis p=0.57, m=n+4→p=0.938, m=n+10 →p=0.999024;

see the appendix for exact formula) there exists a subset B⊂Oa(B) such that ai∈B

are a basis over {0,1}n. Then, by the linearity of the dependent part, Alice can generate

proper answers c(x)foranyx∈{0,1}nso that a pair (x,c(x)) is accepted by a Reader as

proper answer of the Tag T(i. e. Alice ﬁnds a re pB(x)).

More precisely:

Algorithm 1. Passive attack on CKK protocol

1. Collect a set O of m observations of the CKKTag T

2. Choose B ⊂Oa(B)such that B is independent over {0,1}n

3. For any x, compute re pB(x),

c(x):=

i∈{ j:aj∈repB(x)}

4. Send a pair (x,c(x)) – a pair is in the type of T

Let us notice that if Alice collects mobservations then she can generate at most

2min{m,n}diﬀerent authentication strings.

3.2 Passive Attack on the CKK2Protocol

Now, we assume that Alice has collected following set of observations of a Tag T

authentications:

O={r1,...,rm}={(a1,c0

1,c1

1),...,(am,c0

m,c1

m)}.

Again, we assume that m>n. Then, with overwhelming probability (for m=n+10:

p=0.999; for m=n+k:p≈1−1

2k) there exists a subset Oa(B)⊂Oasuch that

B={ai:ai∈Oa(B)}is a basis of {0,1}n.

Conversely to the case of the CKK, one cannot construct proper answers for the Tag

Tbecause one does not know values of bi– so one does not know which of the values

i,c1

iis correct for given ai(correct in a sense: cb1

i=<ai|si>).

If Alice wants to generate correct tuple (x,c0,c1), for any given xwhich is repre-

sented by the lvectors of the basis B(|re pB(x)|=l), she has to pick correct values of

biso the probability of correct answer is about 2−l=2−| repB(x)|(it is not an exact result

because sometimes wrong choices of the values bican lead to the correct answer). Let

us notice that for randomly chosen x∈{0,1}n,|repB(x)|≈ n

2>k. So this kind of attack

is not eﬀective.

Basing on the following observations, we construct an algorithm, which performs

passive attack on the CKK2.

Attacks on CKK Family of RFID Authentication Protocols 245

Observation 1. Let us notice that although expected number of basis vectors in repre-

sentation of random vector from x∈R{0,1}nis equal to n/2, random variable |repB(x)|

has Binomial distribution, i. e. P(|repB(x)|=l)=1

2nn

l, so the probability that a vector

xhas short representation in base Bis equal to:

P(|repB(x)|is smaller than k) =

k−1



i=1

P(repB(x)=i)

If Alice takes r=(a,c0,c1)∈Oand aBand ahas short representation in B(we

assume that |repB(a)|=L) then Alice can perform exhaustive search of all combinations

and ﬁnd out correct values of bi(atmost2

L).

Observation 2. If Alice chooses diﬀerent vectors to a set Bthen a representation of

vectors from observation will change. What is important for us, the length of the rep-

resentation will also change. So, if Alice could not ﬁnd any vector that has short repre-

sentation, she can just pick another basis from Oa(B) and try again.

Observation 3. If Alice takes two observations rs1=(as1,c0

s1,c1

s1),rs2=(as2,c0

s2,c1

s2)

then one of the four possible dependent parts: cf1

s1⊕cf2

s2,forf1,f2∈{0,1}is proper for a

vector: as1⊕as2.

Of course, by taking Mobservations, and xoring them together, Alice has to ﬁnd out

which of the 2Mcombinations of cf1

s1⊕...⊕cfM

sMfor f1,..., fM∈{0,1}is correct.

Algorithm 2. Passive attack on CKK2

1. collect a set O of m observations of authentications of the CKK2Tag T

2. repeat

(a) pick at random set B ⊂Oauntil B is a basis of {0,1}n;C=∅

(b) for j =1,...,M

check if there exists vectors x f1,...,xfj∈Oa\B

such that:

|repB(xf1⊕... ⊕xfi)|=L−|repB(xf1⊕...⊕xfi)∩{ai:i∈C∧ai∈B}| <k

if short representation is found

ﬁnd correct values of biby checking at most 2L+jpossible cases; add indexes

of bi(index of biis i) into a set C

until |C|=n

It should be noticed, that in the step 2(a) of the algorithm, set Bpicked at random of

the size nis be basis of {0,1}nwith probability Pnequal to

Pn=

n−1



i=01−2i−n.

and it can be checked that limn→∞ Pn=0.2887 ... and that the convergence of this

sequence is very fast. For instance, we have P10 =0.28907 (see the appendix for exact

formula).

246 Z. Goł ˛ebiewski, K. Majcher, and F. Zagórski

The step 2 (b) of the above algorithm, we are looking for the vector with short rep-

resentation. The lower bound on the probability of ﬁnding such a short representation

is Ps– the probability that in the set Oa\Bthere will be a vector that has the length of

representation smaller than k.Psis equal to

Ps=



j=1t

j1

k−1−j



i=0n

i,

where t=|Oa\B|. This is because the probability that a vector vpicked at random has

the representation of length lwith probability 1

2nn

l, thus if we are looking for a vector

that have the representation smaller than kthen we have to sum these probabilities for

i=0,...,k−1. The size of the set of vectors that take part in the test Oa\Bis equal to

t, so we can test t

jvectors created by xoring together jvectors from Oa\B.

For proposed in ([2]) tag with n=128, k=30, M=3 and a set of observation of

size 512 we have Ps=0.000037, thus the expected number of vectors that should be

tested is equal to (t

=2.4945 ·1011. Simulations shows that home PC is able to ﬁnd

out correct solution in a couple of hours.

3.3 Passive Attack on CKKp

Let us notice that cheap implementation of the permutations, like it is required by

CKKpprotocol, might be hard. Thus for the practical reasons, a possible scenario is

when the Tag perform only one iteration of a permutation in the CKKpprotocol. The

following passive attack on the CKKpworks only if the Tag permutes response bitstring

exactly once in each authentication.

We assume that Alice has collected a set O={o1,...,on}of the observations (inde-

pendent vectors) of the Tag T.ThesetOcan be treated as a matrix of size (n+k)×n

where each row is a vector obtained from the diﬀerent observation. Next we have to

ﬁnd any non-degenerate minor Bof size n×nof a matrix O. From the deﬁnition of the

minor we know that the rows of Bare linearly independent. Therefore Bis a basis of

{0,1}n. Now, if we want compute the correct response bitstring for v∈R{0,1}n, we need

to ﬁnd its representation in the basis B(repB(v)={bi1,...,bit}). Next, we perform XOR

operation of the vectors {oi1,...,oit}form the set Othat corresponds to the vectors from

repB(v). The result of this operation is a proper answer that allows Alice to perform

successful authentication. As we can see, we do not need to know the permutation σ

because it is hidden in the vectors {oi1,...,oit}. Form the linearity of the permutation

we have σ(w1⊕w2)=σ(w1)⊕σ(w2)wherew1,w2∈{0,1}n, thus we know that result

of XOR operation of the vectors {oi1,...,oit}will retain the permutation.

4 Active Attacks on the CKK Protocols

In current section we present attacks in which, we allow Alice not only to listen to

the communication between a tag and a reader, but also to perform other actions, i. e.

retransmit modiﬁed messages.

Attacks on CKK Family of RFID Authentication Protocols 247

4.1 Repetitive Attack on the CKK Protocol

Let us notice that CKK is not immune for the replay attack. Namely, let us assume

that an attacker, Alice listens to one execution of the protocol CKKAuth and records

r=(a,c). Then Alice can act as tag Tby sending the same, previously recorded value

(a,c).

The only solution for that kind of attack is that the Reader remembers all values a

sent by the Tag. Then the Reader can accept only those values which have never been

used before. Let us notice that for any proper transmition r=(a,c), cis in fact a linear

function of a. If Alice have listened to mtransmitions r1,...,rm, she can send as an

authentication string any linear combination of some of recorded values. So a reader

should check if a value received from a tag is not a linear combination of the previously

transmitted tokens. This kind of attack shows that the lifetime of CKKtag is limited by

the length of the independent string, i. e. maximum number of secure transmitions is

limited by n.

This leads us to the summary that CKK tags’ lifetime is bounded by ntransmitions

(if every transmition is linearly independent from the previous ones then there are only

nlinearly independent vectors on {0,1}n).

4.2 Active Attack on CKK2

If Alice collects a set of observations O={r1,...,rm}={(a1,c0

1,c1

1),...,(a1,c0

m,c1

m)},

she does not know which of the values c0

j,c1

jis correct and which is a fake. But then,

she can tell the fake from correct value in the following way.

Algorithm 3. Active attack on CKK2

1. Listen to m authentications of a Tag T

2. For each i =1,...,m send to a Reader tuples: (ai,c0

i,c1

i),(ai,c0

i,c1

i); one of them

will be accepted – remember bi

After execution of the algorithm presented above, Alice can generate correct values

of a dependent part for any independent part awhich is a linear combination of vectors

from Oa.

5 Conclusions

We have presented a bunch of attacks (both active and passive) on the CKK family of

the authentication protocolsdesigned for RFIDs by Cichon et al. ([2]). Our paper shows

that modiﬁed version of the CKK protocol has the same level of security (against active

and passive attacks) as more complicated CKK2and CKKp. So, there is no sense to use

them anymore. Moreover, our work, together with the original paper ([2]) show that

modiﬁed CKK protocol, where a reader remembers independent parts used by each

tag, can be securely used exactly ntimes, where nis the length of the independent part.

If dependent part is of the length k,wehaveshown,afternexecutions, an active attacker

can easily act as a tag. But after any i<nexecutions of a protocol every active attacker

has only 1

2kprobability of successful authorisation.

248 Z. Goł ˛ebiewski, K. Majcher, and F. Zagórski

References

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statistical query model. Journal of the ACM 50(4), 506–519 (2003)

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tiﬁers. In: Indulska, J., Patterson, D.J., Rodden, T., Ott, M. (eds.) PERVASIVE 2008. LNCS,

vol. 5013, pp. 298–314. Springer, Heidelberg (2008)

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rithms. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18.

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authentication protocol. IEEE Electronic Letters 41, 1169–1170 (2005)

7. Hopper, N.J., Blum, M.: Secure human identiﬁcation protocols. In: Boyd, C. (ed.) ASI-

ACRYPT 2001. LNCS, vol. 2248. Springer, Heidelberg (2001)

8. Juels, A., Weis, S.A.: Authenticating Pervasive Devices with Human Protocols. In: Shoup,

V. (ed.) CRYPTO 2005. LNCS, vol. 3621. Springer, Heidelberg (2005)

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SCN 2006. LNCS, vol. 4116, pp. 348–359. Springer, Heidelberg (2006)

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key cryptosystems. Commun. ACM 21(2), 120–126 (1978)

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Heidelberg (2004)

A Appendix: Mathematical Facts

Let us assume that in one execution of the authentication algorithm, exactly one vector

can be eavesdropped. Our aim is to calculate how many executions of the algorithm we

need to gather a basis of the vector space created by the eavesdroppedvectors.

Lemma 1. Let V denote vector space created by the vectors of the length n. Let Pn+k

be the probability that a basis of the vector space V is gathered after collecting n +k

vectors. Then

Pn+k=n−1

i=01−2i−n·k−1

i=02i+n−1

2kn ·k

i=12i−1.

(1)

Attacks on CKK Family of RFID Authentication Protocols 249

Proof. Let us consider simple procedure S. One round of Sconsists of three steps:

1. Draw uniformly random vector v∈{0,1}n,

2. If vis linearly independent with vectors form set Lthen put vto the set L,otherwise

go to the step 1,

3. If |L|=nthen end procedure, else go to step 1.

Our goal is to calculate the probability that the number of rounds in procedure Sis

equal to n+k.

Let vibe the vector that is drawn in the i’th round and Bi,jbe the set of linearly

independent vectors that was collected from i’th to the j’th round of the procedure S.

Let Ai,tdenote the event that the set B1,i−1∪viis linearly independent and |B1,i−1∪vi|=t.

Then it is easy to see that

Pn+1=



i=1

P(A1,1∩...∩Ai−1,i−1∩¬Ai,i∩Ai+1,i∩...∩An+1,n).

It is obvious that the event ¬Ai,ihas not any impact on the events Aj,jfor all j<i.The

event ¬Ai,ihas not an inﬂuence on the probabilities of events Aj,tfor all j>i∧t≥i,

because it does not change the size of set L. Therefore we can write as follows

Pn+1=



i=0

P(A1,1∩...∩Ai−1,i−1∩Ai+1,i∩...∩An+1,n)·P(¬Ai,i).

Next observationis that the linearly independent vectors are collected in some nrounds.

The numbers of rounds in which vectors are included to the set Lhave not any impact

on the value of probability that nlinearly independent vectors are collected. Therefore

the probability of collecting nlinearly independent vectors is equal for any numbers of

rounds in which those vectors are chosen. The value of this probability was introduced

in ([2]) and it is equal to

p(n)=

n−1



i=01−2i−n.

So, we can simplify our formula for the probability that a basis of the vector space Vis

gathered after collecting n+1 vectors and write it as follows

Pn+1=p(n)·



i=1

P(¬Ai,i).

The probability of event ¬Ai,t(for all t≥i) is equal to 2i−1

2n=2i−1−n. Thus we can

calculate n

i=1P(¬Ai,i)=1−2−n.

Now we can generalize our reasoning to Pn+k. If the number of rounds that are

needed to gather a basis of the vector space Vis equal to n+kthen it will be kevents

¬Ai1,t1,...,¬Aik,tk. It should be notice that the order of events ¬Aij,tjis important in case

of calculating Pn+k. Therefore we can write as follows

Pn+k=p(n)·



i1=1

P(¬Ai1,t1)·⎛

⎜

⎝



i2=i1

P(¬Ai2,t2)·⎛

⎜

⎝



i3=i2

P(¬Ai3,t3)·...

⎞

⎟

⎠⎞

⎟

⎠

Since n

a=bP(¬Aa,t)=n

a=b2a−1−n=1−2b−1−nwe can simplify formula for Pn+kand

write it as follows

250 Z. Goł ˛ebiewski, K. Majcher, and F. Zagórski

Pn+k=p(n)·k−1

i=02i+n−1

2kn ·k

i=12i−1.

Now putting formula for p(n) to this equation we get what we want to prove. 

Fact 4. Let K denote the number of vectors gathered above n to collect a basis of vector

space V. The expected value of K is given by formula

E[K]=

∞



k=0

k·n−1

i=01−2i−n·k−1

i=02i+n−1

2kn ·k

i=12i−1

and it can be checked that limn→∞ E[K]=1.6067 ...and that the convergence of this

sequence is very fast. For example, for n =10 we have E[K]=1.60572,forn =20 we

have E[K]=1.60669 and for n =25 we have E[K]=1.6067.

On Backoﬀ in Fading Wireless Channels

SeonYeong Han and Nael B. Abu-Ghazaleh

Computer Science Dept.

State University of New York at Binghamton

and

School of Computer Science

Carnegie Mellon University - Qatar

{shan6@,nael@cs.}binghamton.edu

Abstract. We consider the impact of transmission errors on the backoﬀ

algorithm behavior in the IEEE 802.11 protocol. Speciﬁcally, since the

backoﬀ algorithm assumes that all packet losses are due to collisions, it

unnecessarily backs oﬀ when a packet is lost due to a transmission error.

Two performance problems arise as a result: (1) low throughput, due

to unnecessary loss of transmission time; and (2) unfairness when two

competing links have diﬀerent transmission error rates. In this paper, we

characterize this problem and propose three solutions to it. The solutions

aim to provide discrimination between transmission errors and collisions

such that the sender can back oﬀ appropriately. The ﬁrst algorithm relies

on receiver discrimination and feedback; the receiving radio can in many

instances diﬀerentiate between collisions and transmission errors. The

second algorithm estimates the clear channel quality, and backs oﬀ if

the observed quality deviates from the clear channel quality (indicating

collisions). The third algorithm develops the probability of collision as a

function of the number of observed idle slots during contention, and uses

this probability to control the backoﬀ algorithm. We show via simulation

that the techniques signiﬁcantly improve both performance and fairness

of IEEE 802.11 in the presence of transmission errors.

1 Introduction

The IEEE 802.11 MAC protocol [1] is the de facto standard for wireless LANs,

including ad hoc and mesh networks. It is a contention based protocol that

uses Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) to

reduce the probability of collisions. In contention protocols, collisions cannot be

eliminated; this is especially true for wireless networks due to the well-known

hidden terminal problem [2,3]. Thus, an important component of contention

MAC protocols is the backoﬀ mechanism which is used to regulate the oﬀered

load to the shared channel in the presence of contention. Speciﬁcally, when a

collision occurs Binary Exponential Backoﬀ (BEB), is invoked, typically doubling

the size of the backoﬀ window. BEB is used in other contention protocols such

as Ethernet.

This work is partially supported by NSF grant CNS-0454298.

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 251–264, 2008.

Springer-Verlag Berlin Heidelberg 2008

252 S.Y. Han and N.B. Abu-Ghazaleh

IEEE 802.11 interprets all packet losses as collisions and invokes the BEB

algorithm. However, in the presence of wireless transmission errors, the BEB

protocol is invoked unnecessarily (since a transmission error is not an indication

of contention), leading to the following two performance problems:

(1) Ineﬃcient use of the available bandwidth: this is a consequence of un-

necessarily increasing the backoﬀ window. This problem is exacerbated when

one considers that contention occurs in IEEE 802.11 using the lowest trans-

mission rate, to allow fair contention among connections with heterogeneous

rates. As a result, at higher rates, data packet transmission time becomes

shorter, but the backoﬀ period stays the same as the lowest rate;

(2) Unfairness: when two links with diﬀerent loss rates are in interference range

of each other, unfairness arises. The weaker link backs oﬀ more frequently

due to transmission errors, creating unfair competition for the medium and

long-term unfairness. We characterize the impact of fading on IEEE 802.11

performance under diﬀerent scenarios in Section 2.

This paper contributes three solutions for remedying these problems. A success-

ful solution should discriminate between losses due to collisions and those due to

transmission errors. This discrimination does not necessarily have to be at the

granularity of the individual transmission; rather, the technique should provide

insight into the probability of a loss in the aggregate being due to collisions. We

investigate the following three solutions, which are presented in more detail in

Section 3.

1. Receiver based discrimination: in this solution, the receiver uses any infor-

mation available to it to determine the cause of the packet loss. Increasingly,

the physical layer at the receiver is able to provide information about the

transmission that is helpful in speculating on the reason for the loss. The

speculation results are fed back to the sender on subsequent acknowledg-

ments, allowing it to adjust its backoﬀ window proportionately. This ap-

proach relies critically on the discrimination mechanism at the receiver and

the information available from the wireless card.

2. Link Quality Estimation: in this solution, the sender maintains a running es-

timate of the clear channel link quality (the expected loss rate in the absence

of contention from other sources). The backoﬀ window is then increased in

proportion to the loss rate being observed vs. that expected by the link qual-

ity. However, estimating the clear channel link quality while the network is

active is diﬃcult. We take an approach in which we use the minimum loss

rate period over a period of time as an estimate of the clear channel link

quality.

3. Idle Slot Collision Probability Estimation: Heusse et al. [4] observed that

the number of idle slots in a contention period is indicative of the amount

of local contention for the use of the channel. We adapt the approach to

estimate the probability of collision as a function of the number of idle slots

observed. With an estimate of the collision probability, we can estimate the

On Backoﬀ in Fading Wireless Channels 253

number of extra losses that are due to transmission errors and adjust the

backoﬀ accordingly.

Section 4 presents a simulation-based evaluation of the proposed approaches. The

experiments show that all three approaches are able to address the problem,

coming close to the performance of a perfect predictor. Section 5 overviews

related work. Finally, Section 6 presents some concluding remarks.

2 Impact of Fading on Binary Exponential Backoﬀ

The backoﬀ mechanism regulates the oﬀered load to the shared medium. Backoﬀ

algorithms maintain a contention window value in units of ﬁxed-size slots, to

determine how long to wait before transmission. In IEEE 802.11, there is a

minimum contention window CWmin that is used after a successful transmission.

CW is doubled whenever a packet loss occurs until it reaches CWmax. After every

transmission a node picks a number of slots uniformly distributed in the range

[0,CW] as its backoﬀ window.

The underlying assumption in these backoﬀ algorithms is that all packet losses

are due to collisions. This assumption holds true in wired shared media where

transmission errors are exceptionally rare, but not in wireless environments

where they are common. When transmission losses occur, backoﬀ is invoked

unnecessarily, leading to signiﬁcant ineﬃciency and giving rise to long-term un-

fairness among links with diﬀerent qualities.

We deﬁne eﬃciency to be the ratio of the observed throughput to the through-

put of an ideal backoﬀ algorithm that backs oﬀ when collisions occur, but not

when transmission errors occur. Figure 1 shows the eﬃciency on a single hop

link as a function of the link quality (the probability of successful transmission)

for two diﬀerent transmission rates and packet sizes. Clearly, there is a large

drop in throughput as the link quality drops beyond the loss that results from

the loss of the packets to transmission errors. Whenever a transmission error

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Efficiency

Link Qualit

Efficiency vs. Link Quility

2Mbps 1500bytes

2Mbps 500bytes

11Mbps 1500bytes

11Mbps 500bytes

Fig. 1. Eﬃciency vs. Link Quality

254 S.Y. Han and N.B. Abu-Ghazaleh

500

1000

1500

2000

2500

3000

3500

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Throughput(kbps)

Link Qualit

Normalized Throughput Comparison -- Two Contending links(11Mbps) in Shadowing Channel

Link1

Link2

Fig. 2. Unfairness Problem

occurs, the contention window is doubled unnecessarily. The problem is worse

when the packet size is small since the yield from each contention period drops.

Further, since contention is carried out at the lowest transmission rate (for com-

patibility and fairness among transmitters with diﬀerent rates), the problem also

becomes worse when the transmission rate increases. Because the probability of

successive transmission errors increases as the link quality degrades (leading to

exponential backoﬀ), the eﬃciency degradation is not linear.

Unnecessary backoﬀ in response to transmission errors can also give rise to

unfairness. When multiple links compete, if the backoﬀ algorithm is not biased

towards either, then long term fairness will be achieved. However, in the pres-

ence of transmission errors, two links with diﬀerent loss rates experience diﬀerent

average backoﬀ values. This causes unfair competition in accessing the medium

and long term unfairness results. Figure 2 demonstrates this eﬀect between two

competing single hop ﬂows. The link quality for the ﬁrst ﬂow is ﬁxed at 0.95,

while the quality of the second link is varied. The ﬁgure plots the normalized

throughput (throughput divided by link quality); the normalization is done to

remove the eﬀect of the lost packets and provides an estimate of the actual trans-

missions that each ﬂow receives. Clearly, as the link quality disparity increases,

the higher quality links starts dominating the available bandwidth. Discriminat-

ing between transmission errors and collisions can mitigate this problem because

the weaker quality link is not penalized by the backoﬀ algorithm for transmission

errors (which are not indicative of collisions).

3 Proposed Solutions

In this section, we discuss three approaches for informed back oﬀ for CSMA based

wireless networks. The goal of our solutions is discriminate between transmission

losses and collisions so that the back oﬀ algorithm increases back oﬀ only when

collisions occur. An important observation is that this back oﬀ does not have

to be at the granularity of the individual packet. Instead, an estimate of the

On Backoﬀ in Fading Wireless Channels 255

percentage of losses due to collisions is suﬃcient to guide the behavior of the

back oﬀ algorithm.

Overall, discriminating between transmission errors and collisions is challeng-

ing as this information is rarely explicitly and directly discernible for a given

transmission. However, often the combined views at the sender and receiver can

be used to intelligently and speculatively determine the causes behind packet

losses. From the sender’s perspective, little information is available about a given

packet transmission without receiver feedback. On the other hand, at the re-

ceiver, a given lost transmission may be undetected (e.g., due to a deep signal

fade or high interference or noise) or partially detected (a part of the packet

is corrupted). Both the sender and receiver may collect information about the

channel via carrier sense when they are not transmitting to each other; how-

ever, the state of the channel at the receiver is more important than the state

of the channel at the sender. In the remainder of this section, we propose three

solutions to this problem.

3.1 Receiver Based Discrimination (RBD)

Receiver-based discrimination uses the information available at the receiver to

identify the cause of a packet loss. At the physical layer, detailed information

is available during the packet reception that can allow eﬀective speculation on

the reasons behind the packet loss (e.g., [5]). However, commercial wireless cards

diﬀer signiﬁcantly in the information they expose to upper layers. Furthermore,

some events are more diﬃcult to detect than others (e.g., a collision or fade

during the PLCP header causes complete loss of the packet and no information

is available). Therefore, the available information, and the success rate for the

speculation, varies signiﬁcantly with the underlying hardware and drivers. It is

possible to explore diﬀerent alternative algorithms for discrimination based on

the information available to the receiver.

Discrimination Mechanism: As an example for this approach, we use a mech-

anism suggested by Burns et al. for collision detection [6]. For this approach to

be eﬀective, the hardware of the receiver should be able to detect the existence

of a new packet even though it is currently receiving another packet (indicating a

collision). If the receiver is unable to detect the new packet header, it cannot de-

cide if the loss is due to a collision or error. Other approaches for discrimination

are possible (e.g., based on the observed RSSI). Once the receiver detects a col-

lision, the speculation results are returned to the sender so that it can adjust its

back oﬀ behavior. We feedback this information opportunistically by including

it on subsequent ACKs.

Modiﬁed Backoﬀ Algorithm: Once the collision information is received at the

sender, the following approach is used to increase the contention window. The

conditional collision probability (CCP) that a lost packet is lost due to a collision,

rather than a transmission error, is estimated as follows. The receiver feeds

back on the ACK Necol– the number of packets estimated to have been lost to

collisions for a predetermined observation window (in time or number of packets).

256 S.Y. Han and N.B. Abu-Ghazaleh

The estimated CCP is Necol

Nlost ,whereNlost is the total number of lost packets (to

errors or collisions) in the same window. Since Nlost =Ntransmit −Nsuccess , CCP

is Necol

Ntransmit −Nsuccess . When a transmission is lost, we back oﬀ with probability

CCP.

Note that RDB generally underestimates CCP because it can fail to detect

some collisions. Moreover, our implementation does not account for ACK losses

(which in eﬀect considers all of them to be non-collision losses). However, ACK

losses due to collisions are relatively rare because of the small size of the ACK

packet. Furthermore, nothing prevents ACK packet collision detection using the

same approach.

3.2 Link Quality Estimation (LQE)

In this approach, we ﬁrst estimate the clear channel link quality (CCLQ) which

represents the loss rate on the channel in the absence of collisions. Once that

is estimated, the expected probability of loss for each transmission can be de-

veloped. Over a certain window, again measured in terms of time or number

of transmissions, we expect a number of transmission errors based on the num-

ber of attempted transmissions and the estimated link quality. Losses exceeding

this number can be attributed to collisions and the back oﬀ window adjusted

accordingly. Note that the approach can be made robust for diﬀerent packet

sizes and/or diﬀerent transmission rates (e.g., by estimating the bit error rate

instead of the packet loss rate). Diﬀerent ﬂavors of LQE may be developed

based on the approach for estimating CCLQ, and how the contention window is

adjusted.

Estimating Link Quality: CCLQ may be estimated oﬀ-line for static mesh

networks by running clear channel measurements while the network is idle. How-

ever, this approach is not suitable for dynamic environments and does not adapt

to the time-varying nature of link quality. The challenge in dynamically estimat-

ing CCLQ is that the channel is not idle while the network is active. Thus, simply

tracking the percentage of packets received correctly counts both the losses due

to transmission errors and collisions, under-estimating the link quality. We use

the highest observed link quality value over a ﬁxed number of measurement win-

dows as the CCLQ. Our intuition is that this high link quality occurs due to a

window with few or no collisions. However, the estimate remains approximate:

if no period is free of collisions, then the quality is under estimated. Thus, the

estimate of CCLQ is heuristic; the heuristic may be improved based on empiri-

cal evaluation. Further, LQE expects that the link remains stable over multiple

windows and is therefore slow in tracking a dynamically changing window (e.g.,

due to mobility).

Modiﬁed Backoﬀ Algorithm: In a given window the probability of loss is

computed as the ratio of lost packets to total packets Ploss.IfPloss ≤cclq,

we update CCLQ to be equal to Ploss . However, if Ploss > cclq,wehavesome

collisions. To compute the conditional collision probability, note that

On Backoﬀ in Fading Wireless Channels 257

Ploss =cclq +Pc−cclq ∗Pc

Pc=Ploss −cclq

1−cclq

where Pcis the probability of collision. The conditional collision probability

(CCP) is then Pc

Ploss ; when a transmission is lost, we back oﬀ with probability

CCP.

3.3 Idle Slot Collision Probability Estimation (ISCPE)

Another approach to estimating the conditional collision probability (CCP) relies

on the following observation due to Heusse et al [4]. Speciﬁcally, they observe that

the degree of contention, and hence the probability of collisions, is a function

of the number of idle slots after every successful transmission. They use this

observation to derive an optimized back oﬀ algorithm called IdleSense. IdleSense

signiﬁcantly outperforms Binary Exponential Backoﬀ, but is not compatible with

it. Furthermore, IdleSense does not consider transmission losses.

Observing Idle Probability: Because back oﬀ algorithm pause the decrement

of the back oﬀ counter whenever a busy channel is sensed, the length of a run

of continuous idle slots is a good indicator of contention level around a receiver.

Let the probability that each slot is assigned to some node be p,andq=1−p.

Then, the probability that the k’th trial is the ﬁrst success is

Pr(X=k)=qk−1p(1)

for k=1,2,3, ...

The random variable Xthat indicates the number of trials before the ﬁrst

successful slot is geometrically distributed with expected value E(X)= 1

p.The

average observed length of a run of continuous idle slots, L+1, is also E(X).

Then, p=1/(L+1)andq=L/(L+ 1). Because qis the idle probability of a

slot,

q=(1−Pe)N(2)

where Nrepresents the number of contending nodes, and Peis the attempt

probability per slot. From Eq. 2, Pe=1−q1

N. The idle probability, Pi,isthen

(1 −Pe)N=q.

Because each node senses the idle channel ﬁrst and then takes the following

slot to transmit if its backoﬀ is zero, the minimum Lis 1. Thus, L=1means

that the obtained idle probability is overestimated; this is a limitation of idle

slot based solution.

Estimating Collision Probability: According to [4], the successful transmis-

sion rate can be estimated as

Pt=N·Pe(1 −Pe)N−1(3)

258 S.Y. Han and N.B. Abu-Ghazaleh

A slot where a collision occurs is one where more than one transmission occurs.

More formally,

Pc=1−Pt−Pi(4)

We ca n e x pre s s Pcusing Pias

Pc=1−N(1 −P1

i)P

N−1

i−Pi(5)

Ncan be found by sensing the channel and Pican be found by observing the

number of idle slot after every transmission. Thus, from the computed Pcwe

can estimate CCP, and adjust the back oﬀ with that probability on every lost

packet.

Estimating the Number of Neighbors: Though ISCPE mostly relies on local

information, channel observation is still necessary to determine the number of

neighbors, which is needed to calculate the transmission probability and collision

probability from the idle probability. In a mobile environment, the observed

number of neighbors may be either larger or smaller than the exact number

because of tracking lag. The eﬀect of inaccuracy in estimating the number of

neighbors will be evaluated in the following section.

4 Performance Evaluation

In this section we evaluate the proposed solutions using simulations. For all

simulations, we use the NS-2 network simulator [7]. Unless otherwise indicated,

we use the log-normal model to simulate a fading channel. We also investigated

generating fading losses by training hidden Markov models trained with collected

wireless traces, but no appreciable changes in the general trends were observed;

therefore we elected to demonstrate the solutions using the more controllable

log-normal model.

The ﬁrst study revisits the case of a single hop ﬂow with varying link qual-

ity. Figure 3(a) shows that all three solutions successfully address the backoﬀ

problem in the 1-hop case. Since there are no collisions, RBD achieves ideal

performance since it detects no collisions and assumes that all losses are due

to transmission errors (which is the case). Also, ISCPE will detect an always

idle link, correctly predicting that there are no collisions. LQE does not achieve

ideal behavior because it incorrectly guesses that a collision occurs whenever

the number of losses in a window is above that in the lowest detected window.

In other words, since errors do not occur at a constant rate, LQE mispredicts

collisions, and therefore its performance is slightly worse than the other schemes.

In the second experiment, we compare the fairness achieved by two contend-

ing links using the diﬀerent backoﬀ algorithms. The quality of one link is ﬁxed

at 0.95, while the quality of the other is varied (x-axis). Figure 3(b) shows the

fairness improvement of the three solutions. ISCPE and RBD achieve ideal fair-

ness (Jain’s index of 1). RBD calculates the CCD by the periodic observation

of the number of transmitted, successfully received, and collided packets. The

On Backoﬀ in Fading Wireless Channels 259

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.1

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Efficiency

Link Qualit

1Hop Connection Efficiency vs. Link Quality

Naive 802.11

RBD 802.11

LQE 802.11

ISCPE 802.11

(a) Eﬃciency vs. Link Quality

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Jains Fairness Index

Link Qualit

Jains Fairness Index -- Two Contending links(2Mbps) in Shadowing Channel

Naive 802.11

Ideal 802.11

RBD100

RBD70

LQE

ISCPE

(b) Fairness Comparison in Two Contend-

ing Links (11Mbps)

Fig. 3. Eﬀect of the Solutions

level of accuracy of collision detection aﬀects fairness,especially with low link

quality. If only 70% of collisions are detected by the receiver,the CCD is un-

derestimated, leading to a smaller contention window than ideal. Surprisingly, a

lower accuracy of the RBD does not appreciably harm fairness. Moreover, LQE

shows sensitivity to the asymmetric measurement error as link quality decreases.

This is because LQE is a solution based on estimated link quality, which is in-

accurate if collision loss events occur frequently. However, as can be seen in the

ﬁgure,fairness improves signiﬁcantly in all approaches.

We considered a WLAN scenario where ﬁve senders and ﬁve receivers are in

range of each other. In this scenario, neither hidden terminals nor exposed ter-

minals exist; however, collisions due to concurrent transmissions (two or more

nodes attempting to transmit in the same slot) can occur [8]; persistent or tran-

sient unfairness due to hidden terminals cannot be solved using the schemes in

this paper, which focus only on avoiding backoﬀ when transmission losses occur.

By ﬁxing the number of transmitters and the transmission rate, the probability

of collisions is ﬁxed [8]. In a homogeneous scenario, all ﬁve links have the same

link quality. In a heterogeneous scenario, link qualities are uniformly distributed

in the range of [Min(pj),Max(pj)]. Each point represents an average of twenty

simulation runs to tightly bound the conﬁdence intervals.

Figure 4(a) shows Jain’s fairness index for the homogeneous scenario; un-

fairness is not present because all links have an equal opportunity to access a

wireless channel and no persistent asymmetry exists. Jain’s fairness index in a

heterogeneous scenario is shown in Figure 4(b), where the x-axis represents the

lower bound of link quality and the y-axis represents the fairness index. In this

case, all three proposed solutions dramatically improve unfairness.

Achieving fairness may result in degradation of overall throughput. The pri-

mary reason behind this degradation is that by giving more chances to the

weaker links to transmit, we end up losing more of the transmitted packets due

to errors, harming overall throughput. Thus, aggregate throughput is reduced

even though weak links achieve improved throughput.

260 S.Y. Han and N.B. Abu-Ghazaleh

0.7

0.75

0.8

0.85

0.9

0.95

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

Jain’s Fairness Index

Link Qualit

Jain’s Fairness Index Comparison in Homogeneous Scenario

Naive 802.11

Ideal 802.11

RBD100

RBD70

LQE

ISCPE

(a) Homogeneous Scenario

0.65

0.7

0.75

0.8

0.85

0.9

0.95

0.4 0.5 0.6 0.7 0.8 0.9 1

Jains Fairness Index

Lower Bound of Link Qualities

Jains Fairness Index --- Heterogeneous Scenario

Naive 802.11

Expected 802.11

RBD100

RBD70

LQE

ISCPE

(b) Heterogeneous Scenario

Fig. 4. Jain’s Fairness Index

0.86

0.88

0.9

0.92

0.94

0.96

0.98

0.4 0.5 0.6 0.7 0.8 0.9 1

Jains Fairness Index

Lower Bound of Link Qualities

Jains Fairness Index in RBD --- Heterogeneous Scenario

RBD100

RBD70

RBD50

(a) Jain’s Fairness Comparison

100

102

104

106

0.4 0.5 0.6 0.7 0.8 0.9

Average Throughput(kbps)

Lower Bound of Link Qualities

Throughput Comparison in RBD --- Heterogeneous Scenario

RBD100

RBD70

RBD50

(b) Throughput Comparison

Fig. 5. Comparison in Several Accuracy Level of RBD

Figure 5(a) and 5(b) analyze the impact of discrimination accuracy on the

performance of RBD in a heterogeneous scenario. RBDxx indicates that only

xx%of collisions are detected in the receiver. For the case of RBD50, where

only half of the collisions are detected, the fairness increases due to the small

contention window but average throughput decrease due to collision losses. In

fact, our simulation result showed that the number of collisions for RBD70 and

RBD50 increase by 3.7% and 5% respectively compared to that for RBD100.

Figure 6 shows aggregate throughput of all proposed solutions. Because the

strong links cannot dominate the channel in the solutions, the aggregate through-

put of the proposed solutions is lower than that of the naive 802.11.

Figure 7(a) and 7(b) show the fairness index and throughput as the node

density is increased when the lower bound of link qualities is ﬁxed to 0.6. By

increasing node density, we increase the collision probability. Naive 802.11 shows

pretty stable unfairness through the various node density, though the aggregate

throughput decreases. This is because the collision losses in a high density sce-

nario happen fairly to the senders, while fading losses happen unfairly. However,

On Backoﬀ in Fading Wireless Channels 261

750

800

850

900

950

1000

1050

1100

1150

1200

1250

0.4 0.5 0.6 0.7 0.8 0.9 1

Aggregate Throughput(kbps)

Lower Bound of Link Qualities

Throughput Comparison --- Heterogeneous Scenario

Naive 802.11

Expected 802.11

RBD100

RBD70

LQE

ISCPE

Fig. 6. Throughput Comparison of Solutions

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

0 5 10 15 20 25 30

Jains Fairness Index

Node Densit

Jains Fairness Index -- Heterogeneous Scenario

Naive 802.11

Ideal 802.11

RBD100

RBD70

LQE

ISCPE

(a) Unfairness Result

650

700

750

800

850

900

950

1000

1050

0 5 10 15 20 25 30

Aggregate Throughput(kbps)

Node Densit

Throughput Comparison -- Heterogeneous Scenario

Naive 802.11

Ideal 802.11

RBD100

RBD70

LQE

ISCPE

(b) Throughput Result

Fig. 7. Unfairness And Throughput Comparison As The Node Density Increases

the high collision loss due to high node density aﬀects the performance of each

solution. RBD needs to refer the returned feedback to estimate collision rate. As

the node density increase, the feedback is more likely to be collided with, which

results in incomplete feedback. LQE and ISCPE show stable improvement in

fairness, because they do not depend on feedback.

Figure 8(a) presents a 2-hop connection throughput improvement for a 500

bytes packet size at 11Mbps, where the ﬁrst hop has a 95% link quality and

the second hop has various link qualities which are represented on the x-axis. A

problem with unfairness in chains where a stronger link is upstream of a weaker

link is that the stronger link wins more often, creating a mismatch between input

and output at intermediate nodes and consequently packet drops. Increasing

fairness, signiﬁcantly improve performance by eliminating this eﬀect.

The 2-hop scenario is extended to multiple chain connection as shown in

Figure 8(b). Link qualities for each hop were assigned randomly. Each point

represents an average of twenty simulation runs. All proposed solutions show

improved throughput over any hop counts due to increasing fairness among hops,

262 S.Y. Han and N.B. Abu-Ghazaleh

100

150

200

250

300

350

400

450

500

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Throughput(kbps)

Qualit

of Second Ho

2Hop Connection Throughput vs. Link Quality

Naive 802.11

Ideal 802.11

RBD100

RBD70

LQE

ISCPE

(a) Throughput in a Two-hop Connection

100

150

200

250

300

350

400

450

500

3 4 5 6 7 8 9 10

Throughput(kbps)

Count

Throughput Comparison in Multiple Chain (11Mbps)

Naive 802.11

Ideal 802.11

RBD100

LQE

ISCPE

(b) Throughput in a Multiple Chain

Connection

Fig. 8. Throughput Improvement in a Multi-hop Connection(11Mbps)

which provides further support for using mechanisms that intelligently back oﬀ

in the presence of transmission losses.

5 Related Work

Chua and Lye discuss the need to distinguish collisions from errors in time-

varying channels [9]. They observe that backoﬀ algorithms should be modiﬁed

to consider packets that fail due to channel errors, but oﬀer no solution to the

problem.

Nadeem et al [10] modify Bianchi’s model to study noisy environments. They

proposed smartBEB , which adjusts the contention window in increments based

on the loss probability p. The proposed solution needs time to achieve opti-

mal value. Furthermore, it represents a completely diﬀerent backoﬀ algorithm

that does not inter-operate with the standard IEEE 802.11. The IdleSense algo-

rithm [4] is a similar algorithm to that proposed by Nadeem et al; it also is not

inter-operable with IEEE 802.11.

Discrimination of wireless errors from congestion errors has received signiﬁ-

cant attention with respect to TCP. Since TCP uses packet loss events as an in-

dicator of congestion, it also suﬀers from undetected wireless losses. Speciﬁcally,

when a transmission error cause s apacket to be lost, TCP incorrectly activates

its congestion control mechanism, resulting in poor performance. Much of the

literature proposes end-to-end solutions that analyze the Round Trip Time of

received packets [11,12] or use excplicit congestion notiﬁcation to distinguish

the cause of loss [13]. End-to-end solutions do not help to solve the unfairness

problem in the MAC layer because they do not inﬂuence the backoﬀ algorithm.

6Conclusion

In this paper, we studied the impact of transmission losses on the backoﬀ mech-

anism of IEEE 802.11. Speciﬁcally, the backoﬀ algorithm treats all losses as

On Backoﬀ in Fading Wireless Channels 263

collision losses, leading to unecessary backoﬀ. The problem leads to two nega-

tive side eﬀects: loss of channel time and unfairness. We proposed three diﬀerent

solutions to the problem that attempt to discriminate between transmission er-

rors and collisions then backoﬀ only when a collision occurs. Speciﬁcally, Receiver

Based Discrimination uses available information at the receiver to determine if

a packet loss was due to collisions or errors, and feeds this information back

to the sender. Link Quality Estimation estimates the clear channel link quality

and backs oﬀ whenever the number of losses in a window exceeds the number

expected by the link quality (the deviation indicating potential collisions). Fi-

nally, we proposed an Idle Slot Collision Probability Estimation mechanism that

uses recent results that show that the number of observed idle slots can be used

to estimate collision probability and thus to guide backoﬀ behavior. Simulation

that the proposed approaches signiﬁcantly improve the problem and increase

throughput and fairness overall.

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D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 265–278, 2008.

TSLA: A QoS-Aware On-Demand Routing Protocol for

Mobile Ad Hoc Networks

C. Mbarushimana and A. Shahrabi

School of Engineering and Computing

Glasgow Caledonian University

Glasgow G4 0BA, U.K.

{Consolee.Mbarushimana,A.Shahrabi}@gcal.ac.uk

Abstract. The complexity of Mobile Ad Hoc Networks (MANETs) has led to

the extensive research in the development of their routing protocols as reported

in literature. Although most of the proposed routing protocols are based on the

shortest path algorithm, some other metrics like load and network congestion

have also been considered in some other research. However, with the introduc-

tion of traffic differentiation in IEEE 802.11e, congestion effect becomes more

distinct as the nodes with delay-sensitive multimedia applications tend to be

busy for prolonged periods. This has received little attention in the literature to

date. In this paper, we first expose that the performance of MANETs routing

protocols is highly dependent on the type of traffic generated or routed by in-

termediate nodes. We then propose Type of Service and Load Aware routing

protocol (TSLA), an enhancement to AODV that uses both the traffic load and

the type of service as additional metrics. To our knowledge, TSLA is the first to

avoid congestion by distributing the load over a potentially greater area and

conducting the traffic through less busy nodes and, therefore, less congested

routes. Our simulation study reveals a persistent improvement in throughput

and packet delay of both low and high priority traffic.

Keywords: 802.11e, MANETs, QoS, routing protocol.

1 Introduction

Due to MANETs dynamic characteristics, their routing protocols have received a

great deal of attention over the past few years. They are mainly classified as reactive

(e.g., AODV and DSR) and proactive (e.g., DSDV and OLSR) routing protocols. In

several studies carried out to evaluate their performance [1], [2], the negative points

of reactive protocols were found out to be high delay and packet loss due to stale

routes, whereas the performance of proactive protocols is very much affected by their

routing overhead. The shortest path method used by most of the existing protocols in

route selection does not provide optimal results, especially if the primary route is

congested. This issue has led research on congestion and load aware routing protocols

based on the fact that besides route failures, network congestion is the other main

cause of packet loss in MANETs.

266 C. Mbarushimana and A. Shahrabi

Today’s networks are more prone to congestion due to large volumes of UDP-

based multimedia traffic (e.g., voice, video). UDP flows do not typically back off

when they encounter congestion. They aggressively consume more bandwidth than

TCP flows. The traffic differentiation introduced by 802.11e assigns high priority to

UDP-based delay-sensitive multimedia applications. This is exacerbated by the pro-

longed duration of data transmission in multimedia applications. For example, the

PSTN is sized for average call duration of two minutes, but VoIP connections usually

last longer than this.

Several load aware routing protocols for MANETs have been reported in the litera-

ture [3], [4], [5], [7], [10]. However, to our best knowledge, the effect of the type of

service of the traffic hold in queues of the intermediates nodes has not been investi-

gated. In this paper, we first explore how the type of traffic affects the congestion

status of a node, along with the load. We then propose TSLA; a new routing protocol

which is a cross-layer enhancement to AODV using both the traffic load and the type

of service (ToS) as additional metrics. In TSLA, MAC layer notifies the network

layer about the amount and type of service of traffic held in its queue. Based on this

information, nodes can adjust and advertise their congestion level to neighbouring

nodes. Using OPNET simulation, we then comparatively evaluate the performance of

the proposed scheme and AODV.

The rest of the paper is organised as follows. Section 2 briefly reviews the related

works. In Section 3, we explain our proposed routing protocol in details. We present

the performance evaluation and simulations results in Section 4. Finally, some con-

cluding remarks are given in Section 5.

2 Background

2.1 Related Work

Congestion avoidance routing has been investigated over the past years. Lee and

Gerla proposed a dynamic load aware on demand routing protocol (DLAR) in [4].

The destination chooses the least congested path based on the load information at-

tached in the RREQs and sends a RREP back to the source via the selected route.

Another scheme is proposed in [9], which relies on intermediate nodes not to reply to

route request messages when their load exceeds a certain threshold. A different ap-

proach of load balancing is used by the Dynamic Load-aware Based Load-balanced

(DLBL) routing proposed in [11] to distribute the overhead among all intermediate

nodes. Saigal et al. proposed load aware routing in ad hoc (LARA) in [6], which uses

a metric called traffic density to represent the degree of contention at the MAC layer.

MAC layer channel contention information, number of packets in the interface

queue, and the traditional hop count are the three metrics used for route selection by

CSLAR (contention sensitive load aware routing protocol) proposed in [5]. A similar

protocol, Contention and Queue-aware Routing (CQR) was proposed in [3], which

bases its route selection on the queue size and the contention window. A congestion

adaptive routing (CRP) in which a route is adaptively changeable based on the con-

gestion status of the network is proposed in [7]. Similar to the others, the number of

data packets in the node buffer is used to quantify its congestion status.

TSLA: A QoS-Aware On-Demand Routing Protocol for Mobile Ad Hoc Networks 267

Fig. 1. AODV Route Selectiion

Some other approaches using metrics indirectly related to the network load have

been proposed. Like the Load Balance Routing using Packet Success Rate proposed

in and Lifetime-aware Leisure Degree Adaptive Routing protocol (L-LDAR) [10]. In

[8], Ye et al. investigated the possibilities of spatially separating concurrent TCP

connections using congestion aware routing.

The above reported congestion aware approaches converge in evaluating the nodes

level of activity by measuring either the load or the delay. However, none of the re-

ported studies has evaluated the effect the ToS of the traffic carried by the nodes has

on the routing algorithm. This aspect is investigated in this paper.

2.2 QoS-Aware MANETs

There has been a tremendous increase in multimedia applications over the past few

years. This type of applications requires QoS guarantees in terms of delay, bandwidth,

packet loss and jitter. With the prospects of future MANETs commercial applications,

it is desirable to support these services in MANETs as well.

The IEEE 802.11e EDCA provides a priority scheme to differentiate different ac-

cess categories (ACs) by classifying the arbitration interframe space (AIFS), and the

initial (CWmin) and maximum (CWmax) contention window sizes in the backoff proce-

dures. EDCA uses different AIFS for each AC to achieve the access differentiation,

where the AIFSi for a given ACi is given by

SIFSAIFSNAIFS ii +×=

(1)

where the AIFSNi is an integer dependent on each AC and δ is the time interval of a

slot. With small values AIFSN, high priority classes start decreasing their backoff

counter earlier than low priority classes. The backoff interval (BI) is randomly chosen

in the range [0, CWi] where CWi=2ki-1 CWmin (k is the backoff stage). High priority

classes are given smaller values of CWmin and CWmax, which result in shorter backoff

intervals. In real life, multimedia traffic like voice (AC3) and video (AC2) are as-

signed higher priority over best effort (AC1) TCP based applications (e-mail, FTP).

2.3 Ad Hoc On-Demand Distance Vector Routing Protocol (AODV)

AODV minimizes the number of broadcasts by creating routes on-demand. Figure 1

illustrates a simple route discovery in AODV. The node S seeking a route to a

268 C. Mbarushimana and A. Shahrabi

Fig. 2. Problem Description; Example

Net work with AODV

Fig. 3. FTP Throughput in presence VOIP traffic

destination D broadcasts a RREQ (route request) message to neighbouring nodes. In

the simple case scenario where nodes 1, 2, 3 and 4 have a route to the destination,

they reply with a RREP (route reply) message containing the number of hops (hop

count hc) to the destination. AODV as a distance vector protocol that uses the hop

count as the metric will choose the path through node 4 as it is the shortest.

3 TSLA Routing Protocol

The approaches discussed above converge in evaluating or assessing the level of ac-

tivity in intermediate nodes by measuring either the load or the delay. However, none

of the research reported has evaluated the effect that the type of service of the traffic

carried by intermediate nodes has on the performance of routing protocols.

The problem can be clearly illustrated using the example scenario in Figure 2.

Consider that the different nodes support IEEE 802.11e with the default parameters.

At time t1 a voice connection is opened between nodes VS and VD. While the connec-

tion is still active at time t2, the node TS generates FTP traffic destined for destination

TD. Based on AODV route selection criteria, the node TS will establish a route to TD

through node VS or node VD as they provide the shortest path to TD. TS will therefore

try to route the FTP traffic through the nodes that are already engaged in a VoIP con-

versation. With the limited bandwidth in MANETs, it is highly unlikely that TS will

have residual bandwidth to service the FTP connection as well. FTP traffic has a low

priority compared to the voice traffic; it will queue at the source waiting for an oppor-

tunity to be transmitted. If the voice connection lasts for too long, this might results

into buffer overflow and some packets might get dropped. Another important point to

be taken into consideration is that in real life networks, high priority traffic conversa-

tions tend to last longer than lower priority traffic. Downloading a webpage or e-mail

lasts just a few seconds, while voice calls and video streaming can last several

minutes.

The graph in Figure 3 visualizes the throughput achievable by FTP in presence of

voice traffic. It can be clearly seen that FTP throughput is very significantly decreased

in presence of voice traffic, where its value drops to around one tenth of the expected

TSLA: A QoS-Aware On-Demand Routing Protocol for Mobile Ad Hoc Networks 269

Tabel 1. Node congestion Level Classification

Load ToS Congestion

Level (n)

Node Type

0 0 0 Green

0 1 1 Yellow

1 0 2 Orange

1 1 3 Red

throughput. Similarly, if the node TS had generated a high priority traffic, it will not

get a chance to be transmitted through VS or VD as they are already busy with a simi-

lar priority traffic, and it is a know fact that nodes which are already transmitting tend

to monopolise the channel.

In this paper, we suggest TSLA; a simple yet effective routing protocol to alleviate

this problem and at the same time to achieve load balancing. TSLA is a cross-layer

approach to enhance AODV by considering the effect of traffic ToS and coupling it

with the existing congestion avoidance approach, which considers the load on inter-

mediate nodes in the route selection process. The focus of TSLA is on the route dis-

covery process. For a node wishing to transmit data, it broadcasts a RREQ like in

AODV. On receiving a RREQ, a node checks its routing table for a route to the desti-

nation. In case it has a route to the destination and therefore wishes to generate a

RREP, it first checks its congestion level. Using a similar colour scheme as in [7],

nodes are classified into four categories; green, yellow, orange and red.

The load congestion level is determined based on the ratio between data currently

buffered and the buffer size. This ratio can be adjusted dynamically, but in this study,

a node with half buffer full is considered load congested. As for the ToS based con-

gestion, nodes with best effort and background traffic are considered available

whereas those with voice or video traffic are considered less available for new con-

nections. The individual congestion levels are determined by the MAC layer of the

node and given to the IP layer to determine the overall congestion level. The different

possible combinations are shown in Table 1. A node with no traffic or with more than

half buffer empty of delay-insensitive traffic is considered more open to receive more

traffic, it is therefore labelled green. Whereas a node with more than half buffer full

with delay-sensitive traffic is considered as a red node and therefore not available to

accept new connections. A node with low load and delay-sensitive data is labelled

yellow and therefore more open to accept traffic than a best effort traffic highly

loaded node, which is labelled orange. This is because in QoS-aware networks, it is

likely that the node with delay-sensitive traffic will get a chance to transmit it all

before the node with best effort traffic. Moreover, it can be assumed that since delay-

sensitive applications usually last longer, a half buffer is an indication that the com-

munication is close to the end. Whereas a full buffer can indicate that, a communica-

tion is in process and likely to last for several minutes.

270 C. Mbarushimana and A. Shahrabi

Fig. 4. TSLA Route Selection

After the intermediate node determines its congestion level, it generates a RREP

packet. In this approach, we propose to modify the information contained in the

RREP message so that it reflects the congestion status of the node. We therefore pro-

pose to add to the actual number of hops to the destination, additional hops propor-

tional to the congestion level indicated by the node colour type. The resulting hop

count included in the RREP is therefore given by

)_(_ nlevelcongestionhcactualhc ×+= (2)

where n is a constant that can be varied depending on the network size, and therefore

is proportional to the average hop count of the network. For small networks, a small

value of n will be obtained. On receiving the RREPs, the destination will choose the

route with the smallest number of hop count as in AODV.

Let us use the same example network of Figure 1 and consider that the one hop in-

termediate nodes congestion levels are labelled green to red as shown in Figure 4(a).

As it is a small network, lets consider n=1. The intermediate nodes will therefore

reply with RREP with the modified hop count values as shown in the figure. Applying

the shortest path algorithm, TSLA will therefore choose to use the next hop as node 1

(Figure 4(b)), unlike AODV which chose the busiest node 4.

We mentioned earlier that TSLA is a cross layer solution that works in conjunction

with the MAC layer. The MAC layer is therefore responsible for updating the IP layer

whenever there is a change in either the traffic ToS or the buffer load. In our imple-

mentation, this was achieved by creating two interrupts at the MAC layer, one for the

ToS and the other one for the load. The rising edge of the ToS interrupt notifies the IP

layer that this node currently hold in its queues delay-sensitive traffic, while its falling

edge indicates best effort or background traffic. Similarly, the rising edge of the load

interrupt notifies the IP layer that the node is becoming overloaded and a falling edge

indicates the node is lightly loaded. The two interrupts generated by the MAC layer

are directly fed to the IP layer, which in turn will have to notify the MANET process.

TSLA will handle them as explained above.

4 Performance Evaluation

In this section, we evaluate the performance of the TSLA routing protocol described

in the previous section and we compare it to AODV. The performance of the two

TSLA: A QoS-Aware On-Demand Routing Protocol for Mobile Ad Hoc Networks 271

routing protocols is assessed by analysing the network throughput, the packet end-to-

end delay, the amount of traffic dropped and the routing load.

4.1 Simulation Setup and Parameters

Our simulations were conducted using OPNET Modeller 11.5. The simulations were

run for 1000 seconds. We simulated a network consisting of 50 mobile nodes moving

in a 1000x1000 m area and a nominal transmission range of 250m. The MAC layer

protocol used is EDCA, the four standard access categories (ACs) are assigned priori-

ties based on the default parameters for an IEEE802.11e physical layer. The network

traffic consisted of long-lived FTP file transfers. The voice traffic was simulated by

establishing G711 CBR connections between mobile nodes at some predefined time

of the simulation. As the protocol (TSLA) proposed in this paper is a congestion

avoidance routing protocol, we evaluated its performance compared to AODV’s un-

der different congestion levels. We also evaluated the two protocols under different

mobility levels. The simulation results are averaged over five different seeds and the

error bars represent 90% confidence intervals.

4.2 Simulation Results

4.2.1 Number of Sources

The performance of on-demand routing protocols is highly dependent on the number

of nodes concurrently transmitting. TSLA is based on avoiding nodes highly loaded

with high priority traffic; we therefore vary the number of voice traffic sources.

A. Throughput: First, keeping the number of FTP connections to 10, the voice con-

nections were varied from 1 to 5. With the increase in number of VoIP nodes, FTP

performance for the two routing protocols deteriorates as seen in Figure 5(a). We

observe a decrease of 30% in FTP goodput when the number of voice connections is

increased from 1 to 5. This is because more transmission opportunities are given to

the nodes with delay-sensitive voice traffic, and less TCP traffic gets transmitted. The

voice goodput on the other hand (Figure 5(b)) is increased when the number of voice

connections increases. However, the increase in voice throughput is not a linear func-

tion of the number of voice connections. This is because self-contention exists be-

tween the voice connections themselves.

If we consider the difference in the performance of the two routing protocols,

TSLA outperforms AODV in almost all the cases. With TSLA, new connections use

only the least congested nodes and therefore the load is uniformly distributed across

the network. More specifically, the best effort traffic avoids the nodes with voice

traffic, therefore avoiding being dropped due to lack of transmission opportunities. It

is also observed that it is not only best effort traffic that benefits from the TSLA load

balancing approach. The voice traffic goodput is also higher in TSLA. Even though

voice traffic is high priority, if a new voice connection has to be established while

there is already an ongoing voice conversation, it is less likely to be transferred

through the nodes that are already busy with voice traffic as they are of the same

priority. It is better for the new connections to be routed through less busier paths

even if they are longer, therefore avoiding same priority traffic crashes at some nodes.

272 C. Mbarushimana and A. Shahrabi

(a) (b)

Fig. 5. Effect of Voice Connections on Goodput: (a) FTP, (b) Voice

(a) (b)

Fig. 6. Effect of Voice Connections on Packet Delay: (a) FTP, (b) Voice

B. Packet End-to-End Delay: The total delay experienced by any packet consists of

queuing and propagation delay. The queuing delay of a specific packet will depend on

the number of other, earlier-arriving packets that are queued and waiting for transmis-

sion across the link. In MANETs, the queuing delay also depends on the medium

contention from neighbouring nodes as the medium access is through distributed

mechanisms. The propagation delay on the other hand depends on the speed of the

medium and the length of the path.

Most of the load balancing or load aware routing protocols developed for

MANETs have been reported to achieve better delay than normal routing protocols.

Similarly, TSLA is able to constantly deliver both TCP and voice traffic with delays

smaller than AODV’s. As expected, the end-to-end delay increase is observed in all

the cases when the number of traffic sources increases (Figure 6(a) and 6(b)). This is

a result of increased medium contention.

FTP traffic is routed avoiding nodes busy with delay sensitive voice traffic, but if

they encounter best effort traffic on the chosen route, they might face a little bit of

waiting since the priority is the same. Nevertheless, the waiting is shorter than being

routed through nodes with higher priority traffic, hence the decrease in the TCP seg-

ment delay (Figure 6(a)). Similarly, TSLA voice delays are smaller than AODV in all

the cases as seen in Figure 6(b). Another important point to note in dealing with the

TSLA: A QoS-Aware On-Demand Routing Protocol for Mobile Ad Hoc Networks 273

(a) (b)

Fig. 7. Effect of Voice Connections on Traffic Dropped: (a)FTP, (b)Voice

(a) (b)

Fig. 8. Effect of Voice Connections on Routing Load Normalized on: (a)FTP, (b)Voice

end-to-end delay is that since TSLA packets are routed through longer paths, they

would be expected to have higher propagation delay. However, as the chosen paths

are the least congested, it is less likely that the packets will face long propagation

delay. Moreover, since the queuing delay is much reduced, the overall packet (seg-

ment) delay is reduced.

C. Traffic Dropped: In 802.11e, a queue is held for each access category. The rate at

which packets arrive at the MAC layer might exceed the rate at which they are trans-

mitted. This is common in wireless networks due to the fierce way in which the sta-

tions contend for the medium. This would results into overflow of the buffer used to

store the ACs data awaiting transmission in which case some of them might be

dropped by the MAC layer itself. Moreover, in wireless networks, when the MAC

ACK is not received, the source station retransmits the same frame repeatedly until

the MAC ACK is received or it exceeds the limit of transmissions attempts allowed

per frame.

The combined traffic dropped by the MAC layer for the two types of traffic when

the number of sources is varied is shown in Figure 7. All the graphs show an increase

in data traffic dropped for the two routing protocols due to increased congestion.

Packet drops is one sign of congestions in any network. Load aware routing protocols

274 C. Mbarushimana and A. Shahrabi

(a) (b)

Fig. 9. Effect of Voice Connection Time on Goodput: (a)FTP, (b)Voice

(a) (b)

Fig. 10. Effect of Voice Connection Time on Packet Delay: (a)FTP, (b)Voice

are designed to avoid network congestion, thus reducing packets drop. TSLA is no

exception, and it is able to achieve smaller numbers of packets drop compared to

AODV. Both FTP and voice suffer from increase in the number of voice connections

which results into more packets drops.

D. Routing Overhead: High routing load usually has a significant performance impact

especially in low bandwidth wireless links. It is therefore important to evaluate how

much routing load is produced by a reactive protocol. The routing load produced by

reactive protocols is proportional to the generated data. For AODV and TSLA who

have the same route discovery process, they would generate similar amount of routing

overhead in the same network setting. They however are able to deliver different

amount of data traffic. This paper evaluates the normalized routing load, which is the

ratio between routing traffic generated to the successfully received data traffic.

The graphs shown in Figure 8(a) and 8(b) are the variation of normalised routing

on FTP and voice goodput respectively. With increasing the number of voice connec-

tions, the FTP traffic generated still stays the same; therefore, the routing load pro-

duced stays similar as well. Nevertheless, as the FTP traffic received drops when the

number of voice connections increases, the normalized routing load steadily increases

as seen in Figure 8(a). As TSLA delivers more FTP traffic than AODV does (Figure

5(a)), its normalized routing load is consequently smaller than AODV’s. The routing

TSLA: A QoS-Aware On-Demand Routing Protocol for Mobile Ad Hoc Networks 275

(a) (b)

Fig. 11. Effect of Voice Connection Time on Traffic Dropped: (a)FTP, (b)Voice

load normalized on voice traffic decreases as the voice goodput increases as shown on

Figure 8(b), and TSLA shows the lowest as it achieves better goodput than AODV.

4.2.2 Voice Connection Time

We mentioned earlier that in today’s networks, multimedia traffic connections tend to

last longer than best effort traffic. We therefore evaluate the effect of voice connec-

tion time on the performance of the two routing protocols. The voice connection time

was varied as a percentage of the total simulation time.

The goodput achieved by FTP connections is very much affected by the voice con-

nection time (Figure 9(a). As best effort opportunities to be transmitted when voice

transfer is taking place are almost none, the longer the voice connections last, the poor

the FTP goodput becomes. Although an increased number of voice connections were

proven harmful to FTP goodput (Figure 5(a)), it is clear in this section that long-lived

voice connections have the worst effect on FTP, whose goodput drops below 25%

when there is constant voice traffic transfer.

Using TSLA as the routing protocol, the route selection tries to bypass those nodes

with voice traffic. TSLA is therefore able to achieve a remarkable improvement of

30% in FTP goodput in case of long-lasting voice connections. As for the voice traf-

fic, TSLA is also able to deliver a large amount compared to AODV (Figure 9(b)). In

TSLA networks, new connections voice traffic is routed through less loaded nodes, or

through nodes with best effort traffic, in which case they will be able to get through

immediately. Whereas in AODV, if the voice traffic is routed through a node already

with voice traffic, there will be self-contention and some might be dropped.

The packet delay behaviour mirrors that of the goodput. AODV and TSLA TCP

segment delays are similar for short time connections, but as the voice connection

time increases, the improvement in TSLA segment delay becomes remarkable as seen

in Figure 10(a). As for the voice packet delay (Figure 10(b)), TLSA is constantly

achieving better values than AODV (improved by 50%). The reason it is bigger in

voice delay is that, for any packets which bypass red nodes, they are automatically

transferred ahead any existing best effort traffic as they have higher priority, whereas

the best effort packets will have to wait their turn for transmission in a FIFO fashion.

276 C. Mbarushimana and A. Shahrabi

(a) (b)

Fig. 12. Effect of Date rate on Goodput: (a)FTP, (b)Voice

(a) (b)

Fig. 13. Effect of Data Rate on Packet Delay: (a)FTP, (b)Voice

The packet dropped metric has characteristics similar to those of throughput and

delay. The longer the voice connections last, the large the amount of traffic dropped

(both FTP and voice as seen in Figures 11(a) and 11(b) respectively). For FTP traffic,

time slots during which transmission is possible are reduced, the queues build up and

more traffic end up being dropped. As for voice traffic, traffic dropped over long

periods is logically bound to be more than shorter ones. TSLA networks drop fewer

packets than AODV as congested nodes are bypassed, and only nodes less likely to

drop packets are used on the primary path.

4.2.3 Data Rate

In TSLA implementation, the best effort traffic is not meant to affect significantly the

performance of the routing protocol unless its load is high. We evaluated how the two

protocols behave under different FTP load. In these scenarios, the FTP traffic rate is

varied, and the voice traffic is generated in 60% of the total simulation time. As seen

on Figure 12(a), there is an increase in FTP goodput, and TSLA is able to deliver

successfully more packets than AODV. The difference is more significant at higher

loads. This is because in TSLA, following the nodes highly loaded with voice traffic;

the nodes highly loaded with best effort traffic are the next one to be avoided. This

Similar to the previous cases, the increase in FTP data generation rate results into

increase in network contention hence the deterioration of voice performance as seen

on Figure 12(b). TSLA shows a better performance than AODV in all the cases.

TSLA: A QoS-Aware On-Demand Routing Protocol for Mobile Ad Hoc Networks 277

(a) (b)

Fig. 14. Effect of Mobility on Goodput: (a)FTP, (b)Voice

(a) (b)

Fig. 15. Effect of Mobility on Packet Delay: (a)FTP, (b)Voice

Similarly, the packet delay for the two types of traffic is increased with FTP load.

With congested networks, packets take longer to reach the destination and the queuing-

delay is longer as well. A considerable improvement is observed in TSLA networks, for

both FTP and voice traffic delay as shown on Figure 13(a) and 13(b) respectively.

4.2.4 Mobility

In MANETs, nodes mobility plays a significant role in determining the performance

of routing protocols. We therefore evaluated how the two routing protocols perform

under different mobility levels. The nodes were set to move following a random way-

point mobility model, with an average speed of 10 m/s. Different mobility models

were obtained by varying the pause time from 0 to 100 seconds.

The best effort traffic throughput and voice throughput are shown on Figure 14(a)

and 14(b) respectively. We observe an improvement in network throughput in low mo-

bility scenarios. This is because with large values of pause time, the routes are broken

less frequently, the packet loss is reduced, hence the increase in the network throughput.

The two protocols behave similarly, the difference in favour of TSLA being due to its

use of congestion avoidance. Similarly, the packet end-to-end delay is reduced for the

two protocols. As the route breakages are less frequent in low mobility scenarios,

shorter time is spent in discovering and repairing routes, hence the decrease in TCP

segment delay and voice packet delay as seen on Figure 15(a) and 15(b).

278 C. Mbarushimana and A. Shahrabi

5 Conclusion

During the route discovery process in ordinary routing protocols in MANETs, nodes

advertise themselves as capable of reaching the destination irrespective of the type of

service and the load of the traffic in their queues. The new arriving traffic might there-

fore face long delay or get dropped failing to get transmitted ahead of existing high

priority traffic. The adverse effect of this issue has been investigated in this paper.

As such incidents are common in QoS-aware MANETs that are concerned with

QoS guarantees for delay sensitive applications, we then propose a new Type of Ser-

vice and Load Aware (TSLA) routing protocol which avoids such nodes in the route

discovery process. TSLA is a cross-layer congestion-avoidance routing protocol in

which the routes through nodes engaged with large amount of delay-sensitive traffic

for extended periods are only selected as the last resort, even when they are shorter.

Avoiding intermediate nodes heavily occupied with high priority traffic can poten-

tially alleviate congestion resulting in less packets drop and incurring shorter end-to-

end delay. Our heavy simulation study has confirmed the advantages of TSLA over

AODV in QoS-aware MANETs. Although TSLA has been implemented as an en-

hancement to AODV, the idea is applicable to any other reactive routing protocol; a

scenario for our future study.

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Query Dissemination with Predictable

Reachability and Energy Usage in Sensor

Networks

Zinaida Benenson1,,MarkusBestehorn

2, Erik Buchmann2, Felix C. Freiling1,

and Marek Jawurek3

1University of Mannheim, Germany

2University of Karlsruhe, Germany

3Fraunhofer IESE, Germany

Abstract. Energy-eﬃcient query dissemination plays an important role

for the lifetime of sensor networks. In this work, we consider probabilis-

tic ﬂooding for query dissemination and develop an analytical framework

which enables the base station to predict the energy consumed and the

nodes reached according to the rebroadcast probability. Furthermore, we

devise a topology discovery protocol that collects the structural infor-

mation required for the framework. Our analysis shows that the energy

savings exceed the energy spent to obtain the required information after

a small number of query disseminations in realistic settings. We veriﬁed

our results both with simulations and experiments using the SUN Spot

nodes.

1 Introduction

Wireless sensor networks have been established in many important applica-

tion areas from ambient intelligence over scientiﬁc research to industrial uses.

Such sensor networks usually consist of numerous battery-powered nodes [3,2]

equipped with sensing devices, low-power wireless communication and limited

computational resources. In order to fulﬁll complex measurement tasks, the

sensor-nodes use self-organization techniques to form ad-hoc networks where

the nodes (1) forward queries from a central base station, (2) measure sensor

values, (3) do in-network query processing and (4) return the results to the base

station. In this paper, we focus on the query dissemination phase, i.e., the ﬁrst

step of query processing in sensor networks.

One of the most important optimization goals in sensor networks is to maxi-

mize their lifetime by minimizing the energy spent for communication. However,

saving communication eﬀort obviously may have a negative eﬀect on quality-of-

service parameters of the query. For example, if energy is saved by querying only

50% of the nodes, the accuracy of the query degrades. How much it degrades de-

pends on many factors and is not very well understood. Quantifying this tradeoﬀ

Zinaida Benenson was supported by Landesstiftung Baden W¨urttemberg as part of

Project “ZeuS” and by the Schlieben-Lange scholarship.

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 279–292, 2008.

Springer-Verlag Berlin Heidelberg 2008

280 Z. Benenson et al.

between communication strategy and service quality for query dissemination is

the topic of this paper.

Related Work. While numerous sophisticated in-network query processing tech-

niques have been developed [11,12,18,19], they mostly focus on operator process-

ing, optimization and aggregation techniques. The dissemination of the query

from the base station into the network has either been disregarded or is done

via simple ﬂooding [8,14]. It is well known that ﬂooding wastes energy. For ex-

ample, analyses [13] have shown that a rebroadcast increases the area where

the message is received by 61% at most, dropping to ≈20% for average net-

works. Therefore, most of the rebroadcasts will not result in additional nodes

receiving the query. Furthermore, most nodes receive the query more than once,

which results in additional energy consumption because receiving messages also

consumes energy.

To avoid the disadvantages of simple ﬂooding, several mechanisms for broad-

casting in wireless networks have been proposed (see [17] for an overview). Gen-

erally, these approaches try to control which nodes rebroadcast a message in

order to keep the number of nodes that receive the query more than once as

small as possible. For example, in counter-based ﬂooding schemes [13,17], if a

node hears kor more of its neighbors rebroadcast the message, it suppresses

its own transmission. In neighbor knowledge broadcasting schemes [10,15], nodes

use local topology information to determine which nodes must rebroadcast a

message. The advantage of these approaches is that the overlap of recipients

can be reduced in a controlled manner, but this comes at the signiﬁcant cost

of acquiring and updating the neighborhood information. Furthermore, [16] has

shown that ﬁnding a minimal set of rebroadcasting nodes can be reduced to the

Dominating Set Problem, which is NP-complete [6].

A very promising approach are probabilistic or epidemic broadcast algorithms

[13,5] where every node forwards a message with a predeﬁned probability p.

Compared to schemes using neighborhood knowledge, these methods do not in-

duce the overhead of acquiring, storing and updating neighborhood knowledge.

However, these schemes require information about the network in order to de-

termine an optimal p.Ifpis set too high, the disadvantages of simple ﬂooding

arise, and if pis too low, the probability that all nodes receive the broadcast

message decreases. In this paper we will focus on probabilistic ﬂooding.

Contributions. In this paper, we study query dissemination techniques that can

be seen as a combination between neighbor knowledge broadcasting and prob-

abilistic ﬂooding. Using extensive simulations we explore the tradeoﬀ between

energy, reachability and structural information required. We show that using

very moderate structural information on the network it is possible to predict

the number of nodes reached according to a certain broadcast probability p.

Furthermore, the number of transmissions can be estimated in advance.

In particular, we make the following contributions:

1. We introduce an analytical framework to estimate the reachability and the

number of transmissions in dependence to the rebroadcast probability p.Our

Query Dissemination with Predictable Reachability and Energy Usage 281

framework bases on connectivity information and a histogram containing the

number of nodes reached with each rebroadcast, starting at the base station.

2. We describe a lightweight distributed topology discovery protocol which ob-

tains the required information. Our analysis shows that gathering structural

information and computing an optimal psaves energy after a small number

of probabilistic ﬂoodings in realistic settings.

3. We conducted simulations with up to 425 nodes to verify the results of our

framework for large numbers of nodes. Furthermore, we tested our ﬁndings

on a testbed consisting of 17 Sun Spot sensor nodes.

Outline. In Section 2 we present a framework which estimates the number of

nodes reached and energy spent by probabilistic ﬂooding for a particular re-

broadcast probability p. The framework depends on topological information. In

Section 3 we show how to gather the required information eﬃciently. In Section 4

we present simulation and experimental results, and we conclude in Section 5.

2 Reachability and Energy Consumption Prediction for

Query Dissemination

In this work we focus on probabilistic ﬂooding where each node rebroadcasts

queries with a ﬁxed probability p. Parameter pallows to ﬁne-tune the tradeoﬀ

between energy spent for query dissemination and the number of nodes reached.

Moreover, in most (densely connected) sensor networks there exists a p0<1

such that all nodes are reached by the base station. Thus, if the rebroadcast

probability pis larger than p0, more queries are rebroadcast than necessary,

and the query dissemination can save energy by using p0. On the other hand, if

p<p

0, the query reaches only a fraction of nodes. This can be useful to trade

energy with result quality.

Our goal is to develop a framework to predict for every pthe number of

reached nodes Rand the energy Econsumed by the query dissemination pro-

cess. Knowing the dependencies between p,Rand Eallows the base station to

estimate how many nodes can be reached using a ﬁxed amount of energy, or

at which pthe reachability cannot be improved any more (at least, for reason-

able energy cost). Obviously, energy usage prediction depends on reachability

prediction, which in turn depends on the network topology. The more the base

station knows about network topology, the more precise prediction can be made.

On the other hand, gathering information about network topology consumes en-

ergy. Thus, we are interested in making predictions using a set of topological

information which can be obtained without exhausting potential energy savings

due to deriving an optimal p.

In the following we will present our framework for predicting reachability R(p)

and energy consumption E(p) according to given topological information and a

rebroadcast probability p. More speciﬁcally, R(p) estimates the number of nodes

reached, and E(p) provides an estimate for the number of sent and received

messages, which is proportional to the energy consumed.

282 Z. Benenson et al.

2.1 Assumptions and Notations

Our estimation of the reachability bases on two assumptions:

–The sensor network is in a stable state while ﬂooding the query, i.e., the num-

ber of nodes in each hop set does not change signiﬁcantly between obtaining

topology information and ﬂooding.

–A node is either reached by a node that is one hop closer to the base station,

or has the same hop distance to the base station.

A ﬂooding disperses through a topology in multiple steps, beginning at the base

station. The nodes which receive the query directly from the base station (1 hop)

rebroadcast it, so that the query reaches the nodes two hops away from the base

station in the next step. The procedure recurs until each node has forwarded the

message once.

If a node Areceives a previously unknown ﬂooding message from a node B,

we say that Ais reached by Bin this particular ﬂooding instance. In addition,

we will denote all nodes reached with hhops as hop set H[h].

2.2 Topological Information

Our analytical framework depends on the following topological information (Sec-

tion 3 will introduce a protocol that collects it eﬃciently):

–histogram[h]: stores the number of nodes reached at each hop from the base

station, i.e., ∀i∈{1···n}:histogram[i]=|H[i]|.

–connectivity[h] stores the average number of connections from one node in

hop set H[h] to a node from H[h−1].

–interconnectivity[h] stores the average number of connections between the

nodes from the same hop set, i.e., the connections a node in H[h]hasto

another node in H[h].

Figure 1 illustrates this with an example. In this ﬁgure the hop set H[i]consists

of 3 nodes, the previous hop set H[i−1] consists of 2 nodes. Edges connect the

nodes that can hear each other’s broadcast. Figure 2 shows the histogram and

(inter-)connectivity for the example in Figure 1.

2.3 Reachability Prediction

Let Rdirect(h, p) be the number of nodes in hop set hwhich received their ﬂooding

message directly from a node in the hop set H[h−1], and let Rindirect (h, p)denote

the number of nodes which received the ﬂooded message from a node in the same

hop set H[h]. Then the number of nodes reached at the h-th hop for a speciﬁc

rebroadcast probability pcan be computed as follows:

R(h, p)=min(Rdirect(h, p)+Rindirect(h, p),histogram[h]) (1)

The total reachability for some pis the sum over all hops:

R(p)=

R(h, p)(2)

Query Dissemination with Predictable Reachability and Energy Usage 283

Fig. 1. Example for hop sets and their (Inter-)Connectivity

... i−1i...

... 2 3 ...

(a) Histogram

... i−1i...

... 1.5 2 ...

(b) Connectivity

... i−1i...

... 0 4/3...

Fig. 2. Histogram, Connectivity and Interconnectivity in Figure 1

Note that Rdirect(h, p)+Rindirect (h, p) can be larger than the actual number

of nodes in the hop set H[h], because rebroadcast messages can be received

from nodes which might have received the message before. Thus the minimum

function ensures that at most the actual number of nodes in the hop set is

returned. Rdirect(h, p) can be computed recursively: histogram[h−1] nodes could

forward a message directly to a node in H[h], but only k=p∗R(h−1,p)of

histogram[h−1] nodes have received the message in the previous step.

Let P(event) denote the probability for a certain event. Now we need the

probability for the event “A node from hop set H[h] receives its message from a

node from hop set H[h−1]” The probability for this event is:

P(reached directly) = 1 −P(not reached directly) (3)

The counter-event “not reached directly” can be obtained by considering the

nodes which did not receive the message in the previous step. Thus, the problem

corresponds to an urn model where kblack and n−kred balls are placed

in an urn, and P(not reached directly) means to draw red balls only. Let l=

connectivity[h] be the number of connections a node in H[h] has to the previous

hop set H[h−1] on average. The probability P(not reached directly) can be

computed as follows:

P(not reached directly) = connectivity[h]−1



l=0

n−l−k

n−l(4)

After having obtained this probability, we can calculate the number of nodes

from hop set H[h] receiving the ﬂooding directly by multiplying the probability

for the opposite case with the number of nodes in the hop set:

Rdirect(h, p)=P(reached directly) ∗histogram[h](5)

284 Z. Benenson et al.

The remaining nodes in hop set H[h] can still be reached indirectly, i.e., by a

subsequent broadcast by nodes from the same hop set. To calculate the number of

nodes reached indirectly, we assume that the nodes which received the message

are equally distributed over the hop set, i.e., if kfrom nnodes are directly

reached, each node in the hop set obtained the message with probability k

n.Our

experimental evaluation will show that this simpliﬁcation is legitimate, i.e, it is

not necessary to collect topological information in more detail. We calculate the

number of neighbors of a node which directly received the ﬂooding message and

then rebroadcast it as:

ndr =P(reached directly) ∗interconnectivity[h]∗p(6)

Finally, we estimate the number of nodes which received the ﬂooding message

indirectly: Rindirect (h, p)=ndr ∗histogram[h].(7)

2.4 Energy Consumption Prediction

After having estimated the number of nodes reached, we will estimate the energy

required by probabilistic ﬂooding. Therefore, we distinguish between sent and

received messages. The number of messages sent in hop set H[h]isasfollows:

msgssent (h, p)=R(h, p)∗p(8)

Next, we estimate the number of messages received from the nodes of the previ-

ous hop:

Rec1(h, p)=R(h−1,p)∗p∗connectivity[h]∗histogram[h]

histogram[h−1] (9)

connectivity[h]∗histogram[h]

histogram[h−1] calculates the average number of outgoing links from

hop set H[h−1] to H[h]. The number of all “receive” events induced at nodes

of the hop set H[h] and hop set H[h−1] by the rebroadcast of reached nodes of

hop set H[h] can be calculated as follows:

Rec2(h, p)=R(h, p)∗p∗(connectivity[h]+interconnectivity[h]) (10)

Finally, the total number of received messages can be estimated as

msgsreceived(h, p)=Rec1(h, p)+Rec2(h, p) (11)

The total energy cost of the probabilistic ﬂooding is calculated by vector mul-

tiplication of the tuple of sent and received messages with the vector of energy

costs for sending and receiving and adding them up for every hop set:

E(p)=

(msgssent ,msgs

received)(h,p)∗energy P erSend

energy P erReceive(12)

Query Dissemination with Predictable Reachability and Energy Usage 285

3 Topology Discovery Protocol

We now describe the light-weight topology discovery protocol used in our exper-

iments. It is an adaption of the well-known echo algorithm by Chang [4], i.e., it

is structured in two waves: The ﬁrst expansion wave of messages is ﬂooded from

the base station and is used to explore the network. When this waves reaches the

borders of the network, a second cont raction wave ﬂows back to the base station,

aggregating topology information / histograms on its way. The prediction for-

mulas presented in Section 2 use these histograms to determine the parameter p

for probabilistic ﬂooding. Due to space limitations, we only present the general

idea of the protocol here.

The base station initiates the topology discovery by broadcasting a Topolog y

Discovery Message (TDReq), thus starting the expansion wave.

Expansion Wave. When a node receives a TDReq for the ﬁrst time, the receiver

must accomplish 4 steps:

1. Create an empty histogram data structure as described in Section 2.2 and

mark the sender of the TDReq as its parent node. The receiver also extracts

the hop number from the TDReq and stores it.

2. Start a timeout to ensure that the receiver does not wait forever for potential

children.

3. Broadcast own request message with the receiver as sender, an incremented

hop number, and parent id of the receiver.

4. Wait until the afore mentioned timeout expires. Note that the timeout should

be suﬃciently long to allow the children of the node to receive, process

and rebroadcast their own TDReq messages. When the timeout expires, the

contraction phase starts.

If a TDReq is received, then it could have three diﬀerent originators. It could

either be (1) a sibling of the node’s parent, (2) a sibling of the node itself, or (3)

a node in the subsequent hop set. Note that all three cases can be distinguished

from the information contained in the TDReq. For example, in case (3) the request

will contain the id of the receiver node. Depending on the case, the connectivity

or inter-connectivity value in the histogram data structure is modiﬁed.

Contraction Wave. While a node waits for the timeout to expire, all incoming

Topology Discovery Responses are recorded into the histogram data structure.

On leaf nodes, the timeout expires without any incoming response messages, thus

leaf nodes create response messages containing their hop number and appropriate

values for connectivity and inter-connectivity1. Every leaf node sends such a

response message to its parent and thereby starts the contraction wave.

1The average values for connectivity / inter-connectivity are stored as tuples to allow

aggregation: The ﬁrst value contains the sum of connections and the second stands

for the number of nodes which have aggregated these connections. This allows the

aggregation at every node and avoids ﬂoating point numbers in messages.

286 Z. Benenson et al.

In case the node has children, the histogram lists of every response are aggre-

gated in a way that the position iof the resulting list contains the sum of the

histograms of the children. These aggregates histograms are always forwarded to

the parent node and eventually reach the base station. Based on these values, the

base station is able to predict reachability and energy consumption as described

in Section 2.

Energy Cost and Message Size of Topology Discovery Protocol. As

every node only broadcasts one Topology Discovery Request and only sends one

Topology Discovery Response, the energy costs per node can be estimated as

follows:

ENode =Esend(b1)+Esend(b2)+AverageNodeDegree∗(Ercv(b1)+Ercv(b2)) (13)

The value b1stands for the number of bytes in the Topology Discovery Request of

the node, b2stands for the number of bytes in the Topology Discovery Response.

Later we calculate energy consumption of Topology Discovery Protocol for a

particular scenario and show after how many probabilistically ﬂooded queries

the protocol pays oﬀ.

4 Evaluation

In this section we evaluate the prediction framework with diﬀerent node setups

using simulations and a deployment of 17 Sun SPOT sensor nodes [2] in our

faculty building. We compare the predictions made by our framework with the

ﬂooding of queries in simulated networks of up to 425 nodes and in the real

sensor network, showing the following:

1. For all simulated networks and the real sensor network, the accuracy of the

reachability prediction based on the topology information is suﬃciently high.

2. Any inaccuracy related to the probabilistic ﬂooding is clearly outweighed by

the amount of energy saved through decreased communication overhead.

Our framework produces stochastic results for the average case, i.e., it works well

for suﬃciently dense networks or for large numbers of trials.Thus, we expect a

deviation between the predicted values and experimental results. Nevertheless,

our predictions can be successfully used for query optimization purposes, life-

time estimation or the computation of the rebroadcast probability with a small

additional safety margin.

4.1 Simulations

For the simulation we used a custom Karlsruhe Sensor Networking Simulator

which is interface-compatible to Sun SPOT sensor nodes, thus enabling us to

deploy the prediction framework as well as the topology discovery protocol in

both the simulated environment and the real deployment.

Query Dissemination with Predictable Reachability and Energy Usage 287

Simulations Setup. We considered the following simulation scenarios: uniform

and Gaussian distributed nodes, a scale-free distributed scenario, and a real

world set up from the Intel Lab Website [1]. Due to space limit we only present

the results for the ﬁrst two scenarios below.

Uniform node distribution. All topologies of this scenario distribute the sensor

nodes uniformly in a circular area around the centre where the base station is

located. The parameter of this scenario is the average number of neighbors of

every node. The radius of the simulation area is ﬁxed, and the number of nodes

is adjusted accordingly to obtain the respective average node degree. We used

networks of node degrees 4, 8, 12 and 16, and generated for each node degree 40

diﬀerent topologies. For each topology we ran 100 experiments.

Table 1 . Average node degree in Uniform scenario and resulting amount of nodes

Average Node Degree Used Sensors

4125

8225

12 325

16 425

Gaussian node distribution. In this scenario all sensor nodes are distributed

using a Gaussian distribution over an area with a ﬁxed radius of 30 units. The

coordinates of the nodes are taken from a Gaussian sampling with the centre of

the environment as mean and a standard deviation of 18 units. By choosing this

standard deviation most of the sensors are placed in the target area, only few

nodes were placed beyond. Most nodes are located close to the centre, and the

further away from the base station the lower the node density. This scenario has

the number of sensor nodes placed as parameter. In order to compare the results

from the uniform scenario with this scenario, we generated instances with the

same average node degrees for scenarios with the same number of nodes (see

Table 1). As in uniform scenario, for each of the four network sizes we generated

40 topologies and run 100 experiments per topology.

Reachability and Energy Consumption. For this series of experiments, we

assume a message payload size of 28 bytes for the query. According to an analysis

[9] of MICAz [3] sensor nodes the energy consumption Formulae 14 and 15 were

determined. Parameter bspeciﬁes the number of bytes sent/received.

Energ yF orSending (b)=0.185191mAs+(b−28byte)∗2.48461mAs∗10−5(14)

Energ yF orReceiving (b)=0.042mAs +(b−28byte)∗2.47915mAs ∗10−5(15)

The energy consumption was ﬁrstly measured for standard TinyOS [7]

message payload of 28 bytes, and then the energy consumption for sending (re-

ceiving) badditional bytes was determined. The results of evaluation of our

288 Z. Benenson et al.

(a) average node degree 4 (125 nodes) (b) average node degree 8 (225 nodes)

Fig. 3. Comparison of simulated reachability/energy cost in uniform scenarios

reachability and energy consumption prediction framework are presented in Fig-

ure 3 for the uniform scenario, and in Figure 4 for the Gaussian scenario.

One can see that our framework works reasonably well in suﬃciently dense

scenarios. It systematically underestimates reachability and energy consump-

tion, but it still allows to save a large amount of energy. For example, in Fig-

ure 3(b–d), although the full reachability is achieved with smaller rebroadcast

probabilities than predicted, ﬂooding with the predicted probability still allows

to save from 10 (b) to 37 (d) percent of energy. Moreover, reachability and

energy consumption predictions for the Gaussian scenario follow the simulated

results so closely that they allow very accurate determination of the rebroadcast

probability needed to reach a particular amount of nodes. Note that in Gaussian

scenarios, some nodes are placed so far from the base station that the network

becomes disconnected.

Topology Discovery and Reachability Prediction Payoﬀ. Assuming a

uniform scenario with 425 nodes, average node degree 16 and a reachability

of about 99%, up to 150 mAs can be saved using our prediction framework

(see Figure 3(d)). Using rebroadcast probability p=0.6 only approximately

220mAs are consumed in comparison to the simple ﬂooding which consumes

Query Dissemination with Predictable Reachability and Energy Usage 289

(a) 125 nodes (b) 225 nodes

Fig. 4. Comparison of simulated reachability/energy cost in Gauss scenarios

370mAs. However, some energy was previously spent for Topology Discovery

Protocol. Using Formula 13 for energy consumption of the Topology Discovery

Protocol, and Formulas 14 and 15 for energy consumption of MICAz nodes,

we estimated that in the above scenario, the Topology Discovery Protocol has

approximate costs of 722mAs (we omit the computations due to space limit).

Thus, the Topology Discovery Protocol would have paid oﬀ after 5 probabilistic

query ﬂoodings.

4.2 Sun SPOT Deployment

After having provided simulation results, we tested our framework together with

the topology discovery protocol in real testbed. Figure 5 shows a map of 17 Sun

SPOT sensor nodes (circles) and a base station (square) that are deployed in

the oﬃces at the Institute for Programming Structures and Data Organization

(IPD) of the University of Karlsruhe. On each node we counted incoming and

outgoing messages, as well as the sizes of the messages in bytes. These values

were stored in the memory of each node and collected after the experiments were

ﬁnished.

290 Z. Benenson et al.

To assess the quality of the ﬂooding prediction, the following experiment was

repeated 10 times:

Fig. 5. Map of 17 Sun

SPOTs and a Base Station

deployed at the IPD

1. A simple ﬂooding of a query was executed to de-

termine the number of reached nodes for simple

ﬂooding.

2. Using the topology discovery protocol, the in-

formation required for the prediction was col-

lected.

3. Using the topology information, the parameter

pfor the probabilistic ﬂooding was computed

with the aim of disseminating a query to all

nodes of the network. Thus, we tried to deter-

mine the lowest pfor which a reachability of

100% was predicted.

4. Based on the computed value of p, a query mes-

sage was ﬂooded into the network using proba-

bilistic ﬂooding.

Despite minor changes between the diﬀerent ex-

periments within the topology information, which

can be attributed to environmental inﬂuences (e.g.

open/closed doors in the used oﬃces), the topol-

ogy information was consistent throughout our

experiments.

Table 2 shows the average results for the 10 ex-

periments: Generally, the accuracy of the prediction

is suﬃcient, even though there is a small diﬀerence

between the 16.3 nodes reached by simple ﬂood-

ing compared to the probabilistic ﬂooding with 15.4

nodes reached on average.

Table 2 shows messages required by the simple

and the probabilistic ﬂooding: The number of mes-

sages sent and received when the probabilistic ﬂood-

ing is used, is by far lower than the amount used

bythesimpleﬂooding.Thustheamountofsaved

energy due to reduced communication clearly out-

weighs the small inaccuracy of the prediction.

Table 2 . Result of the ﬂooding experiment using the Sun SPOT deployment

Flooding Avg. Reached Nodes (of 17) Messages Sent Messages Received

Simple 16.3 16.3 63.8

Probabilistic 15.4 10.2 34

Query Dissemination with Predictable Reachability and Energy Usage 291

5 Conclusions and Future Work

It is challenging to realize energy-eﬃcient query dissemination with predictable

reachability and energy usage in sensor networks: Unnecessary transmissions

should be generally avoided in order to save energy. On the other hand, it re-

quires knowledge about the sensor network to ﬁnd out which transmissions are

actually required, but obtaining these information comes with an additional

communication overhead.

In this paper we have used probabilistic ﬂooding as a model to explore the

relations between (1) energy consumption of the query dissemination phase, (2)

the number of nodes reached and (3) the energy spent to gather structural in-

formation about the network which are required to parameterize probabilistic

ﬂooding. In particular, we have introduced an analytical framework that enables

the base station to estimate the reachability and energy consumption of prob-

abilistic ﬂooding according to based on connectivity information. Furthermore,

we have shown how to gather such information eﬃciently, and we have computed

the break-even between energy saved and energy spent to obtain structural in-

formation. Both experiments with a simulator and an implementation with a

testbed consisting of 17 SUN Spot nodes validate our ﬁndings.

As part of our future work we plan to consider “back links” in ﬂooding,

and other query dissemination strategies. In addition, we are interested in the

relations between the energy spent for query dissemination and the accuracy of

the query result returned.

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D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 293–306, 2008.

A Prediction Based Cross-Layer MAC/PHY Interface for

CDMA Ad Hoc Networks

Pegdwindé Justin Kouraogo, François Gagnon, and Zbigniew Dziong

Department of Electrical Engineering, École de technologie supérieure,

Montréal, Québec, Canada H3C 1K3

{pegwindejustin.kouraogo.1,

francois.gagnon,zbigniew.dziong}@etsmtl.ca

Abstract. Variable environments in ad hoc networks require a joint control of

physical (PHY) and medium access control (MAC) layers resources in order to

optimize performance. In this paper, we propose a framework to perform such

cross-layer control and optimization. The PHY layer and cross-layer engine es-

timate and predict the channel variations to select the users that will meet the

signal-to-interference-noise ratio (SINR) requirement in the next time slot, for

MAC layer optimization. We consider high capacity code division multiple ac-

cess (CDMA) ad hoc networks working at fixed quality of service (QoS) re-

quirement where nodes are equipped with matched filter receivers.

Keywords: Ad hoc network, cross-layer interface, prediction, CDMA systems,

medium access control.

1 Introduction

In ad hoc networks, PHY layer variations strongly affect all the higher layers. For the

optimization of the access to the wireless medium, MAC layer designers need a

knowledge of the distribution over the channel fluctuations, in terms of the packet

error rate (PER), the transmission rate, and the required transmission powers of the

users in contention. Moreover, in high capacity CDMA ad hoc networks, each node

can simultaneously decode several transmissions and the complexity of the problem

grows with the number of the received users. A cross-layer study of the problem is a

good approach to cope with such an issue.

A scheme for user’s access optimization along the traffic variations in CDMA ad

hoc networks was proposed in [1]. Voice activity process was modeled by a Markov

chain to predict data users’ capacity. We address the issue of the access optimization

along the change of PHY layer rather than the change in voice process. The aim of

this paper is to predict the channel variations, the user capacity for the target PER and

the transmission powers in order to provide sufficient information to the MAC layer

for the choice of an optimal operating point. The originality of this work relies on

integrating this task in an entity called cross-layer engine composed of a processing

part and a cross-layer interface (CLI) to ensure the information transport from PHY

layer to MAC layer.

294 P.J. Kouraogo, F. Gagnon, and Z. Dziong

On the cross-layer design area, some analogies may be established to a series of

works published on time division multiple access (TDMA) ad hoc networks [2-5].

The authors introduced an original cross-layer study to control MAC queues stability

over a fading channel. The proposed cross-layer framework works with a Spatial-

TDMA scheduling that admits users transmissions only at a certain distance from the

active receivers [6]. Our framework works with a color based CDMA protocol de-

scribed in [7].

The remainder of this paper is organized as follows: In section 2 we present the

MAC layer architecture used. In section 3 the general problem and the characteriza-

tion of the logical and the physical channel parameters are presented. Section 4 pro-

vides details of the signal processing part of the framework. In section 5 and 6 the

QoS modules and the cross-layer interface are provided, respectively. Section 7 pre-

sents the simulation results. Finally, section 8 concludes the paper.

2 Medium Access Control Structure

2.1 Architecture

The considered network supports two types of CDMA channels: a common CDMA

channel to exchange connectivity informations, and several dedicated CDMA chan-

nels for scheduling and data transmission. Time is divided into super-frames. Each

super frame is split into one connectivity frame and 10 data frames. When a node

enters the network, it waits for the connectivity frame to exchange information with

the neighboring nodes. The other active nodes execute a distributed algorithm to

choose a dedicated CDMA code and update their bases of neighbors’ transmission

codes [7]. The data frame is composed of a scheduling slot and a data transmission

slot as depicted in Figure 1. The scheduling slot is split into three mini-slots. In the

first mini-slots, a node assignment algorithm performs an initial scheduling to set certain

users in transmission mode and the others in reception mode. The second mini-slot gives an

opportunity to the isolated nodes which lost the transmission/reception mode contention, to

establish connections. In the last mini-slot, all the transmitters confirm the connection re-

quest by sending a request-to-send (RTS) packet with their QoS demand. The receivers

decode the packets to extract the demands for MAC schedulers.

correction

Scheduling

slot

Initial

scheduling

Cross-layer

scheduling

Node

assignment

RTS/CTS

Data

slot

Correction

Fig. 1. Data frame

Cross-layer scheduling is then performed to allocate the required PER and trans-

mission rate, and the users’ responses are sent back by a clear-to-send (CTS) packet.

The informations provided to the cross-layer scheduler from the PHY layer are the

following:

A Prediction Based Cross-Layer MAC/PHY Interface for CDMA Ad Hoc Networks 295

- The users that meet the required SINR level

- The required powers of the transmitting nodes

- The channel gain level

- The out-of range interferences level

The cross-layer scheduling principle is illustrated in figure 2.

RTS2

........

RTS2

CTS

PHY:fut ure QoS

evalu

ation

CLI: Admissibles

users

MAC: Decision

Receiver

Transmitters re

uests Acknowledge

Fig. 2. Cross-layer scheduling principle

To transport the QoS demand to the receiver’s MAC layer, the structure of the RTS

packet is modified by adding some fields to carry the packet error rate (PER) and

data rate the transmitter requires. These two fields are followed by a third additional

field that transports a sequence of training bits for the channel estimation and predic-

tion (see Figure 3a). Each CTS packet includes a series of two additional fields to

transport the receivers’ acknowledgement/non-acknowledgment (ACK/NACK) and

the required transmission power, P, to meet the demand (see Figure 3b).

(a)

(b)

Duration Receiver

address

Frame

control

P1 FCS ACK1/

NACK1

ACK2/

NACK2

ACKN/

NACKN

Duration Receiver

address

Frame

control

Sender

address Rate

request

PER

request

FCS Training

sequence

Fig. 3. a) RTS control packet b) CTS control packet

2.2 Neighborhood Topology

Although the nodes’ positions change due to their possible motion, the network

snapshot of the connections is fixed from the cross-layer scheduling mini-slot until the

end of the data transmission slot. This configuration is the basic neighborhood topology

of our study (Figure 4). It consists of a set of receivers connected with certain trans-

mitters in the neighborhood. With multi-user reception capability, the receiver decodes

the intended signal and further listens to the unintended ones. Note that by multi-user

reception it is meant that the nodes use a conventional matched filter and multi-user

detection when a supplementary detection algorithm is implemented after the matched

296 P.J. Kouraogo, F. Gagnon, and Z. Dziong

Out-of-range interference

unintended transmissions

Intended transmissions

Detection

range

Fig. 4. Basic receiver configuration

filters. It is also important to mention that the unintended transmissions are listened

to, in order to reduce the interferences in the network.

3 General Approach

3.1 Cross-Layer Framework

Our approach consists of the designed framework depicted in figure 5. Four main

modules have to be developed.

Observation/estimation module. The observation and estimation module extracts the

demodulated samples from the transceiver to estimate the PHY layer parameters.

Because multi-user reception deals with multiple access interferences, the main para-

meters to be estimated are the channel gain, h(t) , and the out-of- range interferences, 0

Prediction module. The prediction module forecasts the parameters for the next data

slot. The predicted parameters are used by the QoS module and the cross-layer inter-

face to process the admissibility of transmitting nodes.

QoS module. The QoS module calculates the QoS parameters of the different links

and their required transmission powers based on the channel prediction. A more de-

tailed description of the parameters will be given in section 5.

Cross-layer interface (CLI). CLI ensures the communication between the two lay-

ers. It transports the MAC layer synchronization information to the PHY layer to

allow the pilot bits extraction for the estimation and prediction. It also provides the

predicted values from the PHY to MAC layer for the optimization purpose. MAC

layer optimization consists to select the best configuration of transmitters based on the

future state of the channel, the interferences, the packet delay constraints and the

availability of the QoS. This topic will be address in the next work.

3.2 MAC Logical Channel Characterization

Logical channels at the MAC layer are characterized by a transmission rate, R, a

maximum tolerable PER, and a maximum tolerable delay, τ. A given PER corre-

sponds to a target BER at the PHY layerThe BER is well approximated by the

A Prediction Based Cross-Layer MAC/PHY Interface for CDMA Ad Hoc Networks 297

Scheduling

Cross layer

interface

MAC/PHY

Parameters

Prediction

Observation/

Estimations Transceiver

QoS

Models

MAC

LAYER

Fig. 5. Cross-layer framework

probability of error b

P, which depends on the modulation used, and the received

SINR. Several techniques of modulation may be used to transport the bits stream over

the channel. We adopt here the simplest: the binary phase shift keying (BPSK). The

probability of error of the BPSK is a Q-function of the SINR.Finally, MAC required

PER is converted into a targer SINR for the calculations as follows:

1BER

SINR Q 2

−⎛⎞

=⎜⎟

⎝⎠

, (3.1)

where 2

t/2

Q(x) e dt

∞

−

=π∫.

In addition to the SINR control mechanism considered here, the other link error

control mechanisms such that the automatic repeat request (ARQ), the forward error

correction (FEC) or the interleaving may be considered to improve the quality of the

packets reception. Theses topics will be investigated in the future researches.

3.3 Physical Channel Characterization

The SINR reflects the physical impairments introduced by the wireless channel on the

signal. Since logical channels work on frame of few milliseconds, packets received

are mainly affected by small scale channel fading. This type of fading follows a

Rayleigh distribution [8-10]. The standard computer model used to generate the chan-

nel coefficients is Jake’s simulator [9, 10]. Consequently, Rayleigh fading coefficients

are computed by summing M delayed sinusoids to take into account the scattering and

the Doppler effects. The equations of channel gain used in our simulations are

covered in [10]:

298 P.J. Kouraogo, F. Gagnon, and Z. Dziong

()()

()

0dn dn

dn dn

2n 2n

Mj2f cos t j2f cos t

j2 ft j2 ft MM

h(t) e e 2. e e

ππ

⎛⎞⎛⎞

π+φ−π+φ

⎜⎟⎜⎟

π+φ − π+φ ⎝⎠⎝⎠

⎛⎞

⎡

⎤

⎜⎟

⎢

⎥

=++ +

⎜⎟

⎢

⎥

⎜⎟

⎢

⎥

⎣

⎦

⎝⎠

∑, (3.2)

where M is an odd integer such that 01M

M. 1

⎛⎞

=−

⎜⎟

⎝⎠

. The term 1

M is a normaliza-

tion factor to normalize the average power to unity, d

f the maximum Doppler fre-

quency such as c

f.v

=, c

f the carrier frequency and vrepresents the mobile speed.

The n-th sinusoid is received with a delay n

τand a phase n

given by ncn

2f.

=π τ

such that n

is random and uniformly distributed over [0,2 ]π.

4 Signal Processing

4.1 Parameters Observation and Estimation

Observation. We take advantage of the knowledge of the training bits we have in the

RTS packet in order to estimate the channel gain. The observation samples are ac-

quired from the output of the matched filter’s bank. At the i-th bit instant, user k sam-

ple is expressed as:

kkk0k 0k

y (i) h (i)A (i) I (i)W (i)=++η, k 1,..., K users=, (4.1)

where k

h (i) is the channel gain. k

A (i) is the transmitted signal amplitude defined

by kkmax

A(i) d(i) P=, assuming that control packets are sent at the maximum

power level max

d(i)

represents the known training symbol. 0k

I(i) and 0k (i)ηare

the out-of range interference level and the additive white Gaussian noise samples after

the correlation applied by the matched filter.

Estimation of the channel gain. A simple estimate of the channel gain k

he (i) can be

calculated as follows:

kmax

y(i)

he (i) d(i) P

≈, k 1,..., K users=. (4.2)

4.2 Parameters Prediction

With the knowledge of the NPilot bits of RTS packet, a collection of NPilot channel

samples is buffered at the output of the estimator, to feed the input of the predictor.

This involves a bank of K predictors for K transmitters, providing a supplementary

complexity to be considered for the choice of the prediction algorithm. Another

dominant criterion in this choice is the long range prediction capability. For this

purpose we prefer linear prediction, over the heavy computation methods presented in

A Prediction Based Cross-Layer MAC/PHY Interface for CDMA Ad Hoc Networks 299

[9, 10]. Linear prediction is well described in [11]. Channel gain process

he (i) i 1, 2,.......= is modeled as an auto-regressive (AR) process. Then, we deter-

minate the finite impulse response (FIR) filter coefficients l

a, where l 0, 2,....., L 1=−,

that minimize the mean square error (MSE) between the estimated and the predicted

samples. L is the prediction order of the filter. The channel gain k

hp (i) at bit i is then

computed using the L past samples and the filter coefficients as follows:

L1 k

kk k

hp (i) a (i) he (i) a (i).he (i l)

−

=⋅ = −

∑,k 1,..., K=, (4.3)

where T

kkk k

he (i) [he (i),he (i 1),..., he (i L 1)]=−−+is the vector of the L past samples of

the k-th user’s channel gain. The vector 0L1

kk kT

a (i) [a (i), a (i),..., a (i)]

−

=represents the

filter coefficients. The coefficients k

a (i) that minimize the MSE are obtained by the

orthogonality principle [11], and computed using the following matrix inversion:

kkk

a (i) [R (i)] . r (i)

−

=,k 1,..., K=, (4.4)

where k

[R (i)] is the correlation matrix of the channel coefficient at the instant i such

that

[]

kkk

n,m

R (i) E{he (i n).he (i m)}=− −,n, m 0,1,...,L 1=−. The sign

()

∗ repre-

sents the complex conjugate operation. The vector 0

kk k T

k1L1

r (i) [r (i),r (i),...., r (i)]

−

contains the L samples of channel autocorrelation so that *

l,k k k

r (i) E{he (i).he (i l)}=−,

l 0,1,..., L 1=−.

To compute the K users’ channel coefficients, K matrix inversion is performed at

each bit. In order to minimize the impact of processing time on the network delay

jitter, we choose to adaptively update the FIR filter coefficients by the least mean

square (LMS) algorithm. Finally the module is typically a bank of K LMS predictors

which work in two phases:

- During the training phase the prediction coefficients are updated at each instant

according to the prediction error between the estimated and predicted samples as

follows:

kk k k

a(i) a(i 1) e(i 1)he(i 1)=−+

⋅−⋅ −,k 1,..., K=, (4.5)

where

is the step size parameter that guides the convergence of the algorithm, and

takes its value in the interval

[]

0,1 . kkk

***

e (i) hp (i) he (i)=−is the complex conjugate

of the prediction error given by the difference between the predicted and the estimated

sample, k

he (i) the vector of the L past samples of the channel estimate.

- The tracking phase goes from the beginning of the first bit after the training

sequence of the RTS packet to the end of the data packet. During this period there is

300 P.J. Kouraogo, F. Gagnon, and Z. Dziong

no knowledge of the channel estimates. We estimate the desired channel value by

interpolating it by the last predicted sample as follows:

he (i) hp (i 1)=−

%, k 1,..., K=, (4.6)

Accordingly, the error used for the adaptation is calculated by the expression:

()( )

kkk kk

*** **

e(i) hp(i) he(i) hp(i) hp(i 1)=−=−−

%,k 1,..., K=, (4.7)

Assuming a data packet of Ndata bits, the slot level channel gain is obtained by taking

the average of the Ndata predicted samples over the data slot:

RTS CTS data

RTS CTS

NNN

data iN N

hhp(i)

=∑, (4.8)

RTS

N and CTS

Ndesignate the RTS and CTS packets’ lengths, respectively. We compare

our prediction scheme to the current estimation method that interpolates the channel

gain on the next data slot by averaging the estimated samples during the training se-

quence acquisition:

RTS

RTS i1

hhp(i)

=∑. (4.9)

5 QoS Management/Admission Parameters

One class of traffic is considered in this study. Each link is characterized by: a data

rate i

R , a required SINR i

, a transmission power i

P , and a maximum allowable

power max

P . Several objectives exist to optimize the medium access. The simplest way

is to minimize the interference level in order to improve the system’s capacity. Mini-

mum level of interference is achieved when all users send their packets with the strict

minimum power to meet MAC QoS demand with equality. Converting the QoS de-

mand in term of SINR constraint, the condition is expressed by [12]:

iii 0 0

Wi 1, ..., N

RhP (I )W

≠

=γ =

++η

∑, (5.1)

where W is the transmission bandwidth,

[]

12 N

h h ,h ,...,h= the channel gain vector, 0

the spectral density of the noise, and 0

I the out-of-range interferences. Rewriting the equa-

tion (5.1) for N users and proceeding to some transformations lead us to the receiver ad-

missibility condition given by [12]:

()

j1 max

ii i

jj ii i1

In.W

W1 W

1min P h 1

≤−

⎛⎞

⎡

⎤

⎛⎞

⋅+⎜⎟ +

⎢

⎥

⎜⎟

γγ

⎝⎠

⎢

⎥

⎝⎠

⎣

⎦

∑, (5.2)

A Prediction Based Cross-Layer MAC/PHY Interface for CDMA Ad Hoc Networks 301

5.1 User’s Admission Parameters

For a fixed transmission rate, users’ admission at the receiver is limited by the follow-

ing criteria [13]:

max

W11

≤−δ

⎛⎞

⋅+

⎜⎟

⎝⎠

, (5.3)

where parameter

()

max 00

max

00 i 1,.....,N

InW

min P h 1

δ= ⎡⎤

⎛⎞

⎢⎥

⎜⎟

⎢⎥

⎝⎠

⎣⎦

is the ratio of the out-of-

range interferences plus the noise power over the minimum value of the links’ pa-

rameters, i

g, where max

gPh 1

⎛⎞

⎜⎟

⎝⎠

for 1,...,iN=. The parameter

bW1

represents the “bandwidth coefficient” that the receiver can assign to each

admissible user. The statement (5.3) shows that the total bandwidth is affected by the

maximum value of max

δ, corresponding to the weakest link’s parameter. This value

can be predicted since it depends on the users channel gain and the interference term.

The number of signals that can meet the QoS request is calculated by:

()

max

ii1,..,N

N1.1

⎛⎞

=+−δ

⎜⎟

⎝⎠ , (5.4)

One can achieve this limit when the parameter max

δgoes to zero i.e. max

P→∞. So

the maximal capacity is attained at unlimited transmission power such that the capac-

ity is max

⎛⎞

⎜⎟

⎝⎠

. The non-admissibility of a set of N candidate users occurs

when the total bandwidth of the admissible users’ exceeds the difference between

unity and max

δ. In addition, due to the channel variations, the difference

()

max

1−δ

may be reduced more. Based on the predicted value of the parameter max

δ and the

knowledge of the bandwidth coefficient b, we can determine for the next time slot the

admissible set of users. This task is done by the cross-layer interface which uses the

links parameters ii 1,..., Nδ= to perform iteratively the described users’ admission.

5.2 Required Transmission Powers

The CTS packet transport the required powers calculated by the following expression

adopted from reference [13]:

()

InW

h1N

+⋅

=⎛⎞

+−

⎜⎟

⎝⎠

. (5.5)

302 P.J. Kouraogo, F. Gagnon, and Z. Dziong

6 Cross-Layer Interface

In reception mode, nodes execute the following tasks:

Step 1: Listen to the entire neighborhood

Step 2: Analyze RTS packets headers to find the destination addresses,

extract the QoS requests of the transmitters desiring to establish connections,

detect the out-of-range node for interference cancellation.

Step 3: Estimate and predict the channel gain i

h , the out-of-range interferences 0

and calculate the QoS parameters b and ii 1,..., Nδ= .

Step 4: Sort in ascending order users according to the parameter max

δ and execute the

following algorithm to search the admissible users:

Initialization: users

N1=

Repeat until

()

max max

users

Nusers

user

N1orNN

W11

⎛⎞

⎜⎟

>−δ >

⎜⎟

⎛⎞

⎜⎟

⋅+

⎜⎟

⎝⎠

users users

NN1=+

End repeat

Step 5: According to the allowable delay, the evolution channel and interferences in

the next slots, MAC layer schedules the best configuration of transmitter in the set of

the users

N links.

7 Simulation Results

The foundation of the framework relies on the signal processing algorithms. As the

algorithms are destinated to be used in the real time systems, the simulation appears to

be a more accurate tool than the analytical methods to evaluate the performances. We

consider a system where nodes share a bandwidth of W=450MHz, and transmit RTS

packet at max

P5W=. We assume a spectral density of the background noise

of 9

N10

−

=, an out-of-range interferences level of 0

I3dB=− , a spreading gain

of G 128= such that the bit rate is R3.5Mbits/s=. For simplicity, we define the

frame to be a block of RTS-CTS and Data packets. Each frame has a length of

Frame

L 35000bits=with 10ms duration and the observation window w

L20264=× pilot

bits. LMS algorithm is implemented with a step size parameter 0.006

=and a predic-

tion order of L 20=. We first simulate the estimation and prediction for several

node’s speeds. The estimation is performed during the acquisition of the

20 264bits×of the RTS packet as showed in figure 6.a, 7.a, and 8.a. In figures 6.b,

7.b and 8.b we can see the prediction over the whole frame. These results also show

the attenuation experienced by the frames due to the channel fading. The maximum

attenuations are -3 dB and -10dB, in figure 6 and figure 7 respectively.

A Prediction Based Cross-Layer MAC/PHY Interface for CDMA Ad Hoc Networks 303

0246810

-6

-5

-4

-3

-2

-1

Estimation v=60km/h

Time (ms)

Channel gain (dB)

Actual

Estimation

0 2 4 6 810

-8

-7

-6

-5

-4

-3

-2

-1

Prediction v=60km/h

Time (ms)

Channel gain (dB)

Estimation

Actual

(a) (b)

Fig. 6. (a) Channel estimation, (b) prediction

0246810

-12

-10

-8

-6

-4

-2

Estimation v=80km/h

Time (ms)

Channel gain (dB)

Actual

Estimation

0246810

-20

-15

-10

-5

Prediction v=80km/h

Time (ms)

Channel gain (dB)

Prediction

Actual

(a) (b)

Fig. 7. (a) Channel estimation, (b) prediction

The performance of the predictor is evaluated by averaging over 200 realizations

the MSE between the actual channel gain and the prediction on one data packet. A

comparison of the prediction is performed with the classical estimation method. The

results are plotted for a range of Doppler frequencies in Figure 9. By fixing the Dop-

pler frequency to d

f100Hz=, we then plot the average MSE for different signal-to-

noise ratio (SNR) in Figure 10 and several observation windows in Figure 11 Figure 9

shows that estimation gives better performances than prediction for a Doppler fre-

quency inferior to 16.7 Hz as the channel gain is flat at low frequencies. When the

frequency increases, more fading occurs on data packet and the prediction scheme is

superior to the classical estimator. In Figure 10, we can observe that the estimator

performance exceeds the predictor’s when the SNR is lower than 4 dB, this is essen-

tially due to the propagation of the error induced by the noisy observations in the

LMS algorithm. However, over 4dB the predictor gives better performances. Figure

11 illustrates the superiority of the prediction scheme over the estimation when we

variate the observation windows. Moreover we can see that prediction error decreases

when the observation window is enlarged.

304 P.J. Kouraogo, F. Gagnon, and Z. Dziong

0246810

-14

-12

-10

-8

-6

-4

-2

Estimation v=100km/h

Time (ms)

Channel gain (dB)

Actual

Estimation

0246810

-14

-12

-10

-8

-6

-4

-2

Prediction v=100km/h

Time (ms)

Channel gain (dB)

Prediction

Actual

(a) (b)

Fig. 8. (a) Channel estimation, (b) prediction

050 100 150 200 250

-6

-5

-4

-3

-2

-1

0One frame processing

Doppler frequency (Hz)

MSE

Estimati on

Prediction

010 20 30 40

-2

-1

One frame processing

SNR (d B)

MSE

Estimation

Predict ion

Fig. 9. Average MSE as a function Doppler

frequency

Fig. 10. Average MSE as a function of

signal-to-noise ratio

050 100 150

-2

-1

One frame processing

Observation window (x50bits)

MSE

Estimation

Prediction

Fig. 11. MSE as a function of Observation

A Prediction Based Cross-Layer MAC/PHY Interface for CDMA Ad Hoc Networks 305

010 20 30 40

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Variation of the maximum value of the parameter delta

Time (xframe)

Delta

Actual

Prediction

Estimatio n

Fig. 12. Variation of parameter i

δ as a fun-

ction of time, W 83.5MHz=, R 1Mbits/s=,

f80Hz= Frame

L8696bits=,w

L 400bits=

010 20 30 40

15 users admission

Time (xframe)

Admissible users

Actual

Prediction

Estimation

Fig. 13. Number of admitted transmitters as a

function of W83.5MHz=, R 1Mbits / s=,

f80Hz=Frame

L8696bits=,w

L 400bits=

Figure 12 shows the variation of the parameter i

δ in time. The predictor gives a bet-

ter result than the estimator. In figure 13, we plot 15 users’ admission. Due to the high

number of transmitters, many of them experience high channel gain, and the maximum

capacity is easily achieved when the algorithm uses the actual, the predicted and the

estimated values of the parameter delta.

8 Conclusion

In this paper we presented a cross-layer interface between MAC and PHY layer. We

take advantage of the samples produced by the matched filter to predict the channel

change for MAC layer optimization process. As the capacity is influenced by the

channel fluctuations, a cross-layer algorithm determines the set of admissible users

based on minimum interference criteria. Then simulation results presented showed the

superiority of the prediction over the classical estimation scheme. In the future work,

the users’ admission will be study more extensively in the case of different ad hoc

scenarios, with more realistic radio propagation models. MAC layer optimization

process will be also addressed.

Acknowledgment. The authors wish to thank Dr. Mohamed Haidar for his insightful

comments and remarks.

References

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306 P.J. Kouraogo, F. Gagnon, and Z. Dziong

2. Liu, Q., Zhou, S., Giannakis, G.B.: Cross-Layer Modeling of Adaptive Wireless Links for

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ence on Quality of Service in Heterogeneous Wired/Wireless Networks (QSHINE 2004).

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ing Over Wireless Links: Cross-Layer Analysis and Design. IEEE Transactions on Wire-

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tees in Adaptive Wireless Network. IEEE Journal on Selected Areas in Communica-

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D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 307–320, 2008.

Utility-Based Uplink Power Control in CDMA Wireless

Networks with Real-Time Services

Timotheos Kastrinogiannis, Eirini-Eleni Tsiropoulou, and Symeon Papavassiliou

Network Management & Optimal Design Laboratory (NETMODE)

School of Electrical & Computer Engineering

National Technical University of Athens (NTUA)

9 Iroon Polytechniou str. Zografou 15773, Athens, Greece

{timothe,eetsirop}@netmode.ntua.gr, papavass@mail.ntua.gr

Abstract. In this paper we address the problem of efficient power allocation in

the uplink of CDMA wireless networks, emphasizing on the support of real-

time services’ QoS prerequisites. The corresponding problem is formulated as a

non-cooperative game where users aim selfishly at maximizing their utility-

based performance under the imposed physical limitations. A user’s utility

reflects its degree of satisfaction with respect to its actual throughput perform-

ance, QoS requirements fulfillment, and the corresponding power consumption.

The existence and uniqueness of a Nash equilibrium point of the proposed Up-

link Power Control (UPC) game is proven, where all users have attained a

targeted SINR value or transmit with their maximum power, leading essentially

to an SINR-balanced network. The properties of equilibrium in a pure optimiza-

tion theoretical framework are studied, and the tradeoffs between users’ overall

throughput performance and real-time services strict QoS requirements in chan-

nel aware resource allocation processes are revealed and quantified. Finally, a

distributed iterative algorithm for computing UPC game’s equilibrium is pro-

posed and its efficiency is illustrated via simulation and analysis.

Keywords: Wireless networks, utility-based resource allocation, QoS, real-time

services.

1 Introduction

Considerable research efforts have been devoted to the combined problem of power

and rate allocation for the downlink [1], [2] of a code division multiple access

(CDMA) system. Furthermore, users’ selfish behavior as well as the necessity of

efficiently supporting their various QoS requirements, allows the formulation of the

power and rate control problem in the uplink of such systems as a non-cooperative

game, where each node wishes to maximize its own level of satisfaction (as expressed

by an appropriately defined utility function) [3]-[5].

In this paper, we study the problem of power allocation in the uplink of CDMA wire-

less networks focusing on the support of real-time services. We propose a generic util-

ity-based framework for assigning users’ transmission powers, which maximizes the

efficiency of the system in terms of user’s utility-based degree of satisfaction, which

308 T. Kastrinogiannis, E.-E. Tsiropoulou, and S. Papavassiliou

accounts for their actual throughput expectations and QoS requirements, as well as

minimum power consumption. Initially, we formulate the Uplink Power Control (UPC)

problem as a non-cooperative game, where each user aims at maximizing its perform-

ance. The existence and uniqueness of a Nash Equilibrium (NE) of the proposed UPC

game is proven while a distributed, iterative algorithm for reaching equilibrium is pre-

sented. Then, the properties of Nash Equilibrium in the proposed UPC game are ana-

lyzed and the strong correlations among real-time users’ QoS requirements, system’s

modulation and coding schemes and their power limitations are revealed.

In [6], a utility-based approach for allocating resources to real-time (RT) users in

the uplink of a CDMA system is also adopted. However, in that work, even if RT

users’ utilities reflect their services’ satisfaction with respect to the achievable

throughput performance, their corresponding energy consumption has not been taken

into account and hence, utilities abstract definitions avoid reflecting properly their

QoS prerequisites. In [5], linear utilities of users’ achieved goodput are considered

and thus, real-time services’ QoS requirements are expressed as statistical delay con-

straints. Such an approach is not always efficient [7], since even if the delay con-

straints of a real-time user are satisfied, the degradation of their service quality can

not be avoided due to possibly bad channel conditions and variations.

The rest of the paper is organized as follows. In section 2, the system model and

necessary background information is presented. In section 3, real-time users’ QoS

properties are studied and mapped to appropriate utility functions. In section 4, the

proposed uplink power control non-cooperative game formulation is described, while

in section 5 its solution is presented. Section 6, discusses the potential use of users

expected QoS performance properties at equilibrium towards the design of a node’s

self-optimizing approach. Finally, some numerical results are provided in section 7

while section 8 concludes the paper.

2 System Model and Background Information

We consider the uplink of a single cell time-slotted CDMA wireless system with N(t)

continuously backlogged users at time slot t, where S(t) denotes their corresponding

set. A time slot is a fixed interval of time and could consist of one or several packets.

Users’ channel conditions are affected by shadow fading, fast fading and long-time

scale variations and thus, can be modeled as a stationary time-varying stochastic

process. Let as denote by Gi(t) the corresponding path gain of user iS∈at time slot t.

In the following, assuming fixed users’ channel conditions within the duration of each

time slot, we omit the notation of the specific slot t in the notations and definitions we

introduce. At the beginning of each time slot t, users’ Uplink Power Control (UPC)

mechanisms make decisions on their transmission power and resulting rate in a dis-

tributed manner. Note that a node’s transmission power and rate are also fixed within

the duration of a time slot.

Let us denote by Pi the uplink transmission power for user i in the slot under con-

sideration which however is limited by its maximum power value Pi

Max. Let us also

denote by

ibo



the bit energy to interference density ratio for user i and by Ri the

achievable uplink transmission rate. Therefore, the received γi at the base station for

each user i is given by:

Utility-Based Uplink Power Control in CDMA Wireless Networks 309

()

iii i

ii ii

iiii

jj ii

RPP

GP GP

RI P

GP GP I

θθ

−

−−

−+

∑

(1)

where θ denotes the orthogonality factor, W is the system’s spreading bandwidth, i

−

denotes the users’ power allocation vector excluding user i and I0 includes the back-

ground noise and intercell interference. Thus, ()

−−

actually denotes the network

interference and background noise at the base station when receiving data from user i

and is given by:

() N

ii jj ii

IP GP GPI

θθ

−− =

=−+

∑ (2)

To align real-time (RT) users’ various services flow characteristics under a common

optimization framework each mobile user is associated with a suitable utility function

U which represents his degree of satisfaction in relation to the expected tradeoff

between its utility-based actual uplink throughput performance and the corresponding

energy consumption per time slot. Therefore, this can be expressed as:

*(,,) ( (),,)

(,, )

iii i ii ii i i

ii i

TR PP TR f PP

UR PP PP

−−

−

⋅

== (3)

where *()

iiii

RRf

≡⋅ denotes user’s i actual uplink transmission rate (i.e. goodput)

at the under consideration time slot, F

is its fixed designed transmission rate and fi

denotes its efficiency function. The latter represents the probability of a successful

packet transmission for user i, and is an increasing function of his bit energy to inter-

ference ratio γi at any time slot. A user’s function for the probability of a successful

packet transmission at fixed data rates depends on the transmission schemes (modula-

tion and coding) being used, and can be represented by a sigmoidal-like function of its

power allocation for various modulation schemes [1], as Fig.1 illustrates. Therefore, a

user’s i, efficiency function fi has the following properties:

1) fi is an increasing function of γi.

2) fi is a continuous, twice differentiable sigmoidal function with respect to γi .

3) fi (0) = 0 to ensure that Ti = 0 and Ui = 0 when Pi = 0.

4) fi (∞) = 1.

The validity of the above properties has been demonstrated in several practical sce-

narios with reasonably large packet sizes M (i.e. M ≥100bits) [4], [5].

Finally, *

(,, )

iii i

TR PP

− is a sigmoidal function of user’s i actual data rate *

and re-

flects its degree of satisfaction in accordance to its service actual throughput expecta-

tions and QoS requirements fulfillment at every time slot. In the following section, we

first study and specify the desired properties and QoS prerequisites that characterize

310 T. Kastrinogiannis, E.-E. Tsiropoulou, and S. Papavassiliou

Fig. 1. Probabilities of packet transmission success for BPSK, DPSK, and FSK modulation

schemes

the performance of RT users’ services and then, we analyze and justify our proposed

methodology for mapping a real-time user’s degree of satisfaction with respect to its

corresponding service performance into a proper actual throughput utility function Ti.

3 Satisfying Real-Time Services QoS Requirements

Considering a soft QoS requirements framework [6], in the following we assume that

real-time services’ requirements consist mainly of a constant target actual rate per time

slot and an appropriate elasticity factor. The target actual uplink rate *

,Ti

, indicates the

ideal value of its actual transmission rate per time slot, at which its service QoS re-

quirements are fulfilled, while the Elasticity Factor (EFi) determines the expected

bounds of its actual achieved throughput deviations with respect to the target actual rate.

Specifically, a RT user’s elasticity factor determines the minimum acceptable lev-

els of its expected actual throughput (i.e. **

,,Min i T i i

REL=−). Moreover, we argue that

when a user’s achieved actual transmission rate remains within the range of

[,)

Min i T i

R, his actual throughput utility must be a slowly decreasing function of his

actual data rate. On the other hand, when **

,iMini

RR<then his actual throughput utility

should be a rapidly decreasing function of *

, indicating its priority in occupying

additional system resources. The previous design option gives to a user’s power and

rate control mechanism, operating over fast fading channels environment, the en-

hanced flexibility of decreasing its actual uplink throughput up to a certain level

,Min i

R), if required due to its potentially bad instantaneous channel conditions, with-

out however excluding the user from transmitting data at that corresponding time slot.

The later would occur, if a step function of a RT user’s actual transmission rate was

used to reflect the user’s corresponding degree of satisfaction.

Furthermore, we argue that an additional increment of a RT user’s actual data rate

from its target one, must not contribute to an analogous increment of its actual

Utility-Based Uplink Power Control in CDMA Wireless Networks 311

throughput degree of satisfaction and thus, the latter should tend asymptotically to its

maximum value, as *

R→∞(i.e. Ti (∞) = 1). The previous argument is based on the

observation that since RT service QoS prerequisites are fulfilled when its required

target bit rate is achieved, an additional improvement of user’s actual throughput

performance will not further improve its degree of satisfaction.

Actual Transmission Rate

Actual Throughput Utilit

,Mi n i

,Ti

,Max i

Fig. 2. Actual throughput utility function Ti, for real-time services

Moreover, by restricting up to a specific level ( *

,Max i

R) the achieved actual uplink

data rates of RT users, that due to their temporarily good transmission environment

can obtain more recourses than required, we get the advantage of reallocating the

excess system resources to the un-favored RT users (e.g. those with temporally bad

transmission environment) in order to increase not only their performance satisfaction

but also the overall number of RT users that can be simultaneously served. For practi-

cal reasons, due to users’ hardware limitations, we regard that a RT user’s actual

throughput utility has reached a value close to the maximum when **

,,Max i T i i

REL=+

(i.e. *

()1

iMaxi

=− , where ε is an arbitrarily small positive number, e.g. ε = 5 10-5).

With respect to the previous discussion and analysis, a RT user’s i actual through-

put utility Ti has the following properties (Fig.2):

1) Ti is an increasing function of *

2) Ti is a continuous, twice differentiable sigmoidal function of *

, with unique in-

flection point *

,Infl i

determined by:

** **

,,,

()

iMini

Infl i i Min i T i i

iRR

RR RREL

⎧⎫

∂

⎪⎪

===−

⎨⎬

∂

⎪⎪

⎩⎭

(4)

3) Ti (0) = 0 to ensure that Ti = 0 when *

= 0,

312 T. Kastrinogiannis, E.-E. Tsiropoulou, and S. Papavassiliou

4) Ti (∞) = 1 and

5) *

()1

iMaxi

=− , where ε = 510-5.

Finally, in accordance to (3), by setting F

,Max i

R a RT user’s i utility function is

defined as follows:

(())

(, ) iMaxiii

ii i

TR f

UPP P

−

⋅

= (5)

where **

iMaxi

⎡⎤

∈⎣⎦

, since

[]

() 0,1 0

ii i

γγ

∈∀≥.

4 The Non-cooperative Uplink Power Control Game

As the system evolves, at the beginning of each time slot a user’s uplink power con-

trol (UPC) mechanism is responsible for determining an appropriate uplink transmis-

sion power level towards maximizing its overall degree of satisfaction, which is

reflected by the corresponding values of its utility. In addition to the maximization

goal, mobile user’s hardware limitations as well as instantaneous system characteris-

tics mast be taken into account. In this section, the main goals of the proposed PRC

mechanism are analyzed and formally defined as a generic optimization problem in a

game theoretic framework.

Since, each user in the network aims at the maximization of the expectation of its

utility Ui, the corresponding goal of the UPC mechanism can be defined as the maxi-

mization of the objective function:

max [ ( , )]

.. 0

ii i

Max

EU P P

st P P

−

≤≤

(6)

Two crucial observations need to be made. As the channels of the communication

links are assumed to be independent and identically distributed (i.i.d.) the maximiza-

tion of the average utility in equation (6) is obtained by maximizing the utility at

every time slot t. Moreover, due to the users’ selfish operation, in terms of pursuing

optimal power values towards their individual utility maximization, the overall net-

work uplink power control problem at each time slot can be formulated as a non-

cooperative uplink power control game (UPC game).

Let [ ,{ },{ }]

GSAU= denote the proposed non-cooperative game, where S is the

set of users/players and [0, ]

Max N

AP=×ℜis the strategy set of the ith user. Each

strategy in Ai can be written as ai =(Pi). Furthermore, the resulting per time slot non-

cooperative game can be expressed as the following maximization problem:

max max ( , ) 1,..., .

iiii

UUPPforiN

−

== (7)

under the constraint of non-negative, upper bounded powers.

Utility-Based Uplink Power Control in CDMA Wireless Networks 313

5 Towards a Nash Equilibrium for the Non-cooperative UPC

Game

For the non-cooperative UPC game proposed in the previous section, we adopt Nash

Equilibrium approach towards seeking its solution, which is most widely used for

game theoretic problems. A Nash Equilibrium point is a set of power vectors, such

that no user has the incentive to change its power level, since its utility cannot be

further improved by making any individual changes on its value, given the powers of

other users.

Definition 1: The power vector

()

***

1,..., N

PPP= is a Nash Equilibrium of the UPC

game, if for every iS∈ ** *

(, ) (, )

ii i ii i

UPP UPP

−−

≥ for all *

PA∈.

Prior to the investigation of the existence and uniqueness of an equilibrium in UPC

game, we study the properties of RT users’ actual throughout and overall utility func-

tions, over their corresponding definition domains. The following lemma determines

the form and features of a RT user’s actual throughput utility T as a function of the

achieved SINR. It is noted that due to space limitation the proofs of the corresponding

lemmas are omitted.

Lemma 1: Given: a) an efficiency function f(γ), which is a sigmoidal function of γ and

has a unique inflection point f

Infl

, and b) an actual throughput utility function *

()TR ,

which is a sigmoidal function of *

and has a unique inflection point *

Infl

, where

** ()

Max

≡⋅, then function *

() ( ())

Max

TTRf

γγ

≡⋅ is also a sigmoidal function of

γ ( 0

≥) with a unique inflection point Infl

Τ for which:

Infl fInfl f

Infl Infl Infl

Max Max

Infl

Infl Infl

Max

fwhen f

fotherwise

γγ

−Τ −

Τ−

⎧⎛⎞ ⎛⎞

≤≤

⎪⎜⎟ ≤

⎜⎟

⎜⎟ ⎜⎟

⎪⎝⎠ ⎝⎠

⎨⎛⎞

⎪≤≤

⎜⎟

⎪⎜⎟

⎝⎠

⎩

(8)

where

()

1* *

Infl Max

fRR

− is the mapping of function’s *

()TR inflection point at the

access of γ.

Lemma 1 states that the composed function of two sigmoidal functions, as in the case

of a user’s actual throughput utility, is also a sigmiodal function. Henceforth,

the inflection point of the new function is laying between the inflection points of the

generator functions. As it will be analyzed extensively in the following section, the

previous property plays a key role in the attributes of UPC game’s equilibrium and

therefore, in RT services’ QoS requirements satisfaction. We can now characterize the

utility maximization of a single user’s overall utility when other transmission powers

are fixed.

314 T. Kastrinogiannis, E.-E. Tsiropoulou, and S. Papavassiliou

Lemma 2: User’s iS∈utility function (, )

ii i

UPP

−is a quasi-concave function of its

own power [0, ]

Max

PP∈. Moreover, considering other users’ transmission powers

fixed, (, )

ii i

UPP

− has a unique global maximization point:

*()

min{ , }

iMaxii i Max

RIP

−−

= (9)

pursuing a unique target SINR value *

, which is the (positive) solution to

() () 0

iii

γγγ

∂⋅− =

∂.

Equation (9) indicates that if a user’s maximum transmission power is not sufficient

for reaching the targeted *

, due to its potentially bad channel conditions, then the

best policy is to transmit with maximum power. Moreover, lemma 2 reveals that us-

ers’ goal to maximize their utility-based performance can be translated in a constant

attempt of meeting specific SINRs (at the base station), which eventually leads to an

SINR-balanced network.

The following proposition asserts the existence and the uniqueness of a Nash Equi-

librium point of the proposed uplink power control game and hence, determines

nodes’ transmission power vector at equilibrium.

Proposition 1: The Nash Equilibrium of the non-cooperative game (7) is given by *

where

*()

min{ , }

iMaxii i Max

RIP

−−

=, iS∀∈ . Here, *

results from the unique

positive solution of equation

()

() () 0

ii i i ii

γγγ γ

∂∂⋅−=. Furthermore, the equilib-

rium exists and is unique.

Proof: In accordance to lemma 2, the power level that corresponds to the maximiza-

tion of user’s i utility-based performance, given other users’ power levels, equals to

the power level that maximizes the utility in (5) when setting as a designed transmis-

sion rate F

,Max i

R and thus, is given by ***

min{ ( ) , }

Max

iiMaxiiiii

PRIPWGP

−−

where *

is the unique positive solution of

()

() () 0

ii i i ii

γγγ γ

∂∂⋅−=.

So far, we have shown that at Nash Equilibrium (if exists) each user’s transmission

power is pursuing a targeted SINR value which depends not only on the modulation,

coding, and packet size being used (expressed through its appropriate efficiency func-

tion fi) but also, is affected by RT user’s QoS requirements (reflected by its actual

throughput utility).

Following [4], [5], the existence of a Nash Equilibrium of the game in (7) can be

shown via the quasi-concavity of each node’s utility function in its own power. As

shown in lemma 2, (, )

ii i

UPP

−is a quasi-concave function in [0, ]

Max

PP∈, and hence,

Nash Equilibrium always exists.

Utility-Based Uplink Power Control in CDMA Wireless Networks 315

Moreover, for an S-shaped actual throughput utility function Ti,

()

() () 0

ii i i ii

γγγ γ

∂∂⋅−= has a unique solution *

, which is the unique global

maximizer of user’s i utility function. Because of the uniqueness of *

and the one-

to-one relationship between uplink transmission power and corresponding SINR, the

above Nash Equilibrium is unique. ■

Concluding this section, we present an iterative and distributed uplink power control

algorithm for reaching the Nash Equilibrium for the UPC game G at every time slot t.

UPC Algorithm

(1) At the beginning of time slot t, user i transmits with maximum power. Set k=0

and hence,*( 0)

Max

PPiS=∀∈.

(2) Given the uplink transmission powers of other users, which is implicitly re-

ported by the base station when broadcasts its overall interference () ()

()

IP,

the user computes () ()

()

−−

and refines its power level, i.e. computes *( 1)k

P+in

accordance to (9).

(3) If the powers have converged (i.e. *( 1) *( ) 5

+−

−≤) then stop.

(4) Set k=k+1, go to step 2.

6 On Real–Time Users QoS Performance at Equilibrium:

Towards a Self-optimization Approach

In this section, the properties of Nash Equilibrium in the proposed uplink power

control game are analyzed and discussed, in terms of users’ power levels at equilib-

rium, the role of their physical limitations, their actual throughput and overall

utility-based performance. It is shown, that by giving users the autonomicity of

controlling their modulation and coding schemes, as well as their transmission

power levels, their services’ QoS performance optimization can be successfully

self-controlled.

Following the pure optimization analysis of the previous section, we initially point

out that any *

that corresponds to the maximization of a RT user’s i utility Ui, must

be greater than ,Infl i

Τ, that is such an *

must be in the interval over which Ti(γi) is

concave i.e.

,Infl i i

γγ

Τ< (10)

Additionally, in accordance to lemma 1, the inflection point of Ti(γi), as a function of

γi, lays always between the values of the inflection points of its generator functions

(i.e. fi(γi) and *

()

TR as a function of *

). Therefore, from (8) and (10), it is apparent

that the following property regarding *

holds:

316 T. Kastrinogiannis, E.-E. Tsiropoulou, and S. Papavassiliou

1* ,

Infl i Infl i f

iInfli

Max Max i

Infl i i

fwhen f

otherwise

γγ

−−

⎧⎛⎞ ⎛⎞

⎪⎜⎟ ≤

⎜⎟

⎜⎟ ⎜⎟

⎪⎝⎠ ⎝⎠

=⎨

⎪

⎪<

⎩

(11)

Relying on the previous statements, the following proposition determines the influ-

ence of an existing modulation and coding scheme on a RT user’s i service

performance.

Proposition 2: If for real-time user iS∈,

()

1* *

,, ,

iInfliMaxi Infli

fR R

−≤; then at UPC

game’s Nash Equilibrium, where *

PP= and hence *

γγ

=, the achieved actual

throughput rate *

is always greater than its service minimum acceptable actual

throughput **

,,Min i T i i

REL=− i.e.

()

1* *

,, ,

iInfliMaxi Infli

fR R

−≤ then **

,iMini

RR>

Proof: When

()

1* *

,, ,

iInfliMaxi Infli

fR R

−≤ then according to (11)

()

1* * *

,iInfliMax i

fR R

−<

and thus,

()

** *

,Infl i Max i i

RRf

<⋅ since fi is a continuous increasing function of γi when

≥. Moreover, since from definition, a RT user’s utility inflection point is set as

,,Infl i Min i

RR=, with respect to it service QoS requirements, and due to the fact that

,()

iMaxiii

RR f

≡⋅, we can conclude that:

()

1* *

,, ,

iInfliMaxi Infli

fR R

−≤ then **

,iMini

RR> (12)

and hence,

()

1* *

,, ,

i Min i Max i Infl i

fR R

−≤ then **

,iTi i

REL>− (13)

when Max

P is large enough for reaching *

. ■

The previous proposition identifies a strong correlation among RT users’ QoS re-

quirements, system’s modulation and coding schemes (efficiency functions) and their

power limitations. Moreover, it asserts that if user’s i, Max

P is large enough for reach-

ing *

, then at games’ equilibrium, not only its overall utility-based performance is

maximized but also its service actual throughput expectations are simultaneously

fulfilled, if

()

1* *

,, ,

i Min i Max i Infl i

fR R

−≤.

From a RT users’ perspective, given a specific efficiency function and its corre-

sponding inflection point (i.e. for a certain modulation scheme), we can point out that:

A. If

()

1* *

,, ,

i Min i Max i Infl i

fR R

−≤, then it is assured that its actual transmission rate will

always be within the bounds determined by its target actual uplink rate *

,Ti

and its

elasticity factor EFi.

Utility-Based Uplink Power Control in CDMA Wireless Networks 317

B. The greater a RT user’s service elasticity factor, the higher the probability of

satisfying its actual throughput QoS requirements, since 1

f− is an increasing

function of the ratio ** * *

,, , ,

()()

Min i Max i T i i T i i

RRELREL=− +.

C. On the other hand, the stricter its QoS requirements are (i.e. when setting small

values for its elasticity factor which indicates that only small deviations from its

target actual throughput are allowed), the harder its throughput prerequisites are

fulfilled. Moreover, if user’s i, ELi value is such that

()

1* *

,,,

Infl i i Infl i Max i

fR R

−

then, even when its overall utility maximization is achieved, its actual through-

put may potentially be smaller than *

,Min i

In accordance to the previous analysis, we argue on using the boolean criteria of

proposition 2 as a decision indicator on a RT user’s initial acceptance in the system

(i.e. call admission control criteria).

From the system’s perspective, assuming the arrival of a new RT user with fixed

QoS requirements (predefined proper actual throughput utility Ti and its corre-

sponding parameters *

Ti i

EL ), its modulation and coding scheme, reflected to

function fi, should be chosen such that (13) is satisfied. From (13), we can observe

that the stricter a user’s QoS requirements are (i.e. small values for its elasticity

factor) the higher the value of the inflection point of the chosen fi should be. There-

fore, as Fig.1 illustrates, a poorer modulation scheme, with respect to the achievable

maximum transmission rate under that scheme, should be chosen in such case.

Thus, the inevitable tradeoff between users’ overall throughput performance and RT

users’ strict QoS requirements in channel aware resource allocation mechanisms

comes into sight.

The previous controllable criteria favor the design and implementation of autono-

mous users’ mechanisms that will not only control their power levels towards maximiz-

ing their overall utility-based performance (by adopting the proposed UPC mechanism),

but will also control their services’ performance experience by: a) constructing their

proper actual throughput utility functions and b) adjusting users’ modulation and coding

schemes in accordance to predefined criteria (e.g. criteria introduced in proposition 2),

towards optimizing their QoS prerequisites satisfaction.

7 Numerical Results and Discussions

In this section, we provide some initial numerical results illustrating the operation and

features of the proposed framework and UPC algorithm. Throughout our study we

consider the uplink of a single cell time-slotted CDMA system, supporting N=10

continuously backlogged real-time users. Moreover, each simulation lasts 10000 time

slots, while we set Max

P =2 Watt, W =106 Hz and I0 = 5*10-16. We model users’ path

gains as: a

iii

GKd=, where di is the distance of user i from the base station, a is the

distance loss exponent (a=4), and Ki is a log-normal distributed random variable with

mean 0 and variance σ2 = 8(dB), representing the shadowing effect. Furthermore, for

318 T. Kastrinogiannis, E.-E. Tsiropoulou, and S. Papavassiliou

each user i, di=di-1+250 (m) for i=2,..,10, where d0=300 (m). In this way, we emulate

a scenario where users’ average channel conditions are worse as their ID value (i.e.

i=1,…,10) increases.

Two types of real-time users are considered. Users 1 to 5 require actual uplink rate

,Ti

= 64 (Kbps), while users 6 to 10, *

,Ti

=128 (Kbps). For both types of users the

elasticity factor is set ELi = 10 (Kbps) for i= 1,…, N. Fig.3, Fig.4 and Fig.5 illustrate

for each user its average utility-based performance, the corresponding average power

consumption and its achievable average actual throughput, under two different scenar-

ios with respect to the characteristics of the examined efficiency func-

tion ( ) (1 ) 1,...

feiN

−

=− ∀= . In the first scenario (black columns), where M =

100, for both types of users

()

1* *

,, ,

1,...,

iInfliMaxi Infli

fR R i N

−≥∀= , while in the second

scenario (grey columns), where M = 500, we have

()

1* *

,, ,

1,...,

iInfliMaxi Infli

fR R i N

−≤∀= .

The results indicate that as users’ average channel conditions become worse,

their overall utility based performance decreases (Fig.3), while their power con-

sumption increases (Fig.4). On the other hand, their actual uplink data rates are in

line with their predefined actual uplink rates *

, especially when M=500, which

clearly indicates not only the proposed algorithm’s efficiency but also the proper

functionality of user’s actual throughput utilities (Ti) on satisfying real-time users’

QoS requirements.

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

12345678910

Users ID

Users' A verage Utility

M=100 M=500

Fig. 3. Users’ average utility-based performance

Moreover, the results show that the selection of an appropriate modulation

scheme can result in RT users’ QoS expectations satisfaction. Specifically, we can

observe that when M=500, all users’ actual uplink data rates are within their ex-

pected bounds (i.e. *

,Min i

R< E[ *

] < *

Max i

iS∀∈ due to the fact that *

,Min i

R< *

,Max i

R for each time slot t), even for the second type of users (note that in Fig.5 red

,Min i

R) and green ( *

,Ti

) lines represent the respective bounds), while the latter

Utility-Based Uplink Power Control in CDMA Wireless Networks 319

observation does not hold when M=100. These results further demonstrate each

user’s ability to control and adapt its modulation scheme towards the efficient satis-

faction of the corresponding QoS requirements. Moreover, after the initial construc-

tion of its actual throughput utility in accordance to its service QoS requirements, a

user’s modulation scheme selection should always be in line with the criteria in

proposition 2, in order not only its overall performance to be optimized but also its

QoS constraint to be achieved.

0.2

0.4

0.6

0.8

1.2

12345678910

Users ID

Users' Average Power Consumption (Watts)

M=100 M=500

Fig. 4. Users’ average power consumption

105

115

125

135

12345678910

Users ID

Users ' Average A ctual Rate (K bps)

M=100 M=500

Fig. 5. Users’ achieved average uplink actual throughput

8 Conclusion

In this paper we considered the issue of efficient power allocation in the uplink of

CDMA wireless networks, emphasizing on the support of real-time services’ QoS

prerequisites. The corresponding problem has been formulated as a non-cooperative

game and solved through a low-complexity algorithm, which reaches game’s unique

Nash Equilibrium point, taking into account the imposed physical limitations. The

existence and uniqueness of Nash Equilibrium point of our proposed game was

proven and thus, the properties of equilibrium as well as the tradeoffs between users’

320 T. Kastrinogiannis, E.-E. Tsiropoulou, and S. Papavassiliou

overall throughput performance and real-time services strict QoS requirements were

revealed.

Generalizing this work, we are currently studying a concrete uplink recourse allo-

cation utility-based framework, which will accommodate both real-time and non-real

time services using the appropriate utility functions. Moreover, the introduced frame-

work and proposed approach provides a first step towards the realization of auto-

nomic wireless networks, where user self-adaptive mechanisms allow the control and

facilitate the satisfaction of their QoS constraints.

Acknowledgements. This work has been partially supported by EC EFIPSANS

project (INFSO-ICT-215549).

References

[1] Lee, J.-W.R., Mazumdar, R., Shroff, N.B.: Joint resource allocation and base-station as-

signment for the downlink in CDMA networks. IEEE/ACM Trans. Netw. 14(1) (February

2006)

[2] Kastrinogiannis, T., Papavassiliou, S., Kastrinogiannis, K., Soulios, D.: A Utility-Based

Resource Allocation Approach for the Downlink in CDMA Wireless networks with Mul-

timedia Services. In: Proc. of the 18th IEEE International Symposium on Personal, Indoor

and Mobile Radio Communications (PIMRC) (September 2007)

[3] Meshkati, F., Poor, H.V., Schwartz, S.C., Balan, R.: Energy-Efficient Resource Allocation

in Wireless Networks with Quality-of-Service Constraints. Princeton University Press,

Princeton (preprint 2005)

[4] Meshkati, F., Poor, H.V., Schwartz, S.C.: A Non-Cooperative Power Control Game in De-

lay-Constrained Multiple-Access Networks. In: Proc. of the IEEE International Symp. on

Info. Theory (ISIT), Adelaide, Australia (September 2005)

[5] Meshkati, F., Goldsmith, A.J., Poor, H.V., Schwartz, S.C.: A Game-Theoretic Approach to

Energy-Efficient Modulation in CDMA Networks with Delay Constraints. In: Proc. of

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[6] Duan, X., Niu, Z., Zheng, J.: A Dynamic Utility-Based Radio Resource Management

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[7] Kastrinogiannis, T., Papavassiliou, S.: Probabilistic Short-term Delay and Throughput Re-

quirements of Multimedia Services in High Throughput Wireless Networks. In: Proc. of

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[8] Shenker, S.: Fundamental design issues for the future Internet. IEEE J. Selected Areas

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D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 321–332, 2008.

Adaptive Priority Based Distributed

Dynamic Channel Assignment for

Multi-radio Wireless Mesh Networks

Tope R. Kareem1,2, Karel Matthee1, H. Anthony Chan2, and Ntsibane Ntlatlapa1

1 Meraka Institute, CSIR, Pretoria, South Africa

tkareem@csir.co.za,kmatthee@csir.co.za, nntlatlapa@csir.co.za

2 Department of Electrical Engineering, University of Cape Town

h.a.chan@ieee.org

Abstract. This paper investigates the challenges involve in designing a dy-

namic channel assignment (DCA) scheme for wireless mesh networks, particu-

larly for multi-radio systems.

It motivates the need for fast switching and process coordination modules to

be incorporated in DCA algorithm for multi-radio systems. The design strategy

is based on a reinterpretation of an adaptive priority mechanism as an iterative

algorithm that recursively allocate a set of channels to radios in a fair and effi-

cient manner in order to minimise interference and maximise throughputs. The

algorithm, called Adaptive Priority Multi-Radio Channel Assignment (AP-

MCA) is tested for overall performance to assess the effectiveness by determin-

ing its overall computational complexity.

The combined advantages of fast switching time and process coordination

modules make the APMCA a useful candidate towards automating the channel

assignment method in multi-radio wireless mesh network planning and design.

Keywords: Wireless Mesh Networks, Multi-radio, Channel Assignment.

1 Introduction

One of the strategies of improving system throughputs and network capacity in Wire-

less Mesh Networks (WMN) is by coordinated use of multiple radios. Multiple radios

wireless mesh separates client access and wireless backhaul for the forwarding of

mesh traffic. In this type of mesh, each node has a dedicated radio for backhaul con-

nectivity operating at different frequency with performance similar to switched, wired

connections. A downside of deploying a multi-radio system is the herculean task of a

network administrator to statically configure all the available non-overlapped radio

channels. Even if a network administrator painstakingly took up the challenge to as-

sign radio channels statically to all radios in a community based wireless mesh net-

work, we could not be sure of having a network plan that minimizes interference with

other radios in the same network and other radios in the neighbouring networks. It is

322 T.R. Kareem et al.

therefore evident that a new intelligent method of assigning channels to radios in a

multi-radio environment is required.

Previous investigation conducted by Kyasanur [1] classically divided channel as-

signment into three categories viz: static, dynamic and hybrid. While static channel

assignment is used for applications that can tolerate large interface switching delay,

dynamic channel assignment (DCA) is suitable for applications with limited available

bandwidth and unpredictable variable bit rate traffic. A careful review of existing

channel assignment (CA) algorithms for multi-radio (M-R) systems reveals two key

design challenges. Firstly, there is the need for fast switching module for switching of

radio channels among the multiple wireless radios installed on each node. Secondly,

there is also the need for a process coordination module for network monitoring, su-

pervision and control. According to the author of [2], these key challenges, if prop-

erly implemented would subsequently lower the number and the cost of mesh nodes

needed to deploy any community-based wireless mesh network.

In another [3] selected review of literature on DCA a breadth-first search channel

assignment (BFS-CA) algorithm was analysed. The algorithm takes as input, the

interference estimates from the mesh routers and a multi-radio conflict graph (MCG).

The interference estimate is used to select the default channel (i.e., the channel with

the least interference) while MCG is used to model the non-default radios in the mesh

network. Any radio assigned to a default channel is by implication a default radio. A

multi-radio system unlike a single radio system considers all its radio independent,

and therefore does not have a dedicated default radio for each node or a group of

nodes. However, this technique of allocating a radio as default radio for every node in

the network would further increase the process coordination requirements of the algo-

rithm, thereby increasing its complexity.

In the same vein, the work of H. Skalli et al., as published in [4] proposed a similar

algorithm called MesTic. The input parameter of this algorithm includes (as in [3]) , a

traffic matrix in addition to the MCG, connectivity graph, the number of radio at

every node and the number of non-overlapping channels. Both algorithms described

in [3] and [4] use ranking technique to assign channels to radios. Although this tech-

nique is simple and easy to comprehend, a rank function requires a full description of

its underlying parameters and their interdependency. Moreover, in this particular

instance (i.e., channel assignment for multi-radio wireless mesh networks), there is

need to specify in the algorithm whether a node rank or channel rank is referenced

prior to the process of channel assignment.

In [5], a joint distributed channel assignment and routing algorithm is developed.

The algorithm utilises neighbour discovery and routing protocol to allow each node to

connect with its neighbour. Neighbour discovery protocol uses an ADVERTISE

packet that contains the cost of reaching the gateway node. This cost in turn depends

on residual bandwidth require to achieve load balancing in the network. Conversely,

the aggregate load on each virtual link also depends on a given routing algorithm. It is

therefore possible to infer that the interdependency of channel algorithm on specific

class of routing algorithm (also known as path selection algorithm) will not promote

interoperability between devices from different vendors.

Our proposed dynamic channel algorithm will not be tied to a specific routing al-

gorithm to ensure baseline interoperability. Also, it will not differentiate the total

number of radio interfaces on each node into fixed and switchable interfaces. In

Adaptive Priority Based Distributed Dynamic Channel Assignment 323

addition, the number of available non-overlapped channels is expected to be far

greater than the number of radio interfaces installed on each wireless node. Therefore

each wireless node will need to be equipped with channel switching functionality in

order to fully exploit the aggregate bandwidth available in the radio spectrum provi-

sioned by the standard. Furthermore, since network links do not all have the same

importance in carrying traffic, our algorithm should be able to identify links having a

greater capability to carry traffic and therefore prioritised such links.

A solution like this, according to [1] requires fine-grained synchronization and thus

will be difficult to implement without modifying the existing 802.11 MAC protocol.

However, we relax the synchronization constraints by implementing two versions of

the algorithm. The version with the fast switching module is implemented in distribu-

tive manner among all the mesh access point (MAP) and mesh point (MP) in the

network as shown in Fig. 2, while the other version is centralized and has the process

coordination module installed only on a dedicated management information base

(MIB) server node. This process coordination module is responsible for keeping track

and managing the interface switching, initiating the functional call for routing algo-

rithm, monitoring the discontinuity of traffic flow between every communicating

node pair, and setting the value of the ReThreshold attribute that defines the remain-

ing length of frame to be transmitted before calling the routing algorithm.

Consistent with much of the literature radio assignment problem, this paper pre-

sents theoretical bounds on the number of radio channels, as well as some complexity

analysis (NP-completeness) of the problem. It then proposes a multi-channel multiple

radio wireless mesh network architecture. In this architecture, both the MAP and MP

are running fast switching module version of dynamic channel assignment and a cen-

tralized dedicated server node runs the management protocol. Next, the proposed

algorithm is discussed with explicit detail the fast switching and process coordination

modules. An analysis to compute the order of overall complexity is presented. The

computation allows us to evaluate the performance of the proposed scheme; and fi-

nally a concise summary and future work conclude the paper.

2 Problem Definition and Description

We consider the problem of assigning multiple channels to multiple radios so that

each radio receives at most one channel. The wireless radios installed on each node

have preferences (as stated in I) over the available channels, thus, the allocation

mechanism does take the profile of the preferences as part of its inputs. An important

assumption is that the number of available channels is more than the number of wire-

less radio installed on each node; and that the network traffic and conditions may vary

over time.

Let G(V, E, K) be a connected network graph where V = (Mp , M) represent a set of

mesh nodes differentiated to mesh access point and mesh point respectively; and

E(ui , vj) represent a set of links. Let K be the number of wireless radios installed on

each node V, and N be the number of available non-overlapped channels, denoted by

{1, 2, , , , , N}.

324 T.R. Kareem et al.

The DCA considered here is closely related to random assignment problem pub-

lished by Akshay-Kumar et al., [6]. It is defined as probability distribution over static

assignment, and the corresponding convex combination of permutation matrices is a

stochastic matrix, whose (i, j)th entry represents the probability with which the wire-

less radios i receives channel j. The use of the word static in this context implies

deterministic.

Then, given a dynamic channel assignment matrix P, we let Pi be the i th row,

which represents the assignment of radio i in this dynamic assignment. If we let R be

the set of all possible dynamic assignments in a given network, we can therefore de-

fine the mechanism of assigning channels dynamically simply as the mapping from

N n to R.

A solution to the problem is obtained by selecting an assignment relation (as in

Fig. 1) that maximises capacity and minimises interferences; while also satisfying

some efficiency and fairness properties. Efficiency is measured in terms of network

throughput and delay, while fairness is measured in terms of fairness ratio, which

bounds the ratio of maximum and minimum throughputs values.

Formally, let us define the Kth wireless radio over two DCAs, p and q, and given

that K is indifferent between p and q (fairness property), then

∑

≥≥

=⇔≈

jkkjkkii

ik qpqp

(1)

Nj ∈∀

5N-4

Wireless Radio Cards Non-overlapped channels

Fig. 1. Allocation of wireless radio cards to channels in a multi-radio multiple channels mesh

network is modelled as Injective ( and not Bijective) function since the number of radios is less

than the number of independent channels

3 Architecture and System Design

The proposed multi-channel wireless mesh network architecture, shown in Fig.2,

consists of dedicated infrastructure devices known as mesh point (MP) and mesh

Adaptive Priority Based Distributed Dynamic Channel Assignment 325

access point (MAP). Mesh access point is a special type of mesh point which provides

access point (AP) services in addition to mesh services. Users’ devices (not shown in

Fig.2) support mesh services and associate with mesh APs to gain access to the mesh

network. These mesh nodes are equipped with two or more wireless radio cards and

together, they form ad hoc network among themselves to relay traffic to and from

end-user devices. In addition, the wireless radios are running fast switching applica-

tions (this is elaborated in Section IV) that allow them to support channel switching.

A dedicated centralized management information base (MIB) server is connected

to the gateway. MIB server node runs the interface management protocol located

within the process coordination module, and is responsible for keeping track and

managing the interface switching.

Together, the devices are configured in a multipoint-to-multipoint architecture for

internet connectivity. Internet connection to multipoint-to-multipoint mesh network

does not come from a wired router but through the backhaul mesh via the gateway.

As indicated in Section I, the two versions of the proposed dynamic channel as-

signment algorithms are implemented in the network. The version with fast switching

module is implemented in the MAP and MPs, while the version with process coordi-

nation module resides in the MIB server node.

Interne

Ser

ver

Backhaul

link

ISP

Fig. 2. A community-based multipoint-to-multipoint mesh network topology running fast

switching and process coordination modules

4 Dynamic Channel Assignment

The proposed dynamic channel assignment algorithm called APMCA (Adaptive Pri-

ority Multi-radio channel assignment) is designed for a simple network structure

where all the mesh nodes are equipped with equal number of radios, and a pre-defined

number of available non-overlapped channels as shown in Fig.3.

The algorithm uses an iterative application of adaptive priority algorithm that ter-

minates in (at most) N phases, where N is total number of non-overlapped channels

available in the network. Adaptive priority implies that it is possible for the mesh

nodes to reallocate the radio channels after each successful packet transmission from

326 T.R. Kareem et al.

source to destination nodes subject to the channel constraints as defined in the input

sequence Si.

Each radio interface receives Si as an input sequence which is characterised by a

list of 4 elements of non-negative numbers Si = (NodeName, Non-overlapped-

Channels, NodeRadioLabel, AdjList).

The “NodeName” is an identifier that denotes a uniquely assigned node name for

each mesh nodes in the network. “Non-overlappedChannels” denotes the number of

allowable co-located channels with centre frequencies of 5MHZ apart, the channels

are 22MHZ wide, and the number of channels between successive channels is at least

five apart. The NodeRadioLabel is an identifier that provides attributes to radios in

each node. Lastly, AdjList is introduced as an identifier that defines a set of 2-tuples

comprising the spatial channel re-use ratio and an estimate of co- channel interference

in the network.

Fig. 3. Illustrates a network of three radios - four channel systems deployed in a wireless mesh

network. Two of the three radios are dedicated backhaul links and the third radio is for config-

ured for access network.

At start-up, every interface is randomly assigned a radio channel such that no two

radios within the same communication range (as defined by channel reuse principle)

are assigned the same channel, except for a pair of nodes communicating with each

other through a common communication channel. This is done to eliminate selection

biases that may degrade the network performance.

A pair of nodes that wish to communicate must first share a common communica-

tion channel that is used to set up a virtual link. If such common communication

channel has already been established by default, then the algorithm proceeds to test

the constraints as listed in AdjList, otherwise, a fast switching module is enabled on

the source node. The mechanism of fast switching enables each wireless radio in-

stalled on the source node to randomly switch to channels available on the destination

node until at least one communication channel is established. AdjList is a set of 2-

tuples comprising the spatial channel re-use and interference estimation. The channel

reuse factor depends strongly on the environmental characteristics, primarily, path

loss and slow fading, while the estimation of interference depends mainly on the dis-

tance between the nodes.

A positive attempt towards the characterisation of spatial channel reuse in multi-

radio WMN begins by using the concept of a simple classical triangular mesh (as

given in [10]) of L * L square area, and a frequency reuse distance D. Given that equal

number of radios “K” is installed on each mesh node, then we have:

Adaptive Priority Based Distributed Dynamic Channel Assignment 327

K= (2)

Assuming that one MAP manages several MPs as stated in section II, and each MAP

is fairly located at the centre point R, then the channel reuse ratio is calculated thus:

≥ (3)

where

is the parameter that defines the necessary and sufficient condition for good

spatial reuse for the triangular mesh.

Similarly, interference estimation in a multi-radio multiple channel environments is

also characterised by using a combination of heuristic and measurement-based tech-

nique. A modified version of the heuristics developed in [7] and [8] that is based on

the distance between nodes is considered in this design, and a measurement based

technique presented in [9] is extended to a multi-radio environment. We assume a

worst case scenario in which each radio on each node is connected to another radio on

another node thereby resulting in the emanation of multiple simultaneous active links

from a single node. With this, the problem is reduced to that of estimating interfer-

ence among multiple links in a wireless mesh network; and according to [5], this

information is considered necessary for the design of an optimal channel assignment.

A node A that wishes to communicate with a node B must first sense the channel

for the availability of a common communication channel. If it notices that either the

channel is in use or there is no common channel available for the intended communi-

cation, it then backtracks (the default mechanism in 802.11 Protocol). A fast switch-

ing module rather than the backtracking algorithm is called as explained in sub

section A.

In a situation where all available channels assigned to the radios on the same node

are currently in use, a reuse distance is computed as discussed above. The overall

purpose of these processes is to search for a free channel to use for communication

between the nodes.

Algorithm APMCA (Adaptive Priority Multi-Radio Channel Algorithm) To find

an efficient and fair channel assignment P of multiple radios K to multiple

channels N in a wireless mesh network G(V, E, K) that maximizes capacity and

minimises interference. Let Hj be a target graph, T is define as the interference

threshold, and Vk denotes each radio installed on each node in the network.

Step 0. [Initialise] Hj <− G (V, E, K); Pi ≡ 0; Pi ∈ Hj;

KN < for all i , j 1≥, T = 0.65,

= 1.16.

Step 1. [Iterate] testIfCommExist Vk =

dropWhile ( Vk≥2 ) [Vk|Vk< − [1..j]]

Step 2. [Channel assignment] for pair of communicating nodes

328 T.R. Kareem et al.

u, v ∈ V ∃ Kij where Ki ∈ u

and Kj ∈ v;

pickRadio K rnd = K !! rnd;

assignChannelToRadio Ki Ni result =

M.insertWith (++) Ni [Ki ] result;

case intersect Ki, Kj =

filter (\Cn − >any((==)Cn)Ki)Kj of

{assign − > ( Cn <− [Ki, Kj] );

nonAssign − >fastSwitchingSame f}

Step 3.[ fast Switching]

fastSwitchingSame f

lookup ‘Ki ‘ [(‘Ki-1’, Ni), ..’Kn’ Nj)];

if intersect Ni Nj = [V| V< − Ni, V ‘elem’ Nj]

then

swap Ki ; Kj;

else

fastSwitchingNeighbour fn

lookup ‘Ki’ map (*D) [(‘Ki-1’, Ni), ..’Kn’ Nj)];

if intersect Ni Nj = [V| V < − Ni, V ‘elem’ Nj]

then

interferenceEsti x y z --function call;

else

reuseEsti k l r --function call;

Step 4. [update process coordination server]

type State = (Integer, Bool)

update :: State − > State

meshAccessPoint :: [a] − > (a − >a) − >[a]

meshAccessPoint (meshPoint, K) = K+1 ++ map (*n) [meshPoint];

meshPoint :: a − >[a]

meshPoint (radioK : radioKs) = map (t+1) [radioK];

update = [y | y < − [meshAccessPoint(K)t + 1] !! all;

meshPoint(n), filter (\y −> any

((==)meshPoint(K))meshPoint(t)meshPoint(t+1));

Step 5. [Interference estimation]

interferenceEsti x y z =

()

zyx

fff

yxfxzfyzf

Π+Ω+

;

-- where ΠΩ and,,

are const.

values that are environmental and

hardware- dependent.

if interferenceEsti < T;

then

Adaptive Priority Based Distributed Dynamic Channel Assignment 329

processUpdate x y z;

else

reuseEsti k l r ;

Step 6. [Channel reuse estimation]

reuseEsti k l r =

let reuseDistance =

*931.0 ;

in reuseDistance / r ;

if reuseEsti ≤1.16;

then

fastSwitchingNeigbour f;

else

Pi = Pi + 1;

4.1 Complexity Analysis of APMCA

Step 0 of the algorithm APMCA requires )*( nmO operations to initialise each of K

number of radios installed on V number of nodes.

Step 1, the iteration step, essentially requires )(mO operations to determine if there

are more radios not yet randomly assigned a channel.

Step 2 is executed exactly n (m-1) times. Each execution of step 2 requires that the

APMCA search through the list of assigned radios to find a pair of communicating

node whose radio share a common channel. This effort requires ))1(*( −mnO op-

erations, where n (m-1) denote the number of available radios m on a receiving node n.

Step 3 involves four steps divided into two categories (Same node and Neighbour-

hood nodes). Searching process in both the “same node and Neighbourhood node”

requires

* ))(ln(mO operations (where

is a constant define differently for a

case of “same node” and “neighbourhood node”) taking into consideration that the

data in the look up tables for both cases are already sorted. Furthermore, the process

of swapping of radio Ki and Kj also requires )1(O operations, and on the overall, the

complexity of step 3 is bounded from above as ))(log(mO .

Step 4 primarily involves updating a dedicated server at every time t; and for every

successful transmission from a radio K, this process requires )(mO operations. For

each of the notification sent to MAP, a report is sent to the server to notify the server

of any changes in the state of the network. At each successive state, a 4-tuple

constraint Si, is tested and this also requires )(mO operations. Since none of the other

substeps of step 4 requires more than )(mO operations, the complexity of step 4 is

therefore bounded by )(mO using the theorem:

330 T.R. Kareem et al.

)()()( mOmOmO =+ (4)

as in [11].

Step 5 and Step 6 are functional calls. Step 5 comprises two loops whose running time

is proportional to the square of the number of radios on a pair of communicating

nodes. In addition, a computation of the ratio U

Wrequires logarithmic operations,

while the test of validity of ratio U

Whas a linear running time.

In summary, the complexity of step 5 is therefore bounded as )( 2

mO . Similarly,

Step 6 has two linear operations for measurement of l and r. A computation of re-

useDistance also requires a linear combination of quadratic and logarithmic running

times. In addition to this, the last substep in step 6 requires a combination of linear

and logarithm operations. We can therefore conclude that the complexity of step 6 is

also bounded by ))log(*( 2mmO .

4.2 Proof of Correctness

The first step is to show that all radios are randomly assigned to at most one channel.

The next step is to conduct a randomization test only for a pair of communicating

nodes.

In order that to verify the above two steps, we start by denoting the number of ra-

dios installed on a pair of communicating nodes as K1 and K2. If we define the num-

ber of ways of assigning the non-overlapped channels N as W, then W is represented

thus:

!! 21 KK

(5)

The third step is to determine how many of these ways W of assigning the channels to

radio satisfy both the local and global constraints. This number is denoted as “as-

signment” P = {P1, P2, P3… Pn}.

The final step is to test the value of the interference estimated against the allowable

threshold value.

The above four steps simply shows that a unique solution Pn exist for every pair of

communicating radios in the multi-radio wireless mesh network.

4.3 Overall APMCA Complexity

The complexity analysis shown in subsection A which is based on the order-of-

magnitude analysis and not on the coded implementation of the algorithm shows that

the overall complexity is given thus:

Adaptive Priority Based Distributed Dynamic Channel Assignment 331

))log(*(

)()()(log()()*(

mmO

mOmOmOmOnmO

++++ (6)

since K >> N, then we can conclude that )()( mOnO ∈and subsequently,

)()*( mOnmO ≈.

Therefore, the entire complexity of algorithm APMCA computed from equation 6

is )( 2

mO .

5 Conclusion and Future Work

This paper addresses the need for the addition of fast switching and process coordina-

tion modules to the design of channel assignment scheme for multi-radio wireless

mesh networks.

Our proposed design is aimed at maximising the network capacity and minimizing

the interference within the same node and among the nodes in the neighbourhood.

The study commences with architectural and system design consisting of dedicated

mesh routers differentiated into mesh point (MP) and mesh access point (MAP)

equipped with two or more wireless cards, and a centralised management information

base (MIB) server. These infrastructural devices (mesh routers and MIB), respectively

host the two different versions of our proposed algorithm. The algorithm uses an

iterative application of adaptive priority scheme that terminates in (at most) N phases,

where N is the total number of non-overlapped channels available in the network. The

input to the algorithm is a fully connected mesh network where the number of radios

installed on each node out-numbered the available non-overlapped channels. Aug-

mented with the fast switching capability and process coordination module, the algo-

rithm allocates channels to every pair of communicating radios in an ordinally

efficient and fair manner. We illustrate our algorithm in detail, prove its correctness

and calculate the complexity. The order-of-magnitude analysis of its overall complex-

ity reveal a )( 2

mO running time. Thus a more detailed analysis currently studied is

expected to further prove its supremacy in terms of performance over the previous

proposal and lead to better performance of multi-radio wireless mesh network.

References

1. Kyasanur, P.N.: Multi-Channel Wireless Networks: Capacity and Protocols, PhD Disserta-

tion, Graduate College of the University of Illiois at Urbana-Champaign (2006)

2. Strix System, The business cases for wireless mesh networks,

http://www.strixsystems.com/case-studies/

WiFi-Mesh-business-case.asp

3. Ramachandran, K.N., et al.: Interference–Aware Channel Assignment in Multi-Radio

Wireless Mesh Networks. In proc. of IEEE Infocom (2006),

http://www.cs.ucsb.edu/~ebelding/txt/infocom06.pdf

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4. Skalli, H., et al.: Traffic and Interference aware channel assignment for multi-radio Mesh

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Channel Wireless Mesh Network. In: Proc. of IEEE INFOCOM 2005, vol. 3, pp. 223–234

(2005)

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main. Journal of Economic theory 131(1), 231–250 (2006)

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hop wireless routing. In: MOBICOM 2003 (2003)

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In: MOBICOM (2004)

9. Kodiaalm, M., Nandagopal, T.: Characterising achievable rates in mult-hop wireless net-

works: The joint routing and scheduling problem. In: MOBICOM (2001)

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11. Goodman, S.E., Hedetniemi, S.T.: Introduction to the design and analysis of Algorithm.

McGraw-Hill, New York (1997)

Ranking and Sorting in Unreliable Single Hop

Radio Network

Marcin Kik

Institute of Mathematics and Computer Science,

Wro claw University of Technology

Wybrze˙ze Wyspia´nskiego 27, 50-370 Wroclaw, Poland

Marcin.Kik@pwr.wroc.pl

Abstract. We propose simple and eﬃcient sorting algorithm for unre-

liable single hop radio network. (In such network each listening station

receives transmitted message with some probability p<1.) We also pro-

pose a method of periodic transmission of a sorted sequence that allows

for eﬃcient and energetically safe ranking in this sequence.

1 Introduction

We consider the problems of sorting and ranking in unreliable single hop radio

network. Such network consists of nstations s0,...,s

n−1communicating with

each other by exchanging short radio messages. The stations are synchronized.

Time is divided into slots. Within a single time slot a single message can be

broadcast. During each time slot each station is either listening or sending or

idle. If it is sending or listening then it dissipates a unit of energy. We assume that

the stations are powered by batteries. Therefore we want to minimize energetic

cost of the algorithm, i.e. maximum over all stations of non-idle time slots.

Each station is in the range of any other station (i.e. a single hop network). If

two or more stations send messages simultaneously, then a collision occurs. In

this paper we consider only collision-less algorithms. If during time slot tonly

one station sends a message and any other station (say si) is listening, then

sireceives the message with probability p(probability of successful reception).

The special case p=1meansreliable network. The previously proposed sorting

algorithms for this model ([10], [6], [3], [4], [5]) were designed for reliable network.

If any transmission failed then the whole output would be devastated. Since

radio transmissions are vulnerable to many unpredictable external interferences,

we believe that practical algorithms should be robust to occasional losses of

received messages. A simple general strategy of increasing the robustness of the

algorithm is to make each transmission robust by repeating it many times. If

the transmission from single sender to single receiver is repeated rtimes then

the probability of failure is reduced from qto qr,whereq=1−p. However, the

energetic cost of sending is increased rtimes. (The receiver may stop listening

This work has been supported by the ICT Programme of the European Union under

contract number FP7-215270 (FRONTS).

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 333–344, 2008.

Springer-Verlag Berlin Heidelberg 2008

334 M. Kik

as soon as it receives the message.) The situation is still worse if there are m

receivers, m>1. We should ensure that all receivers have received the message

with high probability.

Any sorting algorithm consists of Ω(n) transmissions, and any of those trans-

missions may have a large number of receivers. It seems that constructing an

algorithm with reasonably high probability of success requires a lot of energy.

The number of repetitions for each step should be rather overestimated since

the failure of any robust step makes all the previous and remaining computa-

tions useless. We propose sorting based on simple merge-sort presented in [4].

Because of the asymmetry between sending and receiving energetic costs in that

algorithm, the asymptotic expected energetic cost of our robust algorithm is as

low as that of the sorting algorithms with asymptotically lower costs (e.g. [1],

[10]) with retransmissions of each step, while the low constants and simplicity

make it preferable in practical implementations.

By ranking we mean the problem of locating the position of some key xin a

sorted sequence of keys (i.e. the number of keys in the sequence that are less than

x). One of the many applications of eﬃcient sorting and ranking algorithms may

be the routing of packets. The routing algorithms for single hop network ([2], [7],

[8], [3]) typically consist of some preprocessing reservation phase that allows for

subsequent energetically eﬃcient delivery of the packets. Such preprocessing may

consist of sorting the addresses of the packets, and ranking by each station its

own address and the next address in the sorted sequence (see e.g. [3]). Then the

packets are delivered according to the sorted sequence and each station knows the

interval of time slots in which it should listen. Note that even the approximation

of such interval (its superset) can be useful. The ranking algorithms proposed

in this paper ﬁnd the exact rank by updating its lower and upper bounds (until

they meet each other) while listening to the iterated transmissions of the sorted

sequence. The quality of these bounds after the ﬁrst iteration depend solely

on the probability pand can be used for approximation of such interval. We

also consider the case when the ranking station may start at arbitrary time

slot while the sequence is periodically transmitted. Here we propose that the

sorted sequence is transmitted in recursive bisection ordering (rbo), which is

easily computable permutation. In the case of a reliable network we formally

prove in Section 3.1 that the energy used by the ranking station is then O(lg n).

In our algorithms each message contains only a single key of the input

sequence.

2 Preliminaries

We formulate the problem of sorting as follows: Each station siinitially stores

a key in its local variable key[si]. The task of each station siis to compute the

value idx[si] which is the index of key[si] in the sorted sequence of keys. (The

indexes are numbered from 0 to n−1.)

In Section 3 we consider the problem of ranking: The sorted sequence is trans-

mitted periodically (in some ﬁxed ordering π). Each round requires ntime slots.

Ranking and Sorting in Unreliable Single Hop Radio Network 335

During any time slot any station may start the computation of the rank (or its

approximation) of some key in the transmitted sequence. (By the rank of the

key in the sequence swe mean the number of elements of sthat are less or equal

to the key).

In this paper “lg” denotes “log2”. For simplicity of description we assume

that n(number of keys and stations) is a power of two (i.e. lg nis integer). By

Pr(E) we denote probability of the event E.ByE[X] we denote expected value

of random variable X.By|S|we denote the size of the set S. Whenever we

deﬁne a permutation πof {0,...,n−1},π−1denotes the permutation reverse

to πandwesettlethatπ(NIL)=π−1(NIL)=NIL,whereNIL is a special

constant distinct from all numbers.

3Ranking

Let n=2

k,wherekis positive integer. The generic ranking algorithm is deﬁned

as follows: Let πkbe a permutation of the elements {0,...,n−1}.Letb0,...,b

n−1

be a sorted sequence of keys. The sequence permuted by πkis transmitted pe-

riodically, i.e. for t≥0, bisuch that πk(i)=tmod nis transmitted in time

slot t.Letabe a station that wants to compute the rank of key[a]inthesorted

sequence. acan start in arbitrary time slot. It knows permutation πkand the

numbering of time slots. Station acontains variables minR[a]andmaxR[a]that

are updated during successful receptions. Initially minR[a]=0andmaxR[a]=n.

In time slot t(i.e. when key =bπ−1

k(tmod n)is transmitted), adoes:

Let t=tmod n.IfminR[a]≤π−1

k(t)<maxR[a]thenalistens. If a

received the key,then

if key[a]<keythen asets maxR[a]toπ−1

k(t), otherwise (i.e. if

key ≤key[a]) it sets minR[a]toπ−1

k(t)+1.

Note the following invariant: The rank of key[a]isintheinterval

[minR[a],maxR[a]]. Thus as soon as minR[a]=maxR[a] the exact rank of key[a]

is computed. Station aparticipates in the algorithm as long as it needs or some

limit imposed on time or its listening energy is exceeded.

Lemma 1 can be used for estimating the time needed for exact ranking with

high probability.

Lemma 1. Let cbe a positive integer. After c·ntime slots minR[a]=maxR[a]

with probability at least 1−2·(1 −p)c.

Proof. Let rbe the exact rank of key[a]. To have minR[a]=maxR[a]=rthe

station needs successful reception of the keys br−1and br. The probability that

during the ctrials afails to receive the key is (1 −p)c. Thus the probability that

afails to receive from both br−1and bris not greater than 2 ·(1 −p)c.!"

Lemma 2 estimates the size of the interval [minR[a],maxR[a]] after ntime slots.

Lemma 2. The expected value of ∆=maxR[a]−minR[a]after ntime slots is

not greater than 2/p −2.

336 M. Kik

Proof. Let rbe the exact rank of key[a]. In the ntime slots all the keys bihave

been transmitted. We may think as follows: each transmission was successful

with probability p, and whenever station aactually listened it simply observed

this transmission. Let ube minimal integer such that u=nor r≤u<nand

the transmission of buwas successful. It follows from the construction of the

algorithm that aobserves this transmission and ends up with maxR[a]=u.Let

X1=u−r.Ifuhad not been limited by n,thenX=u−r+1 would have

been random variable with geometric distribution: Pr(X=m)=(1−p)m−1·p

with the expected value E[X]=1/p.SinceX1=min{X−1,n −r},wehave

E[X1]≤1/p −1. It follows (by symmetry) that, for X2=r−minR[a], E[X2]≤

1/p −1. Thus, E[∆]=E[X1+X2]=2/p −2. !"

The choice of permutation πkhas great inﬂuence on the energy used by a.Ifπkis

identity, astarts listening in time slot 0 and rank of key[a]isn,thenais forced to

listen in all ntime slots. Much better option is to use bisection ordering (denoted

by bo): ﬁrst (on level 0) transmit the median xof the sequence, then (on level 1)

transmit the two medians of the sub-sequences neighboring to x, and so on. For

n=2

k, we deﬁne precisely bokby selecting upper median whenever we have to

choose. There is binary tree of depth k+ 1 corresponding to bisection ordering

(see Figure 1). On Figure 1 each argument xis joined by vertical dotted line

with its corresponding node labeled by bok(x). Note the dependence between

binary representation of xand its position in the tree: The level of positive xis

determined by the position of its rightmost one and the digits left to this one

form the position of xwithin the level. x= 0 is the only argument placed on level

k.Forx>0, let irmo(x)=min{j≥0|x/2jmod 2 = 1}(index of rightmost

one), and let irmo(0) = −1. Let lbok(x)=k−1−irmo(x)(levelofxin bok).

Now we can deﬁne bokas follows: bok(x)=2

lbok(x)−1+x/2irmo(x)+1.(There

are 2lbok(x)−1nodesabovethelevellbok(x)andx/2irmo(x)+1is the position

of xon the level lbok(x).) The permutation reverse to bokcan be computed as

follows: Let lev(y)=lg(y+1).Thenbo−1

k(y)=y−2lev(y)−1·2k−lev(y)+

2k−lev(y)−1.(Fory=2

k−1, the result is zero, and, for y<2k−1, the ﬁrst

000

001

010

011

100

101

110

111

3456

level 0

level 2

level 3

level 1

binary:

Fig. 1. Thetreeofbo3

Ranking and Sorting in Unreliable Single Hop Radio Network 337

component of the sum is the position of ywithin the level lev(y) multiplied by

2k−lev(y)and the second component settles the rightmost one.)

In reliable networks the ordering of transmissions πk=bokguaranties that if

astarts in time slot tsuch that tmod n=0,thenahastolistenatmostonceon

each level and therefore uses no more than k+ 1 units of energy. However, if we

let astart its computation in arbitrary time slot, then amay be forced to listen

in many time slots. For example, if astarts in time slot n/2−1andtherankof

key[a]isn,thenamust listen in all n/2 time slots on level k−1. On the other

hand, forcing ato wait until time slot tsuch that tmod n= 0 may cause serious

delays. Therefore we propose slightly more “sophisticated” permutation that

to a large extent eliminates this problem. The permutation recursive bisection

ordering (rbok) is deﬁned as follows: First we permute the elements according

to bisection ordering and then we permute each level (except the ﬁrst and the

last one) according to recursive bisection ordering. The permutations rbokand

rbo−1

kcan be computed by Algorithms 1 and 2, respectively. The permutation πk

can be imagined as a set of parallel vertical blades cutting of parts of horizontal

interval containing the rank of key[a] as it falls downwards. To appreciate the

diﬀerence between bokand rboksee Figure 2. Even if many highest blades of rbo

are missing, the remaining ones perform (less exact) bisection.

function rbok(x)

begin

if x=0then return 2k−1;

y←bok(x);

if y=0then return 0;

above ←2lev(y)−1;

return above +rbolev(y)(y−above);

end

Algorithm 1. Computation of rbok(x)

function rbo−1

k(y)

begin

if y=2

k−1then return 0;

if y=0then return bo−1

k(0);

above ←2lev(y)−1;

return bo−1

kabove +rbo−1

lev(y)(y−above);

end

Algorithm 2. Computation of rbo−1

k(y)

Next we show that if the station astarts in time slot 0 and we use permutation

bo or rbo, then the expected energy used by aduring the ﬁrst iteration is very low.

Lemma 3. Let πkbe bokor rbok. Let the station astart in time slot 0.The

expected energy used by aduring the ﬁrst n=2

ktime slots is at most 1+k·

(2/p −1).

338 M. Kik

bo rbo

Fig. 2. Permutations bo5and rbo5. (Dotted lines denote borders between levels of bo5).

Proof. Let Bl=*bl,0,...,b

l,2l+1−2+be a sequence of keys {bj|lbok(j)≤l}(i.e.

the sub-tree of bisection tree from level 0 to l)sortedbyj. Station ahas to listen

to b0,0(the root of bisection tree). Thus the energy used by aon level 0 is 1. For

l≥0, let rl=|{bl,i |bl,i ≤key[a]}| (i.e. the rank of ain the sequence Bl). Let dbe

maximal integer such that d=−1or0≤d<r

land the transmission of bl,d was

successful. Let ube minimal integer such that u=2

l+1 −1orrl≤u<2l+1 −1

and the transmission of bl,u was successful. As in the proof of Lemma 2, we can

show that the expected value of u−(d+ 1) is not greater than 2/p −2. It follows

from the construction of the algorithm, that the station awill not listen to any

keys that are before bl,d or after bl,u on the following levels of bisection tree. The

sequence Bl+1 consists of the keys from level l+ 1 on even positions and of the

keys from Blon odd positions. Thus awill have to listen to at most Xl=u−d

keys on level l+1 and E[Xl]≤2/p −1. !"

3.1 Ranking with rbo in a Reliable Network

In this subsection we assume that probability of successful reception is p=1

(i.e. a reliable network), and the station acan start in arbitrary time slot t0

(w.l.o.g. we assume that 0 ≤t0<n) and continues until it learns its rank ra.

We also assume that the used permutation is πk=rbok,wherek=lgnis

positive integer.

Note that alistens until the last bjwith j∈{ra−1,r

a}has been transmitted.

This happens within ntime slots. For given subset of indexes S⊆{0,...,n−1}

and rank r∈{0,...,n},letl(S, r)=max{i+1 |i∈S∪{−1}∧i<r}

and u(S, r)=min{i|i∈S∪{n}∧r≤i}.Fort≥t0,letStbe a set of

indexes of keys that have been transmitted during time slots t0,...,t. Then,

just after t,minR[a]=l(St,r

a)andmaxR[a]=u(St,r

a) and, for any S⊆St,

l(S,r

a)≤minR[a]≤maxR[a]≤u(S,r

a).

Ranking and Sorting in Unreliable Single Hop Radio Network 339

For a sequence of non-negative integers αwe deﬁne subset of indexes L(α)as

follows: L()={0,...,n−1},andL(α·l)isthelth level of bisection tree

formed from L(α)(“·” denotes concatenation). Note that if |L(α)|=2

l≥1

then, for l<l

,|L(α·l)|=2

l(full levels), and for l=l,|L(α·l)|= 1 (the

last level is singleton), and for l>l

,|L(α·l)|= 0 (empty levels below the

tree). In rbolg nthe sequence of subsets of indexes is: L(0),...,L(lg n), and

within each L(α) the sequence is: L(α·0),...,L(α·lg |L(α)|).

Lemma 4. Let |L(α)|=2

l≥2,and1≤l<l

.Lett=max{rbolg n(x)|x∈

L(α·l)}. If, just after time slot t,minR[a]≥l(L(α·l),r

a)and maxR[a]≤

u(L(α·l),r

a)then during each of the levels L(α·l+1),...,L(α·l)the

station alistens at most twice.

Proof. During transmission of the level L(α·l+1)thestationalistens only

to the keys bjwith minR[a]≤j≤maxR[a]−1. Since there are no such nodes

in L(α·l), the only such nodes in L(α·l+1) possibly are: the right child

of minR[a]−1(ifminR[a]−1∈L(α·l)) and the left child of maxR[a](if

maxR[a]∈L(α·l)) in the tree L(α). After transmission of L(α·l+1), we

have minR[a]≥l(L(α·l+1),r

a)andmaxR[a]≤u(L(α·l+1),r

a). Thus we

can repeat the same reasoning for each following level in the tree L(α). !"

Lemma 5. Let |L(α)|=2

l≥16,and2≤l<l

.Lett=max{rbolg n(x)|x∈

L(α·l)}. If, just after time slot t,|{x∈L(α·l)|minR[a]−1<x<

maxR[a]}| ≤ 1then during the transmissions of L(α·l+1)the station alistens

at most four times.

Proof. In the worst case alistens in L(α·l+1) to some subset of: right child

of minR[a]−1, both children of the single xbetween minR[a]−1andmaxR[a],

and left child of maxR[a]inthetreeL(α). !"

Theorem 1. If the assumptions formulated in the ﬁrst paragraph of this sub-

section hold then the station alistens at most 4lgntimes before it learns its

rank.

Proof. Let U(α, l)=l

i=0 L(α·i) (i.e. the uppermost l+ 1 levels of the tree

L(α)). Let D(α, l)=lg |L(α)|

i=lL(α·i) (i.e. the lowest lg |L(α)|−l+ 1 levels of

the tree L(α)).

For t≥0, let γ(t) be the shortest sequence such that x=rbo−1

lg n(tmod n)

is the root of the tree L(γ(t)) and let δ(t)=min{δ≥0||L(γ(t+δ))|≥2}.

For 0 ≤i<δ(t), L(γ(t+i)) is the last level (singleton) of some tree Ti. Hence,

L(γ(t+i+ 1)) is a level of some tree Ti+1 such that |Ti+1 |≥2·|Ti|,orof

the whole tree L()if(t+i+1)modn=0(inthiscase:i+1 = δ(t)). Tiis

predecessor of the level L(γ(t+i+1)) in Ti+1.L(γ(t+δ(t))) is a full level, thus

its size is at least 2 ·|Tδ(t)−1|. Hence we have:

Claim. |L(t+δ(t))|≥2δ(t).

340 M. Kik

Let β=γ(t0+δ(t0)). If βis empty sequence, then alistens at most δ(t0)

times and then at most lg n+ 1 times starting from the root of the whole tree

L(). By the Claim: δ(t0)+lgn+1≤2lgn+1.

Otherwise, let β=l1,...,l

Rand let βi=l1,...,l

i.NotethatR(the length

of β) is the level of recursion on which the bisection tree of L(β)isformedand

that lR≥1, since |L(β)|=2

lR≥2.

First alistens δ(t0)times.BytheClaim:δ(t0)≤lR,since|L(β)|=2

lR.

Then alistens to L(β) starting from the root of L(β). Thus it listens at most

lR+ 1 times and, after that, minR[a]≥l(L(β),r

a)andmaxR[a]≤u(L(β),r

a).

Then rbo steps back one recursion level. Then it listens to (possibly empty)

sequence of sets L(βR−1·lR+1), ..., L(βR−1·lR−1). By Lemma 4, alistens

at most twice in each of these sets. After that minR[a]≥l(D(βR−1,l

R),r

a)and

maxR[a]≤u(D(βR−1,l

R),r

a). Then rbo steps back one recursion level. Such

stepping back is repeated R−1times,foritaking values R−1,. . . ,1. For each

such i, initially minR[a]≥l(D(βi,l

i+1),r

a)andmaxR[a]≤u(D(βi,l

i+1),r

a), and

the following (possibly empty) sequence of sets is transmitted: L(βi−1·li+1),

..., L(βi−1·li−1). Note that, since L(βi+1 )=L(βi·li+1 ) is a full (i.e. not

last) level of L(βi), for each x∈U(βi,l

i+1 −1), the predecessor and the successor

of xin L(βi)areinD(βi,l

i+1) and, hence, |{x∈L(βi)|l(D(βi,l

i+1),r

a)−1<

x<u(D(βi,l

i+1),r

a))}| ≤ 1. Thus, by Lemma 5, since L(βi)=L(βi−1·li), the

station ahas to listen at most four times in L(βi−1·li+1) and, by Lemma 4,

at most twice in each of the remaining sets.

Consider the sequence of all the sets mentioned above. For each set L(βi·j)

in the sequence (except L(βR−1·lR)=L(β) – the ﬁrst one) its index “j”is

greater than the index of its predecessor. The greatest possible value of jis lg n

(in the set L( ·lg n)). Thus the number of the sets following L(β)isatmost

lg n−lRandineachofthemalistens at most four times. Each set in which

ahas to listen more than twice (which is a full level) must be followed by at

least one set (e.g. the last level) in which ahas to listen at most two times.

Thus the energy used by awhile listening to the sequence of sets is at most

(4 ·1

2+2·1

2)(lg n−lR)+(lR+1)≤3lgn−2lR+1.

This procedure is ﬁnished, for the last i=1,justbeforetimeslotnthat starts

the next round. In this round alistens no more than lg ntimes (it does not need

to listen in the last level again). Adding δ(t0)≤lRinitial slots, we have upper

bound 4 lg n−lR+1≤4lgnon the energy used by a.!"

The estimation 4 lg nof Theorem 1 seems to be very pessimistic. (In our tests

anever had to listen more than 2 lg ntimes.) Nevertheless, it shows that the

station acan safely start its ranking at any time slot. (This reduces the upper

bound on ranking time from 2n−1ton.) The simulations indicate that rbo is

also energetically eﬃcient on unreliable network (i.e. when p<1).

4Sorting

We assume that lg nis positive integer. Each station sicontains vari-

ables: idx0[si], ..., idxlg n[si], minR0[si], ..., minRlg n−1[si], maxR0[si], ...,

Ranking and Sorting in Unreliable Single Hop Radio Network 341

maxRlg n−1[si]. The variables are initialized by the procedure init (see Algo-

rithm 3). The ultimate goal for each siis to compute idxlg n[si], which is the

procedure init

Each sidoes (in parallel):

begin

idx0[si]←0;

for k←1to lg ndo idxk[si]←NIL;

for k←0to lg n−1do

minRk[si]←0;

maxRk[si]←2k;

end

Algorithm 3. Procedure init

index of key[si] in the sorted sequence of keys. Our algorithm is designed to

perform stable sorting (i.e. the initial ordering between equal keys is preserved).

The basic building block of our algorithm is the procedure rank(k, l, d, πk), where

d∈{0,1}and 0 ≤l<n/2k+1, (see Algorithm 4) that tries to ﬁnd the rank

of each key from the stations sl·2k+1+d·2k, ..., sl·2k+1+d·2k+2k−1in the sorted

sequence of keys from the stations sl·2k+1+(1−d)·2k,...,sl·2k+1+(1−d)·2k+2k−1.

Once the station siknows its rank rin the neighboring sequence and its index

idx in its own sorted sequence, it can compute its index (r+idx) in the sequence

merged from the two sequences. The permutation πkis either rbokor bok(de-

ﬁned in Section 3). For any k,0≤k<lg n, all procedures rank(k, l, d, πk)are

used to produce indexes for sorted sub-sequences of length 2k+1.Thisisdone

by procedure levelRanking(k, πk) (see Algorithm 5). We refer to kas a level.

Sorting algorithms can be built by composing sequences of levelRanking for

various levels. For n>0and0<q,q

<1, let c(q, q,n)=log1/q 2nlg n

q=

(1 + lg n+lglgn+lg(1/q))/lg(1/q). We propose and analyze a simple pro-

cedure sortingq(see Algorithm 6) that successfully sorts with probability 1 −q

by repeating levelRanking c(q, q,n) times on each level. The output consists of

the ﬁnal values of idxlg nin the stations.

Theorem 2. For 0<q

<1, the procedure sortingq(Algorithm 6) sorts any

input sequence with probability greater or equal 1−q.

Proof. Let q=1−pand c=c(q, q,n). Let Qbe the event that sortingqfailed

to sort (i.e. some indexes remained uncomputed). For 0 ≤k<lg n,letQkbe

the event that the ﬁrst failure occurred at level k(i.e. some idxk+1[si]remained

uncomputed, while all values idxk[s], for 0 ≤k≤k, for each station s,are

computed.) Thus Pr(Q)=lg n−1

k=0 Pr(Qk)(Qis disjoint union of all events

Qk). Let Fkbe the event that repeating ctimes levelRanking(k, rbok) fails to

compute all indexes on level k+ 1 under the condition that all indexes on levels

up to khave been computed. Let q=1−p. By Lemma 1, the probability

that some given index remains uncomputed is not greater than 2 ·qc.Thus

Pr(Fk)≤2nqc,aswehavetocomputenindexes. Let Ekbe the event that

342 M. Kik

procedure rank(k, l, d, πk)

for 0 ≤i<2k:

–let aidenote sl·2k+1+d·2k+i,and

–let bidenote sl·2k+1+(1−d)·2k+i.

for time slot t←0to 2k−1do

the (at most one) bjwith πk(idxk[bi]) = tbroadcasts key =key[bj];

let x=π−1

k(t);

each aiwith minR[ai]≤x<maxRk[ai]does:

begin

ailistens;

if aireceived key then

(* comparison for stable ranking *)

if (d=0and key[ai]≤key)or(d=1 and key[ai]<key)then

maxRk[ai]←x;

else

minRk[ai]←x+1;

(* cascading computation of indexes *)

k←k;

while k<lg nand idxk[ai]=NIL and minRk[ai]=maxRk[ai]do

idxk+1[ai]←idxk[ai]+minRk[ai];

k←k+1;

end

Algorithm 4. Procedure rank

procedure levelRanking(k, πk)

for l←0to n/(2k+1)−1do

rank(k, l, 1,π

k);

rank(k, l, 0,π

k);

Algorithm 5. Procedure levelRanking

all indexes on levels up to khas been properly computed in sortingq.Then

Pr(Qk)=Pr(Ek)·Pr(Fk)≤Pr(Fk) and, hence, Pr(Q)≤2nqc·lg n.Itiseasy

to verify that c≥min{c|qc·2nlg n≤q}. This completes the proof. !"

Theorem 3. For any input, the expected energy used for listening by any single

station in sortingqis at most lg n·(1 + (c−1)(2/p −2) + (2/p −1)(lg n−1)/2)

+c(n−1)q,wherec=c(q, q,n). The energy used for sending by any single

station is clg n.Timeofsortingqis cn lg n.

Proof. Let the input sequence be arbitrary and let sbe any of the stations.

Let Xbe random variable that is the energy used for listening by s.LetXk

be random variable that is the energy used by sin all clevelRankings on level

k.ThusX=lg n−1

k=0 Xk.LetΩbe the set of all elementary events (i.e. of all

possible computations). Note that E[X]=ω∈ΩX(ω)·Pr(ω), where X(ω)is

Ranking and Sorting in Unreliable Single Hop Radio Network 343

procedure sortingq

init;

Let q=1−p,wherepis probability of successful reception;

for k←0to lg n−1do

repeat c(q, q,n)timeslevelRanking(k, rbok);

Algorithm 6. Procedure sorting

the energy used by sin the computation ωand Pr(ω) is the probability of this

computation. Let the events Q,Ekbe deﬁned as in the proof of Theorem 2. Let

E=Elg n.NotethatΩis a disjoint union of Qand Eand, hence, E[X]=SQ+SE,

where SQ=ω∈Q X(ω)·Pr(ω)andSE=ω∈E X(ω)·Pr(ω).

To estimate SQnote that in the levelRanking on level kthere are only 2k

time slots in which sis allowed to listen. Thus Xk(ω)≤c·2kand X(ω)≤

clg n−1

k=0 2k=c(n−1) and SQ≤c(n−1) ·ω∈Q Pr(ω)≤c(n−1)q(by

Theorem 2).

To estimate SEnote that

SE=

ω∈E

lg n−1



k=0

Xk(ω)·Pr(ω)=

lg n−1



k=0 

ω∈E

Xk(ω)·Pr(ω)

≤

lg n−1



k=0 

ω∈Ek

Xk(ω)·Pr(ω)≤

lg n−1



k=0 

ω∈Ek

Xk(ω)·Pr(ω)

Pr(Ek)=

lg n



k=0

E[Xk|Ek],

where E[Xk|Ek] is expected value of Xkunder the condition Ekthat all indexes

up to level khave been computed. (The ﬁrst inequality above follows from E⊆

Ek, and the second one follows from Pr(Ek)≤1.) Under the condition Ekthe

expected energy used for listening by sduring the ﬁrst levelRanking on level k

is at most 1 + k(2/p −1) (by Lemma 3). By Lemma 2, the expected value of

∆=maxRk[s]−minRk[s]aftertheﬁrstlevelRanking on level kis 2/p −2. During

each of the remaining c−1levelRankings on level kstation scan listen to at

most ∆stations, thus the expected listening energy for these levelRankings can be

bounded by (c−1)·(2/p−2). We have E[Xk|Ek]≤1+k(2/p−1)+(c−1)·(2/p−2).

Thus SE≤lg n−1

k=0 (1 + k(2/p −1) + (c−1) ·(2/p −2)) = lg n(1 + (c−1)(2/p −

2)) + (2/p −1)lg n(lg n−1)

The limits on time and sending energy follow from the fact that each station

broadcasts only once in each levelRanking.!"

Corollary 1. Algorithm sorting1/n sorts any input with probability at least 1−

nin time O(nlg2n)and, for each station s, the expected energy used by sis

O(lg2n).

Acknowledgments

Thanks to Maciej G¸ebala for helpful comments.

344 M. Kik

References

1. Ajtai, M., Koml´os, J., Szemer´edi, E.: Sorting in clog nparallel steps. Combinator-

ica 3, 1–19 (1983)

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Single-Hop Radio Networks. IEEE Trans. Parallel Distrib. Syst. 15, 331–338 (2004)

3. G¸ebala, M., Kik, M.: Counting-Sort and Routing in a Single Hop Radio Network.

In: Kutylowski, M., Cicho´n, J., Kubiak, P. (eds.) ALGOSENSORS 2007. LNCS,

vol. 4837, pp. 138–149. Springer, Heidelberg (2008)

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Stuller, J. (eds.) SOFSEM 2006. LNCS,

vol. 3831, pp. 341–349. Springer, Heidelberg (2006)

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Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 573–583. Springer, Heidel-

berg (2006)

6. Nakano, K.: An Optimal Randomized Ranking Algorithm on the k-channel Broad-

cast Communication Model. In: ICPP 2002, pp. 493–500 (2002)

7. Nakano, K., Olariu, S., Zomaya, A.Y.: Energy-Eﬃcient Permutation Routing in

Radio Networks. IEEE Transactions on Parallel and Distributed Systems 12, 544–

557 (2001)

8. Nakano, K., Olariu, S., Zomaya, A.Y.: Energy-Eﬃcient Routing in the Broadcast

Communication Model. IEEE Trans. Parallel Distrib. Syst. 13, 1201–1210 (2002)

9. Singh, M., Prasanna, V.K.: Optimal Energy Balanced Algorithm for Selection in

Single Hop Sensor Network. SNPA ICC (May 2003)

10. Singh, M., Prasanna, V.K.: Energy-Optimal and Energy-Balanced Sorting in a

Single-Hop Sensor Network. PERCOM (March 2003)

Distributed Monitoring in Ad Hoc Networks:

Conformance and Security Checking

Wissam Mallouli, Bachar Wehbi, andAnaCavalli

Institut Telecom/Telecom SudParis, CNRS/SAMOVAR

{wissam.mallouli,bachar.wehbi,ana.cavalli}@it-sudparis.eu

Abstract. Ad hoc networks are exposed more than traditional net-

works to security threats due to their mobility and open architecture

aspects. In addition, any dysfunction due to badly conﬁgured nodes

can severely aﬀect the network as all nodes participate in the routing

task. For these reasons, it is important to check the validity of ad hoc

protocols, to verify whether the running implementation is conform

to its speciﬁcation and to detect security ﬂows in the network. In this

paper, we propose a formal methodology to collect and analyze the

network traﬃc trace. Observers running on a set of nodes collect local

traces and send them later to a global observer that correlates them into

a global trace thanks to an adapted time synchronization mechanism

running in the network. The global trace is then analyzed to study the

conformance and the security of the running routing protocol. This

analysis is performed using dedicated algorithms that check the collected

trace against a set of functional and security properties speciﬁed in an

adapted formal language.

Keywords: Ad Hoc Networks, Monitoring, Trace Collection and Corre-

lation, Conformance Testing, Security Analysis, Nomad Logic.

1 Introduction

Mobileadhocnetworks (MANET) are infrastructureless networks composed of

asetofwireless mobilenodes.Nodes sendpacketsdirectly todestinationsthat

are in theircoverage zone.Whendestinations are farther thanthe coverage range

intermediate nodes cooperate toestablish the communication path.Thisopen

andcooperativenetwork aspect andthelimited resources ofmobilenodes make

itdiﬃculttodeﬁneaneﬃcienttestingmethodologytovalidate the conformance

ofexistingroutingprotocols(like AODV [11], OLSR[6] orDYMO[5] etc.) and

toguarantee the respect ofpredeﬁned securityproperties.

Formaltestingallowstoinsure the respect ofthefunctionalbehaviorand

the securityrequirements ofasystem;itcanbe either activeorpassive.Active

testingpermits tovalidate a system implementation byapplyingasetoftest

cases andanalyzingthesystem reaction. Itimplies that wehaveaglobalcontrol

on the network architecture which isdiﬃculttoperform in adynamictopology

such as ad hocnetworks.Besides,the activetestingbecomes diﬃculttoperform

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 345–356, 2008.

Springer-Verlag Berlin Heidelberg 2008

346 W. Mallouli, B. Wehbi, and A. Cavalli

whenthe network isbuiltfromcomponents (nodes)that are runningin their

realenvironmentandcannotbeinterrupted ordisturbed.Inthissituation, there

isaparticular interest in usingmonitoringtechniques that consist in testing

passively duringtheruntime the traﬃc ﬂow in adeployed network.Thistesting

consists in analyzingcollected data accordingtosome functionaland security

requirements described in aformallanguage.

In thispaper,weusemonitoringtocollect distributed traces usinglocalob-

servers (called alsoprobes)without interferingwith the network under test.Two

type ofnetworks are considered.The ﬁrst consists ofacontrolled area where a

set ofdedicated probes isinstalled tomonitorthenetwork.Whilethesecond

isanopenarea network where the nodes perform themselves the trace collec-

tion task.Inboth cases,the localtraces are senttoaglobalobserver which

isresponsiblefor the traces correlation andanalysistasks.The correlation is

performed based on anaccurate time synchronization protocol [14]designed for

ad hocnetworks.Thisprotocol followsthereceiver t o receiver mechanism that

eliminates the majorsources ofsynchronization inaccuracy. Whereas,the anal-

ysisconsists ofcheckingwhether the trace isconform toasetoffunctionaland

securityproperties that we describe in aformallanguage adapted todistributed

communicatingsystems.Thischeckingisperf

ormed usingasetof appropriate

algorithms that wedeveloped forthisend.Once a propertyviolation is detected,

weidentifythe irregular node(s)behindit.Our mechanism allowstospotdis-

tantattacksthatcanonlybe discovered bythe analysisoftheglobaltrace.Mo

precisely, the main contributionsofthis paper are:

1. Deﬁnition ofaprecise methodtocollect distributed traces tocover the whole

network.The collection methodologydiﬀers dependingon the network na-

ture (controlled oropenareas).

2.Deﬁnition ofamethodforc

orrelatinglocaltraces toobtain aglobalnetwork

trace.Thiscorrelation rely on anadapted time synchronization mechanism

foradhocnetworks that permits tosynchronize all the localobservers.

3. Analysisofthisglobaltrace usingspeciﬁc algorithms tostudythe confor-

mance and the securityrequirements oftheconsidered routingprotocol. The

proposed algorithms allow tocheck a set offunctionaland securityproperties

speciﬁed in Nomad formallanguage [7]onthe collected trace.

4.Demonstration ofthereliabilityofour approach byapplyingiton diﬀerent

ad hocnetwork scenariosrunningOLSRroutingprotocol todetect recurrent

failures and attacks.

The remainder ofthispaperisorganized as follows.Insection 2,wediscuss the

related work tacklingwith monitoringin ad hocnetworks.Section 3 presents the

distributed collection oftheadhocnetwork traﬃc in acaseofcontrolled network

andanopenarea network.Insection 4,weexpose the approach tocorrelate

the localtraces in order toobtain the globalnetwork trace.Section 5 presents

the methodologytoanalyze thisglobaltrace bycomparingittothe functional

and securityrequirements described in Nomad formallanguage.Insection 6 we

apply our methodologyonOLSRroutingprotocol andtheconclusion idgiven

in section 7.

Distributed Monitoring in Ad Hoc Networks 347

2 Related Work

Many papers [12,3,13,1] tried totacklemonitoringmethodologies in ad hocnet-

works.In[13]the authors presentDAMON, adistributed system formonitoring

multihopmobilenetworks.DAMONuses agents tocollect the network traﬃc

andsends collected measurements todata repositories.Itwas implemented in

anAODV basedadhocnetwork.WiPal[1]isamergingtool dedicated toIEEE

802.11 traces manipulation which enables mergingmultiplewireless traces into

aunique globalone.Although DAMONandWiPalcollect the network trace,

theyprovide no process forits analysis.

The authors in [9] propose anintrusion detection scheme based on Extended

Finite State Machines (EFSM) [8]. Indeed,theyprovide a formalmodelofthe

correct behavioroftheroutingprotocol and detect speciﬁc deviationsofthe

routingpr

otocol implementation usingabackward checkingalgorithm [2]. This

work canonlydetect localattacks that violate the EFSM modelofOLSRpro-

tocol (which isnotthecaseofabigrange of attacks).

The authors in [10] make use ofacombination ofdeonticandtemporallogic

tospecifythe correct behaviorofanode andtoexpress complexsecuritypro-

perties.Theyinvestigate diﬀerent attacks targetingthelinksensingmechanism

ofroutingprotocolsand describe securitypolicies topreventthem.Contrary

toour methodology, thiswork considers only the localtraﬃc trace ofagiven

node.Itdoes notallow todetect remote anddistributed attacks.Moreover,it

canonlydiscover the existence ofanincoherence in the collected traﬃc with-

out determiningthemalicious node.Inthispaperwepropose a diﬀerentformal

end-to-endmethodologytocollect andanalyze globalad hocnetwork traﬃc.

3 Distributed Traﬃc Collection in Ad Hoc Networks

Network monitoringisaninteresting approach that allowstocollect the required

information in order toanalyze the behaviorofthenetwork.Monitoringin ad

hocnetworks canbe local with respect toanode orglobal with respect tothe

network.Inad hocnetworks,localmonitoringisnotsuﬃcienttodetect some

types oferrors and securityanomalies [12,9]. Forthisreason weadopt in this

paper the globalmonitoring approach based on adistributed monitoring.

Controlled Area Network: In thistype ofnetwork,nodes moveinside a

deﬁned limited area.Therefore,itispossibletoplace a set ofwireless observers

responsibleforcapturingtransited packets.These observers are placed tocover

the wholenetwork area.Theycollect the communication traces andsendthem

tothe globalobserver in the network.The choice ofthisnode (globalobserver)

canbe based on administrative preferences.The broadcast nature ofthewireless

medium combined with the interferences problems representaclassicalproblem

in the monitoringofadhocnetworks.That’swhywechose toinstall the observers

in such a waytheycover each zoneportion twice ormore.The advantage of

thismethodisthecollection ofrealnetwork traﬃc (attackers cannotalter the

collected traces).

348 W. Mallouli, B. Wehbi, and A. Cavalli

Open Area Network: In the case ofanopenarea network,the observers are the

network nodes themselves.Theyperform a collaborativeobservation action. Each

network node collects its localtraﬃc trace andsends ittothe globalobserver.

We assume here that all the nodes havethecollectorprogram runningon their

systems.Astheobservers are the network nodes,itispossibleforanode (attacker)

toalter its collected trace.The traﬃc analyzer moduleon the globalobserver must

take thispropertyinconsideration. Thisisthemajordiﬀerence with the limited

area network where the collect ismadebydedicated observers.

4 Traces Correlation Mechanism

The globalobserver receives the localtraces collected bythe localobservers

in order toanalyze them.The ﬁrst step toward performingthisanalysisisto

correlate the traces andorder them chronologically. Weuseareceiver to receiver

network wide synchronization mechanism that wedesigned forwireless multihop

networks.Usingthismechanism all the nodes in the network runwith the same

clock value allowingthustoperform the trace correlation. In the followingwe

brieﬂy describe the synchronization mechanism in section 4.1 andthendescribe

the correlation procedure in section 4.2.

4.1 Synchronization Mechanism Overview

The objectiveofthetime synchronization mechanism istosupport each network

node with the required timinginformation in order tobuildanadjustmentfunc-

tion that transforms its localclock value tothat of the reference node existingin

the network.Usingtheadjustmentfunctionstheycalculated,nodes,all over the

network,runwith similar clock values achievingtherefore network wide synchro-

nization. The mechanism isbasedon receiver to receiver synchronization which

bydeﬁnition eliminates the majorsources ofsynchronization inaccuracy(send

time and access time). The mechanism consists oftwo complementaryparts;

the sender nodes selection andthesynchronization process.First,ahierarchy

ofsender nodes isconstructed in order toguide the synchronization process

in amultihopenvironment.Sender nodes are responsiblefortransmittingref-

erence messages.Areference message does notcontain anexplicittimestamp;

instead,receivers use its arrivaltime tocompare theirclocks.Usinginformation

exchanged trough reference messages,each node constructs a tablethatcontains

for each received reference message the mappingbetweenits localreception time

andthatof the reference node (oranalreadysynchronized node). Thenthe node

performs least squares linear regression toestimate the best ﬁt linerelatingthe

node’sclock tothe reference node’sclock.The estimated best ﬁt lineisanad-

justmentfunction that transforms the client’slocalclock value tothat ofthe

reference node.Thisadjustmentfunction isgivenbyequation 1 below:

Tsynch =(1+ ,

F)×Tlocal +-

Off (1)

Where ,

Fand-

Off are the estimated frequencyerrorandoﬀset parame-

ters respectively. The synchronization processusestime information exchanged

Distributed Monitoring in Ad Hoc Networks 349

through reference messages toachieveﬁrstaninitialestimate ofthenode’sad-

justmentfunction. Then, byobservingtheoﬀset estimate variationonlonger

time period,itimproves the frequencyerrorestimation andtherefore the time

synchronization accuracy. Detailsabout the synchronization mechanism canbe

foundin [14].

4.2 Global Trace Construction

Usingthesynchronization mechanism,network nodes runinphase with the ref-

erence clock value.Thisnetwork virtualclock will assist the globalobserver in

correlatingthediﬀerentlocaltraces received fromthesetofobservers.In[14]

weshowed that in amultihopnetwork the precision Pofthesynchronization

mechanism isin the order offewmicroseconds (maximum of5µsec fornodes

at 5hops awayofthetime reference)which isbyfar less thanthe time diﬀer-

ence betweentwo message transmissions(aminimum of100µsec)andthetime

diﬀerence betweenthe transmission time of a message andits reception time at

aneighbornode (higher than20µsec). Accordingtothis accurate precision the

followingproperties are alwayssatisﬁed:

–Iftwo nodes,N1andN2,inthe same broadcast region, sendtwo diﬀerent

messages M1thenM2atlocaltimes t1andt2;thent1¡t2.

–Ifanode sends a message at localtime t1, a receiver receives the message

at localtime t2where t1¡t2.

–Iftwo messages M1andM2arecollected at localtimes t1andt2where

|t1−t2|<P theneither M1 andM2 are the same message orM1andM2

are independent(i.e.theyare transmitted in two diﬀerentbroadcast zones).

5 Monitoring Methodology

5.1 Functional and Security Properties Formal Speciﬁcation

Wespecifyasetofproperties that the network nodes havetorespect using

Nomad formallanguage which allowstoexpress privileges on non atomicactions.

Itcombines deonticandtemporallogics andcandescribe conditionalprivileges

andobligationswith deadlines.Itcanalsoformally analyze how privileges on

non atomicactionscanbe decomposed intomore basicprivileges on elementary

actions.More detailsabout Nomad syntaxandsemantics are presented in [7].

Deﬁnition 1. Atomic action

We deﬁne an atomic action as the emission or the reception of a message between

two nodes using the following syntax:

Node1?or! Msg(Par1,Par2,...,Parn)Node

where Node1andNode2representthesource or the destination ofthemes-

sage.’?’and’!’ deﬁne a reception andanemission of a message byNode1.

Msg(Par1,Par2,...,Parn)represents the message exchanged betweenNode1and

Node2with its parameters.Node1,Node2,Msg,andParicanbe replaced bythe

symbol ∗torepresentany node,any message orany parameter.

350 W. Mallouli, B. Wehbi, and A. Cavalli

Deﬁnition 2. Non-atomic action

If αand βare actions, then (α;β), which means ”αis followed immediately by

β”and (α;∗;β), which means ” αis followed by β” are non-atomic actions.

Deﬁnition 3. Formulae

If αis an action then start(α)(action αis being started) and done(α)(action

αis done) are formulae.

Some properties on actionsandformulae:

–IfAandBare formulae then(A∧B)and(A∨B)are formulae.

–IfAisaformulathen¬A,⊕A(”Nextin the trace,” Aistrue), %A(”previ-

ously in the trace,Aistrue”) are formulae.

–IfAisaformulathenO≤dA(”dunits oftime ago, Awas true ifd<0, orin

the nextdunits oftime,Awill be true ifd>0”)isaformula.

–(A|C)isaformula:‘Inthe contextCtheformulaAistrue’.

Deﬁnition 4. Deontic modalities

If A is a formula then modality O( ”A” is mandatory), F( ”A” is forbidden)

and P( ”A” is permitted) are formulae.

5.2 Trace Analysis Approach

To runthe distributed monitoringprocess,the globalobserver needs two diﬀerent

input ﬁles:the traces ﬁles collected bythe localobservers and the properties ﬁle

where are speciﬁed expected functionaland securityproperties.

First,the globalobserver veriﬁes through a syntaxcheckingmodule that the

desired behavioriswell speciﬁed accordingtothe Nomad format.Thisavoids

syntax-related bugs in the test enginemodule.

Second,the collected traces ﬁles havetobe analyzed usingapre-processing

modulethatperforms the followingtasks:(i)ﬁltering the traces ﬁles keepingonly

the relevantinformation for the protocol(s)under test.The basicidea istokeep

in the traces only the messages and parameters correspondingtothe speciﬁed

properties tocheck. (ii) correlation of the traces ﬁles andtheconstruction ofa

unique globaltrace ﬁle. (iii) parsingtheglobaltrace andcreating a trace table

Fig. 1. Monitoring Architecture

Distributed Monitoring in Ad Hoc Networks 351

which constitutes the target ofthe‘Test Engine’modulequeries.Each lineof

the trace tablecorresponds toanemission or a reception of a message in the

network.

Finally, the trace analysisisperformed usingthreealgorithms accordingto

the propertytype:permission, prohibition orobligation. These three algorithms

are based on the same concept:each linein the trace tablecancorrespondto

(i.e.canbe aninstantiation of)oneormany atomicactions described in oneor

many properties.

5.3 Properties Checking Algorithms

In this section we describe the generalidea of the properties checkingalgorithms

andprovide in particular the overviewofthealgorithm verifying the prohibition

properties on anetwork traﬃc trace.

Prohibitions Handler: The algorithm that allowscheckingprohibition pro-

perties beginsﬁrstbyparsing the trace table(buildfromthetraceﬁle) lineby

linetocheck ifany contextofany prohibition propertyisveriﬁed.Foreachline

L,itveriﬁes ifLisaninstantiation ofanaction Adescribed in the contextof

the prohibition propertyPr.Ifitisthecase,itchecksif the the chronological

order oftheactions described in thisc

ontextisveriﬁed (using the procedure

Check Context), thenitcandeduce ifthewholecontextisveriﬁed ornot.Ifthe

contextisveriﬁed,the algorithm has toensure that the action described in the

ﬁrst part of the prohibition rule(the prohibited action) isnotpresentin the trace.

Ifitﬁnds such action (usingCheck Prohibited Activity procedure), the verdict is

FAI L . Otherwise,itconcludes that the currentruleisveriﬁed,the verdict in this

case is: PASS. Ifthetracelength isnotlongenough toensure the veriﬁcation, the

output verdict isINCONCLUSIVE.The algorithm 1presents the pseudo-code

of the procedure used tocheck the prohibition properties on atraceand deduce

the appropriate verdict.ForeachpropertyPr ,wedeﬁne‘Pr.action’ as the pro-

hibited action of the propertyand‘Pr.context’as the contextof the property.

‘Pr.action’ (respectively ‘Pr.context’) iscomposed ofoneormany chronologi-

cally ordered actions‘Pr.act.actioni’(respectively ‘Pr.context.actionj’) where i

(respectively j)isthenumber ofatomicactionsin the prohibited action (respec-

tively context).

Permissions Handler: The permission toperform anaction in aparticular

contextdoes notmeanthat action must be systematically executed whenthis

contextisveriﬁed.Inthe case ofcheckingpermission properties,weﬁrstlookin

the traces ﬁle(the trace table)ifthepermitted activityexists;then, weensure

that the contextwas true toconclude that the propertyis respected (verdict

PASS), otherwise the verdict isFAI L . I fthetraceisnotlongenough tocheck

the context,the verdict isINCONCLUSIVE.

Obligations Handler: Forobligation properties the approach isverysimilar to

that used fortestingprohibition properties.Westartﬁrstbycheckingwhether

352 W. Mallouli, B. Wehbi, and A. Cavalli

Algorithm 1. Prohibition Properties Handler

Require: PPS[Pr] : Prohibition Properties Set + Tr[l] : the trace table.

1: for each property Pr of PPS do

2: Context(Pr) = ‘not veriﬁed’

3: end for

4: for each line lof Tr do

5: for each property Pr of PPS do

6: if (Context(Pr)=‘veriﬁed’) then

7: verdict[Pr] := INCONCLUSIVE

8: if (Prohibition deadline Reached) then

9: verdict[Pr] := PASS

10: Context(Pr)=‘not veriﬁed’

11: else

12: if (l=instantiation(Pr.act.actioni)) then

13: verdict [Pr] := Check Prohibited Action (Pr.action)

14: if (verdict [Pr] := ‘FAIL’) then

15: Memorize error and position in the trace

16: Context(Pr)=‘not veriﬁed’

17: else

18: Memorize veriﬁed parts of the prohibited activity /* (in this case

verdict [Pr] := ‘INCONCLUSIVE’) */

19: end if

20: end if

21: end if

22: end if

23: if (l=instantiation(Pr.context.actioni)) then

24: Context(Pr) = Check Context(Pr.context)

25: if (Context(Pr) = ‘veriﬁed’) then

26: Calculate prohibition deadline

27: else

28: if (Context(Pr) = ‘not yet veriﬁed’) then

29: Memorize veriﬁed parts of the context

/* (Context (Pr) = ‘not yet veriﬁed’ if some actions of the context are

veriﬁed and are in the right chronological order. But the whole context

is not yet veriﬁed. We have to check next messages in the trace, to

deduce if the tested system is in the right context or not.) */

30: else

31: Erase memorized parts of the context if exist

/* (This is case when the context is no more veriﬁed) */

32: end if

33: end if

34: end if

35: end for

36: end for

the contextof the propertyisveriﬁed.Then, wecheckiftheaction speciﬁed in

the ﬁrst part of the property(mandatoryaction) ispresentin trace.Ifitisthe

case,the verdict isPASS o therwise itisFA IL . Ifthetraceisnotlongenough,

the verdict isINCONCLUSIVE.

Distributed Monitoring in Ad Hoc Networks 353

5.4 Irregular Node Determination

Once a propertyviolation is detected,the monitorhastoanalyze the source

oftheviolationinorder todeduce the irregular node.The methodologyofthis

determination isthefollowing:

–Identiﬁcation ofthecorresponding trace section: aviolation isin generaldue

tosome messages in the globaltrace that does not respect a givenproperty.

–Identiﬁcation ofthenodes implicated in a detected violation: in the case of

a message reception related violation, the node claiming the reception, the

assumed sender andits neighbors are implicated.Inthe case ofanemission

related violation, the assumed sender node andits neighbors are implicated.

–Identiﬁcation oftheimplicated trace part:goingbackward in the trace from

the position of the message causing the propertyviolation toextract the

messages related tothe nodes implicated in the violation. The number of

extracted messages depends on the studied protocol. In wireless networks,

messages canbe lost because oftheinterference andcollisionsproblem.For

thisreason, ad hocprotocolslike OLSRandAODV wait a certain number

ofperiods before announcingalinkbreak.Inour study, wegobackward in

the trace for a certain period that guarantees the protocol convergence.For

example,OLSRwaits 3periods of2seconds each before announcingalink

break with a neighborfromwhich he has not received Hello messages.To

guarantee that OLSRhasconverged (i.e.the linkbreakisadvertised)wego

backward onemore period;thismeansweextract the messages exchanged

in the last 8 seconds.

–Construction ofcoherentnodes sets:the extracted trace part isanalyzed

todetect coherentandnon coherentnodes within those implicated in the

violation. Wecompare each pairofimplicated nodes todetect iftheyare

coherentornot.The set with the highest number ofnodes isconsidered

as the regular set whereas the remainingset(orsets)contain the irregular

nodes.We assume that the number ofirregular nodes in the network islower

thanthe number ofregular nodes in all the broadcast regions.

6 Case Study: OLSR

Wetestedour methodologyonOLSRadhocroutingprotocol in anopenarea

network.WestartedﬁrstbyextractingfromtheRFCsome OLSRproperties

that we described in Nomad formallanguage.Thenwechanged in NS2the

behaviorofOLSRin order tomodeltypicalattacks against OLSRlike Hello

message poisoning, linkspooﬁngandblack hole attack.We added in NS2a

specialmodulethatallowseachnode tocollect its localnetwork trace.This

modulegives the attacker the possibilitytoalter its localtrace.Astandalone

moduleisalsodeveloped tocorrelate the collected localtraces andanalyze the

obtained globaltrace usingthealgorithms presented in the previous sections.

Werunasimulation with 100 mobilenodes located in atopologyof1500x1500

for1200 seconds.Amongthesenodes,5are attackers and2ofthemcanalter

354 W. Mallouli, B. Wehbi, and A. Cavalli

theirlocaltrace tosimulate collaborative attack.Intotal20diﬀerent attacks

were launched.The simulation provided us the localtraces that the standalone

modulecorrelated andanalyzed.The globaltrace was around5million oflines.

The analysisoftheglobaltrace gave21fail and2inconclusiveverdicts.The

inconclusiveverdicts are due toincomplete execution trace due tomultiplelink

breaks.The 21fail verdicts correspondtothe attacks andonefalse negative due

tonodes mobility. In the next subsections,we emphasize on 2of these attacks:

6.1 Hello Messages Poisoning

Oneof the ﬁrst properties tocheck isthecorrect logicalorder ofHELLO

messages exchange.That isanode cannotannounce a symmetrical linkto

any neighborwithout havingpreviously received a HELLO message claimingan

asymmetriclinkfromthatnode.The connectivityestablishmentprocess must

respect the followingproperties:

–Pr1:F(start (n?Hello(n:Asym)I)—O≤2sec¬done(n!Hello()∗))

–Pr2:F(start (n?Hello(n:Sym)I)—

O≤2sec (¬done(n!Hello(I:Asym)∗)∧¬done(n!Hello(I:Sym)∗)))

–Pr3:F(start (n?Hello(n:MPR)I)—O≤2sec ¬done(n!Hello(I:Sym)∗))

In ﬁgure 2,node Isends a Hello message claimingasymmetrical linktonode

Aafter receivinganemptyHello fromit.Inaddition tothisprotocol violation

Imayinsert a fake entryinits trace claiming the reception ofanasymmetrical

Hello message fromA.Inboth cases,our methodologydetected the violation:

1. Ihas notchanged its localtrace:InthiscaseIviolates the propertyPr2.

Wecanconclude that Iisthemalicious node.

2.Ichanged its localtrace byclaiming the reception ofanasymmetricalHello

message fromA.Inthis case the trace violates the propertyPr4which

indicates that a message must havebeenemitted in order foranode to

receiveit.

–Pr4:O(%done (Node1!M(p)Node2)—start (Node2?M(p)Node1))

6.2 Link Spooﬁng with Distant Node

In ﬁgure 2,weillustrate anexampleofalinkspooﬁng attack on OLSR.The

intruder Icaninsert Hello messages claiminganon existingsymmetrical linkto

Fig. 2. A distant Link Spooﬁng Attack on OLSR

Distributed Monitoring in Ad Hoc Networks 355

C.Consequently, the intruder might be selected as a MPRbyAandthetraﬃc

fromAtoCwill be disrupted tothe intruder.Ifweanalyze the globaltraﬃc in

thispartofthenetwork,wenotice oneofthesetwo cases:

1. Node Ihas notchanged its localtrace:Node Icannotclaimasymmetrical

linktoCaccordingtothe protocol speciﬁcation violatingthuspropertyPr2.

Wecanconclude that Iisthemalicious node.

2.Node Ihas changed its localtrace toclaim the reception ofaHello message

MfromCspecifyingasymmetriclink.Here,the trace violates the property

Pr5which indicates that ifanode Creceives a message fromnode N,

all the symmetricneighbors ofN(VS(N)) must have received the same

message.Therefore,wearein a message reception related violation; node I

claiming the reception, the assumed sender Candits neighbors B,Dand

Eare implicated.Wesplitthesenodes intotwo sets {I}and{B,D, E},

the ﬁrst claims the reception oftheHello message fromnode Cwhere this

message does notappearin the traces ofthenodes in the secondset.Wecan

conclude that Iistheirregular node.Wenote again that weareassuming

that the number ofirregular nodes islower thanthat ofregular ones in any

neighborhood.

–Pr5:∀B∈VS(N), O(done (B?M(p)N)—done (C?M(p)N))

Wehighlightherethatthispropertyexpresses a distributed network behavior

that allowstodetect distant attacks.This detection canonlybe made through

checkingtheglobaltrace.

7 Conclusions and Future Work

Thispaperproposes a distributed monitoring approach todetect functionaland

securityﬂowsin ad hocnetworks.Itconsiders two types ofnetworks :anopen

area network andacontrolled area network.Dedicated observers collect the local

network traﬃc in acontrolled area network whereas thiscollection isperformed

bythe nodes themselves in anopenarea network.Inboth cases,the localtraces

are senttoaglobalobserver.Thislatter isresponsibleforthelocaltraces cor-

relation andtheiranalysis.The correlation isperformed based on anaccurate

synchronization mechanism designed foradhocnetworks.

Our analysisrely on two main features :(1)functionaland securityproperties

speciﬁed usinganinstantiation ofNomad model, and(2)acorrelated trace ofthe

network traﬃc.Based on dedicated algorithms,weprovethatour methodology

allowstodetect a large range ofﬂowsanderrors.

As future work,weareinvestigatingseveralapproaches toimprove the passive

testingalgorithms in order toperform onlinemonitoring,possibly byincluding

vulnerabilitycause graphs [4]oftheimplementation under test.Wearealso

studyingthediﬀerent reactions that the network has toperform followinga

propertyviolation detection.

356 W. Mallouli, B. Wehbi, and A. Cavalli

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D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 357–368, 2008.

Improved Distributed Dynamic Power Control for

Wireless Mesh Networks*

Thomas Olwal1,2, Felix Aron2, Barend J. van Wyk2, Yskandar Hamam2,

Ntsibane Ntlatlapa1, and Marcel Odhiambo3

1 Meraka Institute at the CSIR

P.O. Box 395 Pretoria 0001, South Africa

thomas.olwal@gmail.com, nntlatlapa@csir.co.za

2 The French South African Technical Institute in Electronics at the

Tshwane University of Technology

jakajode@gmail.com, vanwykb@gmail.com, hamama@tut.ac.za

3 The University of South Africa

ohangmo@unisa.ac.za

Abstract. One of the main objectives of transmission power control (TPC) in

wireless mesh networks (WMNs) for rural area applications is to guarantee suc-

cessful packet transmission and reception (SPT-R) with low power consump-

tion. However, the SPT-R depends on co-channel multiple access interferences

(MAI) including the effects from hidden terminals. In this paper we investigate

how MAI can be minimized through a MAC-dependent transmission schedul-

ing probability (TSP) model. In what follows, we show how a distributed

scheduling probability model improves the dynamic power control algorithm.

The resulting optimal power control is derived from a network centric objective

function. The analytical results show that transmit power solutions converge to

a unique fixed point. The simulation results show that a high average feasibility

rate, given a coexistence pattern, can be achieved. There is significant average

transmission power savings compared to conventional methods.

Keywords: Energy-constrained mesh nodes, MAC-DDPC algorithm, Trans-

mission scheduling probability, WMNs.

1 Introduction

Wireless Mesh Networks (WMNs) deployed in rural areas suffer from battery power

limitations. However, due to architectural complexities and high capacity require-

ments, conventional power control solutions proposed for cellular, Ad Hoc and sensor

networks may not be alternatives for WMNs [1]. In this work we consider the prob-

lem of power control for energy-constrained distributed mesh nodes (MNs) for rural

community applications [2]. We focus on a distributed transmission power control

(DTPC) policy in which power is adjusted in response to cross-layer feedback

* This work is supported by the Meraka Institute at the Council of Scientific and Industrial

Research (CSIR), Pretoria, South Africa.

358 T. Olwal et al.

information [5]. The DTPC policy allows MNs to setup and maintain stochastic wire-

less links with minimum power while satisfying constraints on the quality of service

(QoS). The benefits of power minimization are not only increased battery life but also

the mitigation of effective multiple access interference (MAI). Consequently,

the overall network capacity can also be increased by allowing higher frequency

reuse [2].

Traditional distributed QoS-based approaches for power control has been re-

searched for an uplink power control problem in cellular systems [3], [6], [15]. How-

ever, most of the approaches are deemed greedy in which transmission power is

adapted by an individual node with sole objective of maintaining QoS target metrics

during a communication session [3], [15]. Though suitable for delay sensitive applica-

tions, such approaches may lead to high energy expenditure. The work in [6] presents

power control policies that address various node-centric and network centric objec-

tives adapting power in either a greedy or an energy efficient manner. However, the

work assumes a special case where all sender nodes communicate to a centralised

base station in a CDMA system. In practice, some nodes may become active or inac-

tive during the course of a frame transmission. Thus, a distributed power control

model for such dynamic behaviour in an Ad Hoc fashion would be necessary.

2 Related Work

Recent research focussed on the application of autonomous power control in infra-

structure-less Ad Hoc networks [12], [7], [13]. Most of these schemes use maximum

transmit power for RTS-CTS and the minimum required transmit power for DATA-

ACK transmissions in order to save energy. The work in [8] presents a power control

MAC protocol that allows nodes to vary transmission power level on a per-packet

basis. Simulation results in [8] show that schemes in [12], [7] can degrade network

throughput [2] and result in higher energy consumption than in the case of no power

control. Furthermore, conventional CSMA/CA systems demonstrate low network

capacity and scalability properties. Such performances are undesirable for large-scale

mesh network deployments [1]. In [9], the authors present a joint scheduling and

power control strategy supporting multicasting traffic. The process of power control

entails the elimination of weak connections while maximizing the number of success-

ful simultaneous transmissions and still achieving minimum total transmit power.

However, the contribution does not guarantee power control solutions for hidden

terminal problems.

Our paper presents a power optimization problem similar to the work by So-

rooshyari and Gajic [6]. However, the authors assumed single hop communications in

CDMA cellular systems. In the context of CSMA/CA protocol, we propose a distrib-

uted transmission scheduling probability (TSP) based power control model. Through

bidirectional information exchange among nodes, we show that that cross-layer power

control model yields several advantages. First, the QoS at the receivers can still be

maintained at low transmission power consumptions when both the channel and mul-

tiple transmission activity (MTA) of the network are known to the power control

system. While the physical (PHY) layer encodes the signalling to overcome the chan-

nel impairments, the MAC protocol provides scheduling disciplines for the MTA in a

Improved Distributed Dynamic Power Control for Wireless Mesh Networks 359

shared channel. Second, the transmission power control based on a clear channel

assessment (CCA) reduces the probability of traffic retransmissions. Retransmissions

result in additional power consumptions and cause excessive network delays. Finally,

the distributed dynamic power control (DDPC) algorithm with the knowledge of the

network topology may improve performance metrics on routing decisions for multiple

hop communications.

The paper is organised as follows: Section 2 presented the related work, while sec-

tion 3 analyses the cross-layer probability model. Section 4 formulates the problem.

In section 5, an adaptive transmission power control algorithm is developed. Section 6

presents and analyses the simulation results. Section 7 concludes the paper.

3 Cross-Layer Probability Model

Basic Formulations and Assumptions: Consider an N stationary mesh nodes

(MNs) network randomly distributed in a space S. Let us assume that each MN is

equipped with omni directional antenna with carrier sensing range (CSR) at least

twice larger than the transmission range (TR) [8]. Thus, the resulting wireless net-

work can be modelled as a graph

()

EVG ,= where V represents a set of nodes in the

network and VVE ×⊆ the edge set which gives the available communications:

()

Eri ∈, if nodei can send messages directly in one hop to node

and vice versa.

Let VVr⊆ and VVi⊆ be the two subsets of nodes whose signal powers can be

perceived by nodes

and i respectively. We have rr NV = and ii NV = nodes,

respectively in the sets r

V and i

V. In practice, the wireless links (channels) between

nodes i and

or among any other nodes are typically subjected to large-scale path

loss, shadowing and possibly small scale multi path fading dynamics [11]. This im-

plies that the time-variant channel gain function can be denoted as

()

kg r

i for any

Vi∈ and any r

Vr ∈. If we consider that a sender node i chooses a transmission

power level

()

kl from a finite set

()

ii ll,......,3,2,1=L, containing i

l power lev-

els then, the actual transmission power value corresponding to the lth power level is

given by

()

klpi, . Consider that the transmission power vector pis constrained as

Vi ∈∀≤≤ maxmin ppp , (1)

where

() () ()

[]

Nklpklpklp ,...,, 21

=p.

Thus, at a receiving node

, the received power due to the transmission from the

sender node iis given by

() () ( )

klpkgkp i

i,= (2)

Scheduling Probability Model: Let us consider the spread-spectrum channel signal-

ling system for the MNs [5]. Such signalling methods provide anti-jamming capabili-

ties, robustness to multi path effects and potential for multi user access through

CDMA techniques. In spread-spectrum systems supported by the IEEE 802.11

360 T. Olwal et al.

standard, DDPC methods are affected by MAI powers at the receiver node [6]. The

MAI powers due to other users’ concurrent transmissions degrade the quality of

transmission and reception. This implies a scheme to schedule multiple transmissions

such that significant mesh network capacity is guaranteed. Let’s consider that in a

distributed MAC protocol and in the context of power control, the sender node desires

to minimize the number of retransmissions of its packets. To achieve this, the node

must perform CCA in order to guarantee successful transmission with low power

consumption. Furthermore, the need for bidirectional channel signalling information

can significantly reduce collisions caused by MAI during transmission attempts.

Thus, the transmission power for each packet from node i must overcome the MAI

level at node

[8]. However, due to channel dynamics and heterogeneity of the wire-

less devices, MAI levels may change during the transmission of the packet and a

model to generalize such change is desirable. The instantaneous interference plus

receiver noise (II+N) at node

as defined by

() ()()()

ijVj jii klpkgkxkq r

+= ∑≠∈

−− ,.,p. (3)

Here, r

denotes the thermal noise power at the receiver node r

Vr ∈, while

()

kx j is

a binomially-distributed random variable that dictates the number of nodes in the set

V and i

V that are transmitting concurrently and whose CSRs the receiver happens to

fall. Let

()

kx j be a binomially-distributed random variable with probability of occur-

rence j

for all .

ir VVj ∪∈ Thus, the binomially-distributed random variable

()

kxj

may be defined as

()

⎩

⎨

⎧

=otherwise

ktimeattransmitsjif

kx j0

1. (4)

The information on the number of MTA must be known by a scheduling and a power

control system. If the number of MTA at node

is rr NV =, then there are exactly

2−

Npossible combinations of MTA in the set r

V excluding the transmitting node

itself at any given time. Sets of such combinations of MTA can be denoted as

{}

2,...,1 −

[13], [10]. Correspondingly, we can define a random variable

()

which indicates the occurrence of a specific combination

()

of independent inter-

ferers, interfering with node i’s transmission at a certain time k. Thus, the probabil-

ity that

()

Φ assumes the value of

()

for the nth combination of independent

interferers can be defined as

()

{}

()

∏∏ ∈∈

−==Φ

in l

φφ

ρρφ

1Pr . (5)

Here, r

of the first product term denotes the compliment of r

in the second prod-

uct term. That is, the first term of the product function is the probability describing

nodes which are not transmitting with sender node i at time k. On the other hand,

the second term refers to the probability of those actively transmitting with node i.

Improved Distributed Dynamic Power Control for Wireless Mesh Networks 361

Considering the definition in eq (5), assuming unicast traffic and dropping the time

index k for simplicity reasons, the probability r

that a channel-assessment packet

transmitted with power

()

lpi by the node i is successfully received at the node

conditioned on certain MAI levels is given as:

{}

ratreceptionpacketsuccessful

iPr=

{}{}

receptpacsucc

φφ

=Φ=Φ= ∑

−

Pr|...Pr

(){ }

.Pr

∑=Φ=

φφ

(6)

Here,

()

denotes the probability of successful packet reception by node

due to

transmission of node i, conditioned on a certain MAI level. The functional form of

()

depends on the specific choice of the PHY-layer aspects such as wireless

channel model, modulation and demodulation schemes, channel coding and the re-

ceiver designs. If we assume that the forward and backward transmissions are inde-

pendent then, the joint probability of successful reception of packets at the nodes i

and

can be given as follows:

{}

successbackwardsuccessforward

i,Pr=

()() { }{ }

in ff

Nr i

φφφφ

=Φ=Φ= ∑∑

−−

PrPr

. (7)

The MAC protocol in place exploits the PHY-layer signalling information in eq (7)

and the interaction among other nodes in the topology to determine adaptive schedul-

ing rules for actual application packet transmissions. This can be done in a way that

minimises the number of unsuccessful transmissions. Such MAC-dependent func-

tional may take the form

()

iii

υξρ

=. In general, this functional is a non-linear model

and related analysis is complex. In linear representation,

()

υζ

can be assumed to

have an nth derivative throughout the interval

[]

1,0 such that the Maclaurin series

expansion is given as

( ) () () ()

()

...00 1

εξ

ξυξυξρ

iiiiii nn +

−

+++== −

−

(8)

where i

υε

≤≤0 . The first order approximation of eq (8) is given by

ii m

υρ

≈ where

()

=m, at .0=

(9)

Here, m is a time-varying proportionality design factor for the linear model in eq (9).

This proportionality factor relates the PHY-layer successful packet reception prob-

ability (PRP) i

with the MAC-dependent TSP, i

at any given time. For design

362 T. Olwal et al.

purposes m, can be chosen to be 1<<m since in Maclaurin expansion series, the

conditional successful PRP 0=

when the number of MTA becomes very large.

4 Problem Formulation

If we consider that each sender node i, desires that it’s SINR QoS degradation and

the aggregate network MAI to be minimal, then a corresponding convex cost function

can be given as in [6]

() ( ) ( )

11 2

1+++= kqkkJ iiiii

ωεω

. (10)

In eq (10), the first term describes the action taken by an individual node in order to

achieve its own target quality of service (QoS). That is, how the received SINR

()

deviates from the SINR threshold i

. On the other hand the second term in eq (10)

describes a network-centric cost function i.e., how the action of the transmitting node

impacts on the other network users. As explained in [6], these terms can be defined

as follows:

() ()

11 +−=+ kk iii

γγε

, where

() ()()

()

−1

11,

1kq

kgklp

i, and from eq (10) (11)

() () ()()

1111 ++++=+ −kgkpkqkq r

iiii . (12)

The expression in eq (12) represents the predicted aggregate interference powers that

impact significantly on any receiving node in the network. The reliability of

()

depends on the simultaneous transmissions within an interference range of each link

as shown in eq (5). However, the value

()

dictates the activity state of the random

variable

()

1+kx j in the next power update step in a manner that network MAI levels

are minimised. Thus, the iterative power control system is given as

( ) () () ( )

kqkkpkp iiii −

+=+

1 , subject to:

()

maxmin 1iii pkpp ≤+≤ . (13)

In this formulation a unique fixed point ∗

pcan be achieved if the adaptive control

gain

()

can be optimum for all Vi ∈ in the network. This optimum point can be

derived from:

() ()

kJk lVli minarg ∈

∗=

. The outline of the derivation follows: If we

substitute the value of

()

1+kpi in eq (11) and eq (12) with the expression in eq (13)

and evaluate the first partial derivative of eq (10) with respect to

()

, and set the

result to zero, we get

()

() () () ()()()

{}

()

iii

iiiii

ikg

kqkpkgkq

γγ

⎟

⎠

⎞

⎜

⎝

⎛+++−−

−−

−

∗

11 23

. (14)

Improved Distributed Dynamic Power Control for Wireless Mesh Networks 363

Here, 0/12 ≥= iii

ωωω

is a non-negative power control strategic-weight. The strate-

gic-weight i

and the MAC-dependent

()

are locally assigned to each node de-

pending on the channel states and traffic applications [6], [10]. Using matrix notations

and considering the MTA of the network we have

()( )()

bpAIp ++=+ kk 1 , (15a)

Subject to:

()()

maxmin 1pppp ≤Γ≅+≤ k. (15b)

Here,

() () () ()

⎥

⎦

⎤

⎢

⎣

⎡

∗∗∗∗

kgkgkgkg

NNNNNNNNN

αααα

...

...............

...

321

21232222212

11131121111

() ()

Vrikgkg r

iir ∈∀= ,,

and

[]

ηαηα

∗∗

=......

Theorem 1. If the optimal gain vector ∗

α is unique then it implies that power update

function

()

pΓhas a unique fixed point at the optimal power vector ∗

Proof by contradiction: Suppose a

α and b

α are two distinct fixed points at a and b

for all

[]

ααα

,...,, 21

=α at the same time. Thus, from eq (15), the following

properties can be defined:

• AIAI +≤+ , (Triangle Inequality)

•

(

)

()

,10 ≤<>+ kgij

T0GαI

• 0b > where 0>

, (non zero)

• 0≠⇒i

α Ni ...,2,1=∀ . (non zero)

•

() ()

ba ff αα ≥ if ba αα ≥, (Monotonicity)

•

() ( )

1>∀>

δδδ

αα ff , (Scalability)

Let us assume that there exists j such that b

αα

< for all j. Correspondingly there

exists 1>

such that ba αα ≥

. Thus, there exists for some j, ba αα =

. The

monotonicity and scalability implies:

()

=α

()

fα

≤. (16)

()

αδδ

=α

()

fα

<. (17)

364 T. Olwal et al.

The result in equations (16) and (17) implies that a and b are two distinct points.

Thus, there can be no more than one solution of ∗

α at the same time. Furthermore if

the wireless channels hold their states in the duration of the power control, then

∗

αcan be unique with exact solution as shown in eq (14). From theorem 1, having

shown that ∗

αis unique then the proof that

()

pΓ has a unique fixed point at ∗

p can

be found in [3]. However, uniqueness of ∗

p does not necessarily imply feasibility of

the power vector

()

pΓ in a contention based and a distributive WMN environment

[9]. In such situations, the TSP aware dynamic power control algorithm becomes

necessary. That is, each sender aware of the TSP may decide whether to transmit at a

certain time using a controlled power in a manner that the aggregate MAI component

of the objective function in eq (10) is minimised. The remaining sender nodes can

then attain feasible power solutions via the execution of transmission power iterations

i.e.,

() ()

...10 pp ≥ if

()

00 >p. Hence, the feasibility implies monotonicity [14].

Lemma 1. If p is a feasible power vector for all nodes, then

()

pΓ is a monotonically

decreasing sequence of feasible power vectors that is lower bounded by the minimum

power and

()

pΓ converges to a unique fixed point ∗

p[14]. Conversely starting from

()

00 =p, then

()

pΓ is a monotonically increasing sequence of power vectors that is

upper bounded by a unique fixed point ∗

The proof is developed in [3] and extended in [9].

5 Adaptive Power Control Algorithm

This study presents a scalable CCA model according to the given MAC protocol at

any time. Based on the bidirectional and reliable feedback information, the DDPC

algorithm is outlined as follows:

1) Each node, say node i, measures its thermal noise i

2) Each node, say node i, draws an independent uniform random variable to se-

lect an initial channel assessment power level. If an integer parameter Q repre-

sents the total number of power levels to which a transmitter can be adjusted in

practice then,

()

⎭

⎬

⎫

⎩

⎨

⎧

=maxmaxmax ,...,

0iiiuniform pp

p. (18)

3) Each node, say node i, measures its direct channel gain to any receiver; say

node

, i.e.,

() ( )

kegkg r

i,= as given in [4], where Ee∈is the link between

node i and node

4) Each link, say link Ee∈, evaluates the MAI predictive procedure proposed

in [4].

Improved Distributed Dynamic Power Control for Wireless Mesh Networks 365

5) Each link, say link Ee∈, computes its time-varying signalling information on

the transmission scheduling probability (TSP), i.e.,

()

as in eq (9).

6) The joint CCA and the adaptive power control algorithm can be given as

()

⎪

⎩

⎪

⎨

⎧

<+<

maxmin

max

min

iii

pkppthenotherwise

pkpthen

. (19)

The advantage of the algorithm is that it provides a correction mechanism to the prob-

lem of greedy algorithms. That is, any node iexperiencing

()

0=k

will go on

power-save mode while causing no interference to actively transmitting node

ir VVj ∪∈ in state

()

1+kx j. Conversely, with

()

1=k

, the sender node ican

transmit with up to maximum power taking advantage of the favourable link condi-

tion. However, due to the inherent interference caused to the network, the network

may become disconnected and the sender igets discouraged in the long run.

Node ithen executes the optimal power iteration procedure discussed in this paper.

6 Simulation Results

For simulations, we used MATLABTM version 7.1. We placed collections of 5 to 50

nodes randomly within a 1000 x 1000 m2 area, i.e., a size big enough to deploy a

multi-hop network. Performance metrics were evaluated by Monte Carlo simulations

for 50 independent runs for each random network configuration (instance). It was

assumed that every node has a maximum transmission power (Pmax) of 500 mW and

a minimum transmission power (Pmin) of 0 mW. The propagation path loss model

exponent and a white Gaussian noise (AWGN) were also assumed to be 4 and

0.001mW respectively.

510 15 20 25 30 35 40 45 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Number of Nodes

Average feasibility rate per network instances

Fe as ibility P robabilty Vs Net wor k Inst anc es

ControlMulticastConnections

AdaptiveControlMAI-Occupancy

ControlUser-Network Centric

ControlMAXInterf

Fig. 1. Feasibility probability versus number of senders

366 T. Olwal et al.

Figure 1 shows an average feasibility rate per network scenario versus number of

admitted sender nodes. The average feasibility rate (feasibility probability) indicates

how many senders can be active simultaneously in a specific area without causing

MAI significantly i.e., a case when the power vector

()

pΓ converges to a unique

fixed solution ∗

p. Infeasibility implies that no successful transmission can be ob-

tained and the transmission power vector

()

pΓ does not convergence to ∗

pin the

long run. As shown in Fig. 1 the feasibility probability drops sharply as the number of

simultaneous active senders increases. However, the TSP based DDPC algorithm

(Adaptive Control MAI-Occupancy) can accommodate slightly more nodes than some

recently proposed algorithms [9], [6]. This is significant in improving the WMN

capacity.

Figure 2 shows the simulation result for a non-zero TSP ( 10≤< i

) incorporated

in a greedy and energy-efficient DDPC method. In Fig. 2, sender 4 at the beginning

of simulation adjusts its transmission power to a value minimum enough to achieve

the target SINR threshold in the steady state. At later time, say after 38 seconds,

sender 4 chooses to opt-out of the network participation in response to unfavourable

channel conditions. Sender 1 chooses to stay active in the network throughout the

power control convergence and continue to achieve the target QoS. The rest of the

users remain inactive throughout the power control convergence and the transmis-

sion of a packet.

010 20 30 40 50

0.005

0.01

0.015

Time(s)

Shedu le Rate -Trxt Po wer (W)

= [4,5,6,7,8],

= optimal,

=[100,0] ,

(i)= [0,1]

Trxt 1

Trxt 2

Trxt 3

Trxt 4

Trxt 5

010 20 30 40 50

Time (s)

SINR (Linear-Scale)

= [4,5,6,7,8],

= optimal,

=[100,0] ,

(i)= [0,1]

Trxt 1

Trxt 2

Trxt 3

Trxt 4

Trxt 5

Fig. 2. Scheduled Joint greedy and energy- efficient method

In Fig. 3 a comparative performance of the average transmission power after con-

vergence is shown. The simulation result reveals that the average transmission powers

drops exponentially as the number of allowable senders increases. However, the pro-

posed MAC-DDPC algorithm indicates much more power savings than some conven-

tional methods [9] [6].

Improved Distributed Dynamic Power Control for Wireless Mesh Networks 367

0 5 10 15 20 25 30 35

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Allow able Senders

Average Pow er in (0.1*Watts)

Average Transmit Power Vs Simultaneous No. Senders

Sorooshyari-Gajic DPC

I-MAC-DDPC

Wan g-DJ SPC method

Fig. 3. Average Transmission Powers after steady state

7 Conclusion

In this paper it was shown that if TSP information is known to the power control

system, improved performance of the DDPC algorithm is observed. As revealed in

Fig. 1, MTA can be achieved with TSP model. More average transmission power

savings than in cases of some conventional methods were noted in Fig. 3. Thus, the

information exchange between the PHY and the MAC-layers can be exploited to

improve the conventional power control methods. As future work, we intend to inves-

tigate the effect of MAC-DDPC on throughput performance [1].

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D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 369–379, 2008.

Identifying the Boundary of a Wireless Sensor Network

with a Mobile Sink

Majid I. Khan1, Wilfried N. Gansterer1,2, and Günter Haring1

1 Department of Distributed and Multimedia System, University of Vienna, Austria

majid@ani.univie.ac.at, guenter.haring@univie.ac.at

2 Research Lab Computational Technologies and Applications, University of Vienna, Austria

wilfried.gansterer@univie.ac.at

Abstract. This paper summarizes an effort to evaluate the usability of a mobile

sink for identifying the boundary of a wireless sensor network. In order to

achieve the desired task we transform the problem of boundary identification

into one of edge node identification. The algorithm designed is based on a mo-

bile sink equipped with a directional antenna, which identifies the edge nodes

and connects them to complete the boundary of the sensor field. The proposed

scheme has following distinct features. Firstly, it is independent of the sensor

node deployment, and therefore can be used for fields having very low node

density. Secondly, it does not require sensor field flooding which helps preserv-

ing the nodes’ energy. Thirdly, it works with low cost sensor nodes, i.e., it does

not impose any special requirements on the hardware of individual sensor nodes

(no GPS, no special antennas, etc.), which makes it cost effective.

Keywords: Boundary identification, mobile sink, directional antenna.

1 Introduction

Environmental/habitat monitoring, war field surveillance and monitoring volcanic

eruptions are some application examples for wireless sensor networks which usually

require ad-hoc deployment of the sensor nodes. Such deployments make it impossible

to preprogram nodes with information like routing tables, boundary of the field,

neighbor density, etc. This paper addresses the problem of boundary identification of

a wireless sensor network. Nowak et al. state two fundamental limitations in the

boundary identification process, spatial density of the nodes that can seriously affect

the accuracy of the boundary estimation scheme, and energy constraints of the nodes

which can limit the complexity of the boundary identification algorithm [1]. On the

other hand, it has been observed that the state of the art [2, 3] imposes strong assump-

tion regarding node placement, spatial density and communication model of the nodes

which are very hard to assure during random deployment of the sensor nodes. More-

over, in large scale sensor networks budget constraints is another important factor to

be considered during the development of a boundary identification scheme. Thus,

schemes having assumptions, like each node being equipped with a GPS for position

370 M.I. Khan, W.N. Gansterer, and G. Haring

estimation [7], or each node being equipped with a directional antenna [4], are not

appropriate for the type of sensor field under consideration.

Our major focus in this paper is to reduce the overall deployment cost of the net-

work by using very cheap sensor nodes as well as to increase the lifetime of the sen-

sor network by avoiding message flooding.

It has been recognized that the use of mobile sink in wireless sensor networks is

growing at a very fast rate because of its advantages in terms of increased lifetime of

the network [5], cost effective sensor field localization [14], etc. In this paper, we

show how to use a mobile sink equipped with directional antenna as a tool for the

boundary identification of a sensor network. In order to achieve the desired task we

transform the problem of boundary identification into one of the edge node identifica-

tion, where the sink identifies an edge node, moves to it and then determines the next

edge node. The process continues until the sink completely identifies the boundary of

the sensor field. One very common objection against application of a mobile sink is

that for some types of terrain it is difficult for a sink to move around. However, ad-

vancements in robotics have resulted in the production of machines which can move

in difficult terrains. For example, a DARPA funded research project named BigDog

develops a machine that is mobile even in harsh terrain, can move at 4 miles per hour

and can climb slopes up to 35 degrees [15].

The rest of this paper is organized as follows: Section 2 discusses related work,

Section 3 outlines the basic setup, Section 4 presents the boundary identification

scheme, Section 5 is discussion and analysis, and Section 6 concludes the paper.

2 Related Work

This section presents few state of the art methodologies for the boundary identifica-

tion of a wireless sensor network.

Wang et al. [3] divides the existing methods in the area of boundary identification

of wireless sensor networks into three classes, depending on the techniques used.

Geometric methods are based on the assumption that every node knows its position

coordinates. Statistical methods utilize the probability distribution of the deployed

sensor nodes and identify the boundary nodes on the basis of average neighbor den-

sity. Topological methods make use of sensor field flooding for boundary identifica-

tion. In [3] they have also proposed a flooding-based algorithm that determines the

edge nodes in a sensor field. It is based on the observation that holes in the sensor

field create irregularities in the hop count distances which helps identifying cuts in the

sensor field. These cuts are then utilized to determine the boundary of the sensor field.

Kröller et al. [2] presented an algorithm that is based on a distributed flower struc-

ture for edge node detection; it also identifies the natural geometric clusters in the

sensor field.

Zhang et al. [4] presented a neighbor embracing polygon (NEP) based algorithm

where each node only requires the direction information of the neighboring nodes to

create a convex hull of its neighbors. If the node which created the convex hull is

located outside the convex hull boundary then it is an edge node and vice versa.

Identifying the Boundary of a Wireless Sensor Network with a Mobile Sink 371

Fekete et al. [6] worked on identifying the edge nodes based on the fact that nodes

located close to the center of the sensor field have higher centrality than nodes located

near the boundary, provided that nodes follow a suitable random distribution.

Prerequisite in Zeinalipour-Yazti et al.’s [7] algorithm is that each node knows its

own position coordinates along with the neighboring nodes. Then the node having

minimum y coordinates in the sensor field is determined and marked as starting pe-

rimeter node which then selects the neighboring perimeter node by measuring the

polar angles of all the neighboring nodes on its x-axis. The line obtained by connect-

ing identified edge nodes is the boundary of the field.

Discussion shows that all existing techniques impose one or more of the following

conditions on the sensor field: sufficient node density, special hardware requirements,

or intensive communication requirements. The boundary detection scheme proposed

in this paper operates with low-cost sensor nodes and significantly reduces the com-

munication requirements amongst the nodes.

3 Preliminaries

This section summarizes the basic assumptions underlying the paper.

It is assumed that we have to monitor a highly polluted site, for example, contain-

ing toxic or radioactive materials. However the terrain of the area is assumed to be

suitable for sink mobility. Deployment of the nodes is performed by dropping them

from an airplane or cannon fire which leads to uniform random distribution of the

nodes as shown in Figure 1. Deployed nodes are static and inexpensive having omni-

directional antennas with the same fixed transmission range which is very small com-

pared to the size of the sensor field. Each node is equipped with limited power supply

that cannot be recharged or replaced, and thus nodes are programmed to operate at 1%

duty cycle. Moreover, it is assumed that the nodes have no knowledge of their posi-

tion coordinates in the field.

Each node in the sensor field acquires a “valid” or “invalid” status. The validity of

a sensor node is determined by the number of its neighboring nodes. A node x is

called neighbor of node y if x lies within the transmission range of y. It is assumed

that the sensor field contains only one cluster of valid sensor nodes and other nodes

located outside this cluster are invalid nodes (see Figure 1).

The sink is a special node which is mobile and equipped with an unlimited energy

resource, a GPS and a compass that are used to determine its position and direction of

mobility. Moreover, the sink is also equipped with a sectored directional antenna

having fixed transmission range equal to that of the sensor node. It can be used to

determine the angle of arrival (AOA) of a message from a sensor node [8] and to

roughly estimate the distance between a node and the sink using RSSI [9] based dis-

tance measurement.

The sink knows the area of interest (AOI). The AOI is a rectangular region which

contains all the deployed sensor nodes. Assumption regarding AOI does not affect the

generality of our algorithm as it is only used to locate the sensor field by the sink

(discussed in Section 4.1). In the following, some terminology frequently used in this

paper is defined.

372 M.I. Khan, W.N. Gansterer, and G. Haring

The boundary of a sensor field is a subset of valid sensor nodes with the property

that the line obtain by connecting each node in this subset with its neighboring edge

node “encloses” all the other valid sensor nodes as shown in Figure 1.

Edge Nodes are valid sensor nodes that are connected to obtain a boundary line

which enclose all the other valid sensor nodes as shown in Figure 1.

Invalid nodes

Edge nodes

Inner nodes

AOI

Boundary line

Hole

5 6

Secto

Fig. 1. Network model Fig. 2. Directional antenna

A directional antenna model presented in [13] is considered in this paper. The an-

tenna system is composed of N beams such that their intersection is zero and their

union covers the entire 360 degree plane as shown in Figure 2. The width of each

beam is equal to 360/N and the area covered by one beam is called a sector. We con-

sider a large value for N therefore the size of a sector is very small.

Edge node position estimation refers to the estimation of the position coordinates

of an edge node by the sink. For this purpose the sink uses its directional antenna to

measure the angle of arrival (AOA) [10] and the received signal strength (RSSI) [11]

from a sensor node. Then, based on its own position (calculated using GPS), the sink

estimates the position coordinates of the sensor node (discussed in Section 4.12

and 4.2).

4 MObile Sink Based BOundary Detection (MoSBoD)

This section presents the new algorithm MoSBoD for boundary detection using a

mobile sink. The two main phases are (i) bootstrapping (for sensor node validation

and identification of a starting edge node) and (ii) edge node identification and

boundary traversal using the mobile sink.

4.1 Bootstrapping Phase

The bootstrapping phase is an initialization phase of the MoSBoD algorithm. During

this phase sensor nodes prepare themselves for the arrival of the sink by calculating

their validity status. Simultaneously, the sink locates a valid edge node in the sensor

field and marks this node as the starting edge node.

Identifying the Boundary of a Wireless Sensor Network with a Mobile Sink 373

4.1.1 Bootstrapping of the Sensor Nodes

In the bootstrapping phase sensor nodes are divided into two groups of valid and

invalid nodes. As input for this phase, each node is preprogrammed with a time value

t1 and neighbor density (validity_cnt) required for calculating the validity status of a

node. After the deployment of a sensor field each node performs the following op-

erations: activate message reception mode and broadcast a message containing the

own ID (on expiration of time t1). On receipt of messages from neighboring nodes

create a list of neighbors containing their ID’s and set their validity status to false.

Then,

(i) If the neighbor count becomes equal to validity_cnt, then set own validity equals

true and broadcast a message containing the ID and the validity status.

(ii) On receipt of a validity message update the sender nodes’ validity status.

4.1.2 Identification of Starting Edge Node

During this phase the sink calculates the mobility direction to reach the boundary of

the AOI and afterward locates the starting edge node. In order to achieve this task the

sink carries out the following operations: Determine its current location and alignment

with respect to the boundary of the AOI using GPS and compass; calculate mobility

direction and move to reach the closest boundary point at the AOI.

Fig. 3. Identification of the starting edge node

Upon reaching the boundary of the AOI, the sink calculates the center of the AOI

(utilizing AOI coordinates), switch on its antenna, starts transmitting a hello message

and begins to move towards the center of the AOI. The sink continues until a response

(ID, validity) from a valid sensor node is received. On receipt of a response message,

the sink marks the responding node as a starting edge node and saves own current

coordinates as (x1, y1) (see Figure 3(a)). Also, by utilizing the AOA of the received

response and the edge node position estimation procedure explained in Section 3, the

sink calculates and moves to the position of the starting edge node (x2, y2). Excep-

tional situations, such as when multiple valid nodes respond to the sink, are also han-

dled in the pseudo code of Module-1. Moreover, it should be noted that unlike [7]

where the starting node is the node with minimum y coordinates (calculated using

GPS) and identified by sensor field flooding, Module-1 does not impose any such

requirements.

Module-1 engender following outputs: coordinates of the location when the sink

receives first response from a valid sensor node (x1, y1); coordinates of the starting

edge node (x2, y2), and starting edge node ID.

374 M.I. Khan, W.N. Gansterer, and G. Haring

Module-1: Locating the AOI and the starting edge node

INPUT: AOI coordinates, AOI = false, s_node = null

1: Calculate and move to the nearest boundary of AOI using AOI coordinates and own

position (calculated using GPS)

// Sink moves inside the AOI in search of valid sensor nodes

2: while s_node == null

3: Move towards center of AOI, broadcasting hello message

4: if single node responds AND nodeValidity == true then

5: s_node=respondingNodeID & (x1,y1)=current position

6: else if multiple nodes responds then

7: if responding nodes are at same shortest distance from the sink then

8: starting node = node with minimum ID

9: else s_node = node at shortest distance from the sink

// (Calculated using RSSI based distance estimation)

10: end if

11: end if

12: if (s_node !== null)

13: Utilize received response from s_node to perform edge node position estimation,

calculate (x2, y2) and move to the calculated location of the s_node

14: end if

15: end while

4.2 Edge Node Identification and Boundary Traversal

This section presents Module-2 that enables the sink to identify the neighboring edge

nodes of a current node (the node where the sink is currently positioned). The line

then obtained by connecting all the identified edge nodes with their corresponding

neighboring nodes is the desired boundary of the sensor field.

Module-2 is based on the use of mobility and a directional antenna by the sink.

Prerequisites for the execution of this algorithm are, the sink is positioned at an edge

node i, it knows the position coordinates of the current node i and identified neighbor

edge node i-1 of the current node.

The sink initiates execution of Module-2 by calculating the reference line which is

defined as the line obtained by joining the position coordinates of the current node i

and it’s identified neighboring edge node i-1. Then the sink numbers the sectors start-

ing from the one located beside the reference line towards the mobility direction of

the sink. We specify that the sink traverses the boundary of the sensor field in coun-

terclockwise direction. In this case, the sink will mark the sector located in counter-

clockwise direction of the reference line as sector 1 as shown in Figure 4(b).

Once the sectors are numbered, the sink broadcasts a hello message to the

neighboring nodes of the current node. The node whose response is received in the

lowest sector number is assigned the status of next edge node i+1 by sending an edge

node confirmation message. For example, in Figure 4(b) response from node i+1 is

received in Sector 4 while the responses from all the other nodes are received in sec-

tors having ID greater than 4. Therefore, node i+1 is assigned the status of next edge

node. Moreover, position coordinates of node i+1 are estimated using edge node

position estimation and the sink moves to its position.

Identifying the Boundary of a Wireless Sensor Network with a Mobile Sink 375

(b)

Case of an arbitrary edge node

i+1

Reference line

+ boundary li ne

i-1

Boundary

line

k+1

Reference line

(a)

Case of starting edge node

d2 > d1

(a) (b)

Mobility path

of the sink

Obtained

oundary line

n2 n3 n 4

Fig. 4. Neighboring edge node identification Fig. 5. Special cases in Module-2

On reaching node i+1, the sink again executes Module-2 to identify the neighboring

edge node of node i+1. Thus, by moving from one edge node to the next, the sink even-

tually returns to the starting edge node after completing the boundary trace.

The discussion so far leaves one open question: How the sink determines the refer-

ence line when it is positioned at the starting edge node? It is known that the starting

edge node is the first node to be identified as an edge node and at this point of time

the sink has no information about the neighboring edge nodes of the starting node.

Thus, the starting edge node is a special case for the reference line identification proc-

ess. In this case we utilized the coordinates of the current node (x2, y2) and the coor-

dinates (x1, y1) (obtained from Module-1) to define the reference line. Since it is

assumed that the sink traverses the boundary of the field in counterclockwise direc-

tion, the sink assigns numbers to the sectors in ascending order starting from the one

located towards counterclockwise direction of the reference line, as shown in Figure

4(a). The rest of the procedure for the identification of the next edge node is the same

as already discussed.

During the neighboring edge node identification some exceptions can arise which

are handled in the pseudo code of Module-2. For example, if the sector with the low-

est number (Sector 4 in Figure 4(b)) receives responses from two or more nodes then

it is assumed that the two nodes are located on a line, because it is assumed that the

size of a sector is very small. In this case, the node located at farthest position from

the current node is selected as next edge node as shown in Figure 5(a). There may

also be the case where a group of nodes are connected to the main sensor field via a

single link, like node n1 which connects n2, n3 and n4 with the rest of the field as

shown in Figure 5(b). Since we do not impose any restriction on the number of times

the sink can visit an edge node during the boundary identification process, such cases

can also be handled successfully by our algorithm.

Module-2: Edge node identification and boundary traversal

Input: The sink is positioned at the starting edge node, i. Coordinates of the edge nodes i and i-

1 are (x2, y2) and (x1, y1) respectively.

1: current node = i;

2: do

3: Number sectors according to the reference line

// Identification of the next edge node

376 M.I. Khan, W.N. Gansterer, and G. Haring

4: Transmit a hello message to the neighbors of the current node;

5: if only one node nb responds then i+1 = nb;

6: else if multiple responding nodes are located at same farthest distance from sink then

7: i+1 = node having minimum ID

8: else i+1 = the farthest node; // determined using RSSI

9: end if

10: Apply edge node position estimation for node i+1;

11: Store position coordinates of node i+1 and move to it

// edge node confirmation message

12: Send a message to node i+1 demanding its list of neighbors;

13: Set i-1 = i; i = i+1;

14: until i != current node

Example. Figure 6 shows the implementation of the MoSBoD algorithm on a sample

sensor field. Once the boundary is fully identified, the sink continues its mobility

along the boundary line monitoring possible edge node failures for boundary recon-

structing. Since the later trips along the boundary line are based on the stored position

coordinates of the edge nodes, they will require less time than the first trip.

Starting

edge node

Reference line

Fig. 6. Edge node identification

5 Discussion and Analysis

This section presents an evaluation of the MoSBoD algorithm based on the OM-

NeT++ simulation tool. We analyze the effects of neighbor node density and of the

size of the sensor field on the energy consumption of the MoSBoD algorithm. Also, a

theoretical analysis of the completion time of the MoSBoD algorithm is given. For

completeness we have compared the results obtained with a boundary identification

scheme presented in [3]. We selected this particular scheme for comparison because it

has similar assumptions regarding sensor node hardware, deployment strategy etc.

which we are using in this paper. The graphs show 95% confidence intervals for the

quantities of interest.

The basic simulation setup comprises an area of 800x500 2

m where the sensor

nodes are uniformly, but randomly, deployed. The communication range for the nodes

Identifying the Boundary of a Wireless Sensor Network with a Mobile Sink 377

is set to 80 m. We applied the MoSBoD algorithm to sensor fields with random, U

shaped, circular and rectangular boundary shapes with varying neighbor node densi-

ties of 4, 6, 14 and 18. The boundary obtained with our algorithm remains the same

irrespective of the changes in neighbor node density. It reflects the fact that, in con-

trast to [2], [3] or [12] which require a neighbor density of at least 7 to produce ac-

ceptable boundaries [3], our MoSBoD algorithm is based on sink mobility which and

does not impose any such conditions.

5.1 Energy Consumption

With respect to energy consumption, we investigated two hypotheses:

Hypothesis 1: In the MoSBoD algorithm, the number of messages sent out per sen-

sor node is constant and the number of messages received depends linearly on its

neighbor node density.

Hypothesis 2: Scaling up/down the area of the sensor field with constant node den-

sity has no effect on the number of messages exchanged by the sensor nodes in the

MoSBoD algorithm.

Fig. 7. Messages sent per node vs average

neighbor density

Fig. 8. Messages received per node vs aver-

age neighbor density

Fig. 9. Messages sent per node vs area of

sensor field

Fig. 10. Messages received per node vs are

of sensor field

For a simulation based validation of Hypothesis 1 we set up a simulation environ-

ment where the deployment area for the sensor field was fixed. Then nodes were

deployed with different densities to this area and the MoSBoD algorithm was

378 M.I. Khan, W.N. Gansterer, and G. Haring

executed for boundary identification. Figure 7 shows that the total number of mes-

sages sent out by a node during the boundary identification procedure is basically

constant (slightly larger than 2) irrespective of the neighbor density, while Figure 8

shows that the number of messages received by a node is a linear function of its

neighbor density. In contrast, the scheme discussed in [3] requires each node to

broadcast at least three messages. This implies that the MoSBoD algorithm consumes

at least 33% less energy from the nodes as compared to [3], both in terms of message

transmission and reception which increases the lifetime of the sensor field.

On investigating Hypothesis 2, we observe that for average neighbor node density

equal 7 the number of messages exchanged by the nodes is practically not affected by

a change in the area of the sensor field, as shown in Figures 9 and 10. This is due to

the fact that in the MoSBoD algorithm node to node communication takes place only

to determine the validity status of a node, which is a localized phenomenon and does

not depend on the size of the field. This shows the highly scalable nature of our algo-

rithm where the size of the field does not affect the behavior of an individual node

(for constant neighbor density).

5.2 Completion Time

As explained in Section 4, the MoSBoD algorithm exploits sink mobility to identify

edge nodes and then connects them to obtain the boundary of a sensor field. Since the

mobility speed of the sink is very slow compared to the speed with which messages

can be exchanged between the nodes, the first impression may be that the completion

time of the MoSBoD algorithm is extremely high as compared message flooding

based schemes, for example, as discussed in [3]. It is the topic of ongoing work to

analyze this aspect quantitatively. A potential strategy for reducing the completion

time of the MoSBoD algorithm is a selective increase of the duty cycles of sensor

nodes. It is required, though, to carefully balance the expected reduction in latency

with the resulting increase in energy consumption. A detailed investigation and analy-

sis of this strategy is provided in a forthcoming paper.

Area size of the sensor field. Since the MoSBoD algorithm is based on sink mobil-

ity for the identification of the edge nodes, an increase in the area of the sensor field

leads to a linear increase in the completion time of the algorithm.

6 Conclusion and Future Work

In this paper we introduced a new scheme for boundary identification of a sensor

field. Our approach utilizes a mobile sink for edge node identification which reduces

the communication requirements amongst the nodes. The proposed MoSBoD algo-

rithm has a definite edge over currently available algorithms in terms of energy con-

sumption and in terms of neighbor node density requirements for correct boundary

identification. Moreover, it does not impose any restrictions on the deployment of the

sensor nodes.

We are currently extending this work along two fronts. First, we pursue ideas for

improving the quality of the identified boundary as well as for reducing the comple-

tion time of the algorithm. Second, we are carrying out a detailed analysis of energy

Identifying the Boundary of a Wireless Sensor Network with a Mobile Sink 379

consumption and completion time of the improved MoSBoD algorithm and quantita-

tively compare it with the state of the art methodologies.

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Analysis of IEEE 802.11e Line Topology

Scenarios in the Presence of Hidden Nodes*

Katarzyna Kosek, Marek Natkaniec, and Andrzej R. Pach

AGH University of Science and Technology, Krakow, Poland

{kosek,natkanie,pach}@kt.agh.edu.pl

http://www.kt.agh.edu.pl/

Abstract. In this paper an innovative simulation study of five IEEE 802.11e

network configurations is presented. The conducted analysis is crucial for un-

derstanding how a theoretically simple and, most of all, popular line topology

network can be degraded by the presence of hidden and exposed nodes. The

discussion of the obtained results helps to understand how and why the behav-

ior of IEEE 802.11e based line topologies changes when the number of nodes

increases. Furthermore, the usefulness of the four-way handshake mechanism is

argued. Finally, the need for a better MAC protocol is stressed and a number of

novel conclusions about the IEEE 802.11e nature is provided.

Keywords: ad-hoc, hidden and exposed nodes, IEEE 802.11e.

1 Introduction

Wireless networking technology is quickly evolving and its importance grows con-

stantly. The most interesting technology, not only from the perspective of a researcher

but also from the perspective of an average user, seem to be ad-hoc networking. These

networks without infrastructure do not need complicated admin-istration and may

greatly facilitate Internet access. Unluckily, all wireless networks were created to deal

with data exchanges and not multimedia services. Therefore, the need for QoS assur-

ance for delay sensitive and/or bandwidth consuming services remains an interesting

and unresolved issue. Constantly changing and unpredictable channel conditions, hid-

den and exposed node problems, varying network load, changeable device performance,

different transmission and sensing ranges, and mobility of ad-hoc networks make it an

even more difficult task. In this article the authors focus on the hidden and exposed node

problems which they find the most interesting.

Five different configurations of ad-hoc line topologies are simulated. The purpose

of analyzing line topologies is simple. A good example of such a case in a real envi-

ronment is a simple mesh network in which ad-hoc nodes communicate with a gate-

way (GW) every time they access the Internet services. At the same time, most of

these nodes are out of range of GW and need to send their data through other nodes.

* Disclaimer This work has been realized under the Polish Ministry of Science and Higher

Education project no. N51739133.

Analysis of IEEE 802.11e Line Topology Scenarios 381

Another example are long distance multi-hop links using the same radio channel

which could be used in rural areas where access to infrastructure is highly limited.

Due to the fact that all kinds of topologies require QoS, the authors found it crucial to

check if IEEE 802.11e [1] can assure QoS in such environments. This paper presents

novel results regarding line topologies. To the authors’ best knowledge similar analysis

has not been performed. Related work can be found in [4] in which, however, the au-

thors did not take into account different line topologies and did not analyze how the

length of a line impacts the network performance. Additionally, they did not notice the

undesirable inversion in prioritizing traffic and, furthermore, the values of EDCA access

parameters used were not compatible with the IEEE 802.11e standard.

The analysis presented in this article helps to draw innovative conclusions about

IEEE 802.11e behavior. Among many consequences of the hidden and exposed nodes

presence, the most important seem the unavoidable unfairness in granting medium

access and distortion of the throughput levels of different priority streams. The paper

also argues the usefulness of the four-way handshake method in minimizing their

degrading impact on IEEE 802.11e performance. Additionally, the gathered results

are compared with the results obtained for two different star topology networks pre-

sented in [5].

The remainder of this paper is organized as follows. Section 2 describes the simu-

lation scenarios. Section 3 gives explanation of the obtained results and presents scru-

pulous conclusions. More general conclusions can be found in Section 4.

2 Simulated Scenarios

The simulation analysis was performed with the use of an improved version of the

TKN EDCA enhancement [3] to the ns2 simulator. The adjustments made mostly

affect the RTS/CTS mechanism which was not supported properly by the original

version of the TKN EDCA patch. Additionally, the handling of duplicate drops was

fixed. Important simulation parameters are given in Table 1 and Table 2.

Table 1. EDCA parameter set

Priority AC CWmin[AC] CWmax[AC] AIFSN[AC] TXOP

P0 Vo 7 15 2 0

P1 Vi 15 31 2 0

P2 BE 31 1023 3 0

P3 BK 31 1023 7 0

Table 2. General simulation parameters [2]

SIFS 10 µs DIFS 50 µs

PIFS 30 µs Slot Time 20 µs

Tx Range 250 m Tx Power 0.282 W

Frame Size 1000 B Traffic Type CBR/UDP

CS Range 263 m Node Distance 200 m

382 K. Kosek, M. Natkaniec, and A.R. Pach

The simulation study was performed with the assumptions that all nodes send CBR

traffic1 with a varying sending rate (from 10 kb/s to 10 Mb/s) and the IEEE 802.11b

standard [2] is used as the physical layer type. The nodes form line topologies in

which each node can only detect transmissions of its nearest neighbors (c.f., Fig. 11).

The number of nodes changes from 3 (numbered from left to right N0-N2) to 7

(N0-N6)2. Additionally, for every analyzed network setup, four different EDCA con-

figurations are simulated. In each configuration a different EDCA class is used for the

flows generated by the network-forming nodes. The propagation model used is the

two-ray ground reflection model.

In order to combat the hidden node problem the RTS/CTS mechanism is used. Ad-

ditionally, for the sake of clarity of the presented figures, if two nodes obtain similar

throughput it is presented as a single mean value (e.g., N0/N2 for nodes N0 and N2 in

Fig. 2). For the same reason, in Fig. 3-Fig. 5 only the curves representing Vo and BE

priority are presented because their performance is very similar to that of Vi and BK,

respectively (c.f., Fig. 3). Moreover, in all presented figures the error of each simula-

tion point for a 95 % confidence intervals does not exceed ± 2 %.

3 Simulation Results

In this section the results obtained for the three- to seven-node line scenarios will be

described. Firstly, the overall performance of particular networks will be analyzed by

comparing the obtained throughput by nodes for four different priorities. Secondly,

the six-node line will be described in detail by means of frame dropping probability,

retransmission drops and duplicate drops. Finally, a comparison with two star topol-

ogy networks [5] will also be given.

3.1 Three-Node Line

With the RTS/CTS exchange disabled, hidden nodes with Vo and Vi priorities obtain

smaller throughput than BE and BK in general (Fig. 1a). Furthermore, when the over-

all traffic load exceeds 225 KB/s, the throughput of Vi and Vo streams drops to zero.

For the unhidden node, the order of the throughput levels is in line with the IEEE

802.11e guidelines.

With RTS/CTS enabled, the throughput of hidden nodes slightly increases and

drops for the unhidden node (Fig. 1b). However, the strong unfairness between the

hidden and unhidden nodes is not eliminated. Additionally, when hidden nodes are

transmitting Vo traffic the unfairness is strongest as they obtain the lowest throughput

which is practically equal to zero for traffic load exceeding 500 KB/s.

The above observations lead to a conclusion that with RTS/CTS both enabled and dis-

abled, the three-node line topology network will not work properly. In such a network,

for hidden nodes, low priority traffic will be always prioritized over high priority traffic

and, additionally, the unhidden node will be strongly prioritized over the hidden ones.

1 The authors performed the analysis also with different traffic types however the achieved

results were very similar to those obtained for CBR traffic.

2 The maximal number of nodes was set to 7 because in the real world it is very hard to find

longer line topologies (e.g., long distance links).

Analysis of IEEE 802.11e Line Topology Scenarios 383

100

200

300

400

500

0 500 100 0 1500 2000 2500 3000 3500

Total offe red load [KB/s]

Throughput [KB/s]

N1, P0 N0/N2, P0 N1, P1 N0/N2, P1

N1, P2 N0/N2, P2 N1, P3 N0/N2, P3

100

200

300

400

500

0 500 1000 1500 2000 2500 3000 3500

Total offe red load [KB/s]

Throughput [KB/s]

N1, P0 N0/N2, P0 N1, P1 N0/N2, P1

N1, P2 N0/N2, P2 N1, P3 N0/N2, P3

Fig. 1. Three-node line. Throughput for RTS/CTS (a) disabled (b) enabled.

3.2 Four-Node Line

For a four-node line topology the throughput curves change (Fig. 2a) in comparison to

the three-node line. With the RTS/CTS exchange disabled the throughput order may

be divided into two main sets. Under lighter load (below 2 MB/s), N0/N3 transmitting

BE and BK obtain higher throughput than N2/N4 transmitting Vi and Vo. Under

heavier load, this order changes so the unfairness between these pairs of nodes is even

stronger. Furthermore, under network load exceeding 150 KB/s, for all nodes, BE and

BK priority streams are favored over Vi and Vo.

With RTS/CTS enabled, N1/N2 are prioritized over N0/N3 (Fig. 2b). Moreover,

for all nodes low priority streams obtain higher throughput than high priority streams.

In comparison to the three-node topology, the overall throughput drops and, therefore,

the network performance of four-node line topology is worse for both enabled and

disabled RTS/CTS.

100

150

200

250

0 500 1000 1500 2000 2500 3000 3500

Total offered load [KB/s]

Throughput [KB/s]

N0/N3, P0 N1/N2, P0 N0/N3, P1 N1/N2, P1

N0/N3, P2 N1/N2, P2 N0/N3, P3 N1/N2, P3

100

150

200

250

0 500 1000 1500 2000 2500 3000 3500

Total offere d load [KB/s]

Throughput [KB/s]

N0/N3, P0 N1/N2, P0 N0/N3, P1 N1/N2, P1

N0/N3, P2 N1/N2, P2 N0/N3, P3 N1/N2, P3

Fig. 2. Four-node line. Throughput for RTS/CTS (a) disabled (b) enabled.

3.3 Five-Node Line

For the five-node line, with the RTS/CTS exchange disabled, for Vo priority traffic

nodes N1/N3 obtain the highest throughput, N0/N4 smaller and N2 the smallest

(which is totally unacceptable for network load over 375 KB/s). Moreover, the ob-

served unfairness between certain nodes increases as the total offered load grows. For

BE priority the order of N1/N3 and N0/N4 is reversed (Fig. 3a).

384 K. Kosek, M. Natkaniec, and A.R. Pach

With the RTS/CTS exchange enabled, the throughput level order may be divided

into two sets (Fig. 3b). The throughput levels under non-saturation conditions for

N1/N3 and N0/N4 for Vo are the lowest but they grow with the increase of the of-

fered load. Similarly, also the throughput of N0/N1/N3/N4 sending BE grows line-

arly. At the same time, a decrease in the throughput value of N2 can be observed for

both BE and Vo. Finally, under network load of over 2.5 MB/s the throughput values

are stable and N2 obtains smallest throughput regardless of the traffic priority it

transmits. In all analyzed cases, BE is prioritized over Vo but the strongest unfairness

is present for nodes N0 and N4.

100

150

200

250

0 500 1000 1500 2000 25 00 3000 3500 4000

Total offered load [KB/s]

Throughput [KB/s]

N0/N4, P0 N1/N3, P0 N2, P 0

N0/N4, P2 N1/N3, P2 N2, P 2

100

150

200

250

0 500 1000 1500 2000 2500 3000 3500 4000

Total offered load [KB/s]

Throughput [KB/s]

N0/N4, P0 N1/N3, P0 N2, P0

N0/N4, P2 N1/N3, P2 N2, P2

Fig. 3. Five-node line. Throughput for RTS/CTS (a) disabled (b) enabled.

3.4 Six-Node Line

In case of the six-node line topology, the obtained results resemble the results for the

four-node line in the case of Vo/Vi priority transmission. Which means that the nodes

being in the middle of the line have the smallest throughput, the ones next to them

win the competition for medium access most often and, finally, all other nodes receive

average priority in medium access. However, in this configuration the unfairness

between high priority traffic and low priority traffic is stronger because practically

under every network load for RTS/CTS both enabled and disabled, all nodes sending

Vo obtain smaller throughput than the corresponding ones sending BE (Fig. 4). The

strongest unfairness is observed for the side nodes ― N0/N5 (similarly to the four-

node line’s N0/N4) but it also increases for the nodes N1/N3.

100

150

200

250

0 1000 2000 3000 4000 50 00 6000

Total offered load [KB/s]

Throughput [KB/s]

N0/N5, P0 N1/N4, P0 N2/N3, P0

N0/N5, P2 N1/N4, P2 N2/N3, P2

100

150

200

250

0 1000 2000 3000 4000 5000 6000

Total offered load [KB/s]

Throughput [KB/s]

N0/N5, P0 N1/N4, P0 N2/N3, P0

N0/N5, P2 N1/N4, P2 N2/N3, P2

Fig. 4. Six-node line. Throughput for RTS/CTS (a) disabled (b) enabled.

Analysis of IEEE 802.11e Line Topology Scenarios 385

3.5 Seven-Node Line

The observations for the seven-node line are similar to the ones made for the six-node

line. Once again, regardless of the RTS/CTS exchange, nodes sending high priority

traffic streams obtain smaller throughput than the corresponding ones sending low

priority streams. Additionally, N1/N5 win the competition for medium access most

often, and the one in the middle (N3) less often. The main difference is that the

strongest unfairness can be observed for nodes N1/N5 and not the side-nodes.

100

150

200

250

0 100020003000400050006000

Total offered load [KB/ s]

Throughput [KB/s]

N0/N6, P0 N 1/N5, P0 N2/N4, P0 N3, P0

N0/N6, P2 N 1/N5, P2 N2/N4, P2 N3, P2

100

150

200

250

0 1000 2000 3000 4000 5000 6000

Total offered load [KB/s]

Throughput [KB/s]

N0/N6, P0 N1/N5, P0 N2/N4, P0 N3, P0

N0/N6, P2 N1/N5, P2 N2/N4, P2 N3, P2

Fig. 5. Seven-node line. Throughput for RTS/CTS (a) disabled (b) enabled.

3.6 Overall throughput

The overall saturation throughput levels obtained for the analyzed scenarios are pre-

sented in Fig. 6. As can be seen, for the high priority traffic the saturation throughput

is highest for the shortest line. For the low priority traffic the situation changes be-

cause the saturation throughput grows meaningfully as the number of nodes increases.

Additionally, in all cases the throughput of high priority traffic is smaller than for low

priority traffic which differs from IEEE 802.11e assumptions.

Fig. 6. Overall saturation throughput

386 K. Kosek, M. Natkaniec, and A.R. Pach

3.7 Detailed Conclusions

The performance shown in Fig. 1-Fig. 5 can be explained by the rate of the total

frame loss for each of the analyzed flows in every simulation scenario. Additionally it

can be also justified by the general character of each of the analyzed networks. For

example in the case of the three-node line topology, two hidden and zero exposed

nodes appear. In the five-node line there are five hidden nodes and three exposed

ones, however, the hiddenness and exposedness of particular nodes differs.

Due to the lack of space only the performance of the six-node network will be ex-

plained in great detail with the help of the results presented in Fig. 7-Fig. 10. This

network has been chosen as the most general one. The conclusions regarding this

network will also be valid for the remaining ones.

The frame dropping probability is computed on the basis of the number of dropped

frames in interface queues between the LLC and the MAC layers. In particular, it is

the number of dropped frames to the number of generated frames.

generated

dropped

drop n

P=. (1)

For RTS/CTS disabled (Fig. 7a), N2/N3 almost always have the same frame dropping

probability. However, there is a great difference for N1/N4 and N0/N5 between Vo

and BE. This behavior means that for BE the dropping probability is, in general,

smaller than for Vo which differs from IEEE 802.11e assumptions. The dropping

probability for N0/N5 is non zero for BE for the total offered load exceeding 1 MB/s,

for Vo − exceeding 0.45 MB/s. In both cases, for all remaining nodes it starts earlier.

Such a behavior could lead to an assumption that N0 and N5 should achieve highest

throughput for both Vo and BE. When we look, however, at Fig. 4a and Fig. 4b, we

see that these are N1 and N4 which outperform all other nodes. This is a result of the

fact of the exposedness of N1 and N4 which leads to high number of duplicate drops

(c.f., Fig. 10) described later in this section. In general, for BE non zero frame drop-

ping probability starts later than for Vo which contradicts IEEE 802.11e. It is a result

of less frequent attempts in obtaining medium access by BE. Higher priority means

smaller values of EDCA access parameters and a higher possibility for competing for

medium access. Such a behavior causes a higher probability of collisions for hidden

nodes and, consequently, it leads to a higher number of retransmissions which cause

quicker filling of the four MAC priority queues. As a result, the quicker a certain

queue is filled the higher the probability that it will be overloaded and more interface

queue drops will be observed. Obviously, the more duplicate frames are sent the

higher probability that they will collide in the wireless medium instead of the good

frames. Therefore, duplicate drops and retransmission drops should be analyzed to-

gether in order to understand this complicated behavior. One other thing which mat-

ters in analyzing the frame dropping probability curves is the type of their slopes. The

steepness of slopes show how high is the speed of filling the MAC priority queues.

Curve slopes are gentlest for N0/N5 and steepest for N2/N3. This is a result of the

strength of the exposedness and hiddenness of particular nodes. N0/N5 are only hid-

den and N2/N3 are the most exposed and the most hidden nodes.

Analysis of IEEE 802.11e Line Topology Scenarios 387

With RTS/CTS enabled (Fig. 7b), N2/N3 have a slightly different frame dropping

probability for Vo and BE. Also a smaller difference for N1/N4 and N0/N5 between

Vo and BE can be noticed. The dropping probability for N0/N5 for BE is non zero for

the total offered load exceeding 0.75 MB/s, and for Vo − 0.22 MB/s. However, in

general, frame dropping probability increases for BE and decreases for Vo (it in-

creases slightly only under light network load for N0/N5 and N1/N4) in comparison

with RTS/CTS disabled. The performance of Vo flows can be explained by the small

values of EDCA access parameters which lead to more frequent medium access at-

tempts. Obviously, this time DATA transmissions can be successful more often than

with RTS/CTS disabled due to the small lengths of the RTS and CTS signaling

frames in comparison to DATA frames. The performance of BE can be explained by

the increased signaling overhead which causes that DATA frames to wait in the MAC

queues for the successful RTS/CTS exchange. The increased overhead for Vo is not

as meaningful because of the incomparable gain from successful transmissions of

DATA frames. Due to the fact that the frame dropping probability curve’s slopes are

very similar to the previous ones, the explanation is the same and the strength of the

exposedness is the main reason to blame.

0.2

0.4

0.6

0.8

0 1000 2000 3000 4000 5000 6000

Total offered load [KB/s]

Frame dropping probability

N0/N5, P0 N1/N4, P0 N2/N3, P0

N0/N5, P2 N1/N4, P2 N2/N3, P2

0.2

0.4

0.6

0.8

0 1000 2000 3000 4000 5000 6000

Total offered load [KB/s]

Frame dropping probability

N0/N5, P0 N1/N4, P0 N2/ N3, P0

N0/N5, P2 N1/N4, P2 N2/ N3, P2

Fig. 7. Six-node line. Frame dropping probability for RTS/CTS (a) disabled (b) enabled.

For the sake of further conclusions, it is important to stress that the strongest hid-

denness and exposedness can be observed for N2/N3, weaker for N1/N4, and weakest

for N0/N5. However, nodes N0 and N5 hear only N1 and N4, respectively, and nodes

N1/N4 hear twice as many nodes each.

The number of retransmission drops (c.f., Fig. 9a-b) is a result of the transgression

of the long retry limit (equal to 7, for RTS/CTS enabled) or short retry limit (equal

to 4, for RTS/CTS disabled). When the number of retransmissions is compared with

the number of collisions (c.f., Fig. 8a-b) for particular nodes it is easily noticeable that

with the RTS/CTS exchange disabled the number of retransmissions is in line with the

number of collisions for all of the nodes. With RTS/CTS enabled the situation

changes drastically. The order of curves representing collisions is completely reverse

to those representing retransmissions. This is caused by the fact that in this situation

the RTS frames collide instead of the DATA frames. It is also evident that, in

comparison to all other nodes, the number of retransmissions decreased most mean-

ingfully for N0/N5 and less meaningfully for N2/N3. Such a behavior leads to a

388 K. Kosek, M. Natkaniec, and A.R. Pach

20000

40000

60000

80000

100000

120000

0 1000 2000 3000 4000 5000 6000

Total offered load [KB/s]

Collisions

N0/N5, P0 N1/N4, P0 N2/N3, P0

N0/N5, P2 N1/N4, P2 N2/N3, P2

2000

4000

6000

8000

10000

12000

0 100 0 2000 3000 400 0 5000 6000

Total offered load [KB/s]

Collisions

N0/N5, P0 N1/N4 , P0 N 2/N3, P0

N0/N5, P2 N1/N4 , P2 N 2/N3, P2

Fig. 8. Six-node line. DATA collision drops for RTS/CTS (a) disabled RTS/CTS (b) enabled.

3000

6000

9000

12000

0 10 00 2000 3000 4000 5000 6000

Total offered load [KB/s]

Retransmissi on drops

N0/N5, P0 N1/N4, P0 N2/N3, P0

N0/N5, P2 N1/N4, P2 N2/N3, P2

3000

6000

9000

12000

0 10 00 2000 3000 4000 5000 6000

Total offered load [KB/s]

Retransmission drops

N0/N5, P0 N1/N4, P0 N2/N3, P0

N0/N5, P2 N1/N4, P2 N2/N3, P2

Fig. 9. Six-node line. Retransmission drops for RTS/CTS (a) disabled (b) enabled.

conclusions that with RTC/CTS enabled the hiddenness of nodes is weakly and the

exposedness is strongly evident.

Duplicate drops are a result of collisions of either DATA and ACK frames (in the

case of RTS/CTS disabled) or RTS and ACK frames (in the case of RTS/CTS en-

abled) caused mainly by the exposedness of nodes. The exact reason is that the dura-

tion of ACK frames together with SIFS is shorter than AIFS. Consequently, every

exposed node can start its transmission of a DATA or RTS frame to a destination

node before this destination node receives an ACK from its other neighbor. Collisions

on ACK frames cause the node which does not receive the ACK to send its DATA

frame once again. As a result, the node which previously sent an ACK frame (which

collided) receives the same DATA frame. After the node checks that it already has

this frame, it will drop it.

As can be seen in Fig. 10, with RTS/CTS disabled, a meaningful number of dupli-

cate drops can be noticed only for N1/N4. This is because N0/N5 are not exposed at

all and N2/N3 are most strongly exposed and hidden. Therefore, the frame transmis-

sions triggered by N2/N3 are in many cases either strongly delayed, collide or are

simply impossible. With RTS/CTS enabled, the number of duplicate drops decreases

by half for N1/N4 and increases for N2/N3. Similarly as in the case of retransmission

drops, this is because introducing RTS/CTS reduces the number of collisions of

DATA frames of N2/N3, decreases their hiddenness and emphasizes the exposed

nature of N2/N3.

Analysis of IEEE 802.11e Line Topology Scenarios 389

3000

6000

9000

12000

15000

0 10 00 2000 3000 4000 5000 6000

Total offered load [KB/s]

Duplicate drops

N0/N5, P0 N1/N4, P0 N2/N3, P0

N0/N5, P2 N1/N4, P2 N2/N3, P2

1600

3200

4800

6400

8000

0 1000 2000 3000 400 0 5000 6000

Total offered load [KB/s]

Duplicate drops

N0/N5, P0 N1/N4, P0 N2/N3, P0

N0/N5, P2 N1/N4, P2 N2/N3, P2

Fig. 10. Six-node line. Duplicate drops for RTS/CTS (a) disabled RTS/CTS (b) enabled.

3.8 Comparison with Star Topology Networks

When the behavior of line topology networks is compared with the behavior of star

topology networks (presented in [5]) several important joined conclusions appear. Fist

of all, in both cases the strong unfairness in granting medium access between particu-

lar nodes is present. Second of all, the order of throughput levels of different priority

streams is reverse to the desirable ones (i.e., those expected by IEEE 802.11e). Fi-

nally, the employment of the RTS/CTS exchange does not bring meaningful changes

because it does not eliminate the aforementioned problems.

The behavior of three- and four-node line topologies is most similar to the behavior

of four- and five-node star topology networks. In these configurations nodes being in

the middle of the network are favored over the edge nodes. In all other cases the per-

formance of line topologies changes. This is because the importance of the exposed

nature of certain nodes (especially the middle ones) grows. Additionally, also the

strength of the hiddenness of the middle nodes grows as the line length increases.

These two factors cause the medium access of the middle nodes to be strongly hin-

dered. The transmissions triggered by the middle nodes either collide, are strongly

delayed or even blocked.

4 General Conclusions

This paper presents a novel simulation study of five different line topology networks

based on IEEE 802.11e. The impact of hiddenness and exposedness of particular

nodes is commented in details. Moreover, the paper argues the usefulness of the em-

ployment of the RTS/CTS mechanism in such networks. In both cases, with RTS/CTS

enabled or disabled, nodes sending high priority traffic obtain lower throughput levels

than the corresponding ones with low priority streams. Furthermore, high unfairness

in medium access between different line-forming nodes is stressed. The general pri-

oritization patterns of nodes are presented in Fig. 11.

As can be easily noticed, the higher the number of nodes the more the middle ones

are harmed in terms of throughput. Consequently, it can be noticed that it seems im-

possible for the side nodes to obtain meaningful dominance over other nodes when

there are more than four nodes in a line. It can be also expected that similar behavior

will occur when the line will be lengthened for RTS/CTS both enabled and disabled.

390 K. Kosek, M. Natkaniec, and A.R. Pach

Fig. 11. Prioritization order in (a) three- (b) four- (c) five- (low priority traffic) (d) five- (high

priority traffic) (e) six-, and (f) seven-node line

Additionally, the presented line topology networks are compared with previously

analyzed star topology networks. Several joined conclusions are revealed and the

main differences are highlighted. The cause of the differences is also explained.

Even though the presented analysis is rather thorough, there is a need for further

simulations. The behavior of line topology networks should be checked when the

most harmed nodes, in terms of access prioritization, will generate the high priority

traffic, while the prioritized ones will generate low priority traffic. Such analysis

should be done in order to check if simple changes of EDCA access parameters is a

good direction in solving hidden/exposed node problems within IEEE 802.11e based

networks. Additionally, other topology networks (more spontaneous than star and

line) should be taken into account. Future work will also comprise an analysis of new

scenarios to provide even more general conclusions. The overall aim of the planned

analysis is to show which threats are most dangerous, and which EDCA factors are

most important in building a new mechanism eliminating the degrading impact of

hidden/exposed nodes on IEEE 802.11e.

References

1. IEEE 802.11e: Medium Access Control (MAC) Quality of Service Enhancements. IEEE

Inc., New York(November 2005)

2. IEEE 802.11b: Higher-speed PHY extension in the 2.4 GHz band (1999)

3. TKN EDCA 802.11e extension (2006),

http://www.tkn.tu-berlin.de/research/802.11e_ns2

4. Bai, X., Mao, Y.M.: The Impact of Hidden Nodes on MAC Layer Performance of Multi-

hop Wireless Networks Using IEEE802.11e Protocol. In: International Conference on

Wireless Communications, Networking and Mobile Computing 2007, WiCom 2007, pp.

1479–1483 (September 2007)

5. Kosek, K., Natkaniec, M., Vollero, L., Pach, A.R.: An Analysis of Star Topology IEEE

802.11e Networks in the Presence of Hidden Nodes. In: Proc. The International Conference

on Information Networking 2008, ICOIN 2008, Korea (January 2008)

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 391–400, 2008.

Interference and Congestion Aware Reservations in

Wireless Multi-hop Networks

Stéphane Rousseau, Laure Lebrun, Hervé Aïache, and Vania Conan

Thales Communications, 146 Boulevard de Valmy, 92204 Colombes, France

{stephane.rousseau,laure.lebrun,herve.aiache,

vania.conan}@fr.thalesgroup.com

Keywords: wireless multi-hop, resource reservation, interference, congestion.

1 Introduction

Multi-hop wireless networks are dynamically forming networks of radio equipped

nodes. Most of the early work has been motivated by scenarios where nodes are mo-

bile, leading to both theoretical results for the capacity of the network [1] and to prac-

tical proposals for routing protocols [2]. With the recent deployment of community

wireless networks, more specific attention has been given to multi-hop wireless net-

works composed of both mobile mesh clients and more static mesh routers which

form the backbone of the wireless mesh and provide the clients with access to the

Internet [3].

In the present paper we consider multi-hop wireless networks that require re-

sources to be reserved across the network; such mechanisms may be needed in both

the mobile and static cases. Firstly multimedia applications require different quality of

service guarantees. For example a voice application would require low delay and

jitter, and video streaming would need bandwidth guarantees. The second use case

applies more specifically to the wireless mesh backbone. In this context, different

Service Level Agreements (SLAs) can be provided to users in a wireless mesh com-

munity network. The network provider would thus need means to ensure that the

expected Quality of Service [15] (in terms of average or peak bandwidth) is actually

delivered to its subscribers.

Resource reservation in wireless multi-hop networks is a challenging issue espe-

cially because it involves mechanisms from different layers, especially the MAC and

network layers. The present work focuses on the problem of resource reservation

across the network. We consider that the MAC layer is capable of reserving resources

on the links of this ad-hoc network. This means to be able to rely on TDMA-based

MAC layers, such as in [10], [11], QoS aware scheduling [12] [13] or service differ-

entiation as in 802.11e [14].

We furthermore consider that the multi-hop network runs a proactive or link state

protocol that provides knowledge of the network and resource state to all nodes. Res-

ervation may then be performed by the source, and the route is then pinned by each

router along the path. The aim of the reservation scheme is thus to maximize the us-

age of the network (its capacity) under the constraint that each link and node can only

provide a fixed limited amount of resource.

392 S. Rousseau et al.

First the reservation scheme must be congestion aware. Because of the conforma-

tion of the network and traffic demands, traffic is not routed evenly in the network,

some nodes are more popular than others and then become congested. The scheme

must thus take into account resource utilization to balance the reservations across the

network. In doing so, one also wishes to maintain average utilization of all nodes as

low as possible.

But since we are looking at wireless nodes, the reservation scheme must also be in-

terference aware. Interferences are known to be the major limiting factor of wireless

networks. The issue is that simultaneous transmissions of neighboring nodes may

interfere with one another [16]. This has an impact on many different aspects: on

network capacity [1] [4], transport throughput [5] and routing protocol design [6].

Interferences caused by simultaneous transmissions are also impacting resource reser-

vation. The problem of finding a reservation path that does not degrade existing res-

ervations is called the Path with Remaining Capacity problem. It was shown to be

NP-complete [7] [8]. To make reservations in the network, it is thus necessary to

retort to heuristics. [9] compares three heuristics, called H1, Hinc and HN1: H1 weighs

the links using an estimate of the remaining capacity to route around congested links

(using a weighted Dijsktra algorithm). Hinc is similar to H1 but tries incrementally less

and less stringent weights. HN1 replaces the weights of H1 to integrate the remaining

capacity of the adjacent nodes to compute the routes. They show that HN1 performs

best of the three.

The contributions of the paper are threefold:

First we introduce a model for the computation of the remaining capacity of each

node in the wireless multi-hop network. The model takes into account radio interfer-

ences between neighboring nodes. It also captures capacity reductions implied by

multiple-rate and robust coding schemes that are implemented at the physical layer to

insure communication on pour links. This information is used by the heuristics, but is

also valuable in its own right to provide evaluation grounds for other routing, trans-

port or reservation proposals.

Second we propose and evaluate a new heuristics for resource reservation across

the network. The heuristics combines the estimation of link congestion, knowledge of

link quality and impact of local interferences. We show that it achieves load balanc-

ing of the reservations across the network and outperforms previous metric-based

mechanisms (ETX and HN1).

Third we show in simulation that the proposed algorithm provides a versatile

mechanism that applies in contrasted scenarios. In the case of all nodes working on

the same bandwidth, the scheme manages to reduce interferences, and in the case of a

wireless mesh operating on non-interfering bands; it is shown to minimize congestion.

The remainder of the paper is organized as follows. First we present the interf-

erence model that we use throughout the paper. Second we present the congestion and

interference aware heuristics to solve the resource reservation problem. Third we

present simulation results that compare its performances with state-of-the-art solution.

The paper finishes with a section on related work and a conclusion.

Interference and Congestion Aware Reservations 393

2 Remaining Capacity Model

As outlined in the introduction, it is critical that the MAC layer be capable of reserv-

ing resources on the links [17]. For the sake of clarity, in the remainder of the paper

we will consider that the MAC layer uses time division multiplexing (TDMA), so the

resources that are reserved at MAC layer are time slots. TDMA is the basic mecha-

nism used for example in 802.11 physical layer, where 802.16 may also use Fre-

quency division multiplexing (FDMA).

Furthermore in the model we assume that the MAC layer scheduling is omnipotent

and achieves maximum concurrent transmissions among all nodes. Let us underline

that the problem still remains difficult even for this bestcase simplification [18].

Finally, we consider a transport protocol that ensures fairness in terms of data rate for

all of the flows in the network.

2.1 Interference Model

During a time-slot, each node can transmit packets to one or more nodes located in its

sending area. In this model, if a node receives two packets at the same time and on the

same frequency, interferences can appear. We have to distinguish two cases. The first

one is the case in which both SNRs are equal. In this case the two packets are de-

stroyed. In the second case one of the SNRs is considerably greater than the other one.

In this case, only the packet with the smallest SNR is destroyed.

This problem of interference is a key problem in wireless networks. The crudest in-

terference model is the Boolean link model, which considers a fixed radius of inter-

ference. In the paper, we consider a more realistic interference model taking into

account the distance between the source and the destination. More the destination is

far away from the source, more the link quality is altered and sensitive to noise and

interferers influence.

The quality of the transmission depends on the quality of the link. This quality de-

pends on the SNR (Signal-to-Noise Ratio). Several estimation formulas have been

proposed with the following general shape (for two nodes x and y at distance d(x,y)):

∀x,y nodes, SNR(x,y) = P/d(x,y)^β. (1)

Where P is the transmission power and β, the path loss exponent, ranging from 2 for

the free space propagation model to 5. In our study it is chosen equal to 3, corre-

sponding to a peri-urban propagation model.

As one can see, the SNR decreases fast with distance. If the link has a good quality

then high transmission rate, low redundancy mechanisms are used. Thus a packet of

size one takes exactly one bandwidth resource. However, it is possible that the link

quality is degraded (due to fading, ). The physical layer will then try to compensate

for this loss of quality by lowering the transmission rate and adding redundancy to

send a packet of size one. Then the needed bandwidth resource using this link can be

2, 3 or 4 times more for a packet of size one. Considering for example the Physical

layer of IEEE 802.11 standard, 4 modulation schemes are introduced from BPSK to

64-QAM with coding rates going from ½ to ¾.

394 S. Rousseau et al.

2.2 Remaining Capacity Estimate

In this section, we show how to estimate the remaining capacity for each node. We

consider a capacity C for each node. We assume a packet size is equal to one. Thus, at

each time-slot, a node can transmit at most C packets or receive C packets. Moreover,

this capacity is shared between the sending and receiving processes. Then, the sum of

the transmitted packets and received packets cannot be greater than C. We present

below the remaining capacity model that takes into account the interference assump-

tions given in [8].

3 Interference Aware Heuristics

3.1 Heuristic Based on ETX

ETX is a metric that evaluates the link quality. The heuristic based on ETX consists in

assigning for each link a weight equal to the ETX metric. Then, to compute a new

path for a request, we use the Dijkstra algorithm that returns the shortest path in terms

of link quality.

This heuristic takes into account the link quality but not the load balancing. The

load balancing can be taken into account considering the remaining capacity for each

node. A heuristic has been proposed and we present it below.

3.2 Heuristic Based on the Remaining Capacity

The heuristic based on the remaining capacity consists in avoiding area of saturated

nodes when the path is chosen. This heuristic has been proposed in a context where

all 1-Hop links have the same quality. Thus, the heuristic consists in computing for

each node a weight that indicates the remaining capacity of the node and the weight of

its neighbours. We recall here the formulas given in [9] to compute this weigh:

Weight(x)=1/Cx+Σ1/Cy (2)

Where Cx is the remaining capacity of the node and Cy the remaining capacity of its

1-HOP neighbours.

After having assigned a weigh for each node, a path is computed using the Dijkstra

algorithm to find the shortest path in terms of remaining capacity. Once a new request

is accepted, a new weight is computed for each node with the new remaining capacity.

3.3 New Heuristic

This heuristic combines the heuristic based on ETX and the one based on the remain-

ing capacity. The goal of this heuristic is to return the better path for a request con-

serving a good load balancing in the network for next requests.

The first step of this heuristic consists in assigning a weight for each link. The for-

mula that we proposed is the following one:

Weight(x)=α * (ETX^β) * (1/Cx+Σ1/Cy) (3)

Where α and β are parameters.

Interference and Congestion Aware Reservations 395

In this article we don’t discuss on those parameters and we put α=1000 and β=3.

Thus, ETX metric is more considered than the remaining capacity when the path is

computed. However, if two paths have the same cumulated weight in terms of ETX,

the heuristic returns the one with the most remaining capacity.

Then, we use the Dijkstra that returns the shortest path in terms of link quality and

remaining capacity.

4 Simulation and Analysis

4.1 Model Description

We consider wireless network composed of 100 nodes. These nodes are located in an

1200m*800m area. All nodes are randomly placed. We assume the noise is insignifi-

cant. Thus, we assume the SNR depends only on the distance between the source

node and the destination node. Then, the SNR between two nodes is compute with the

following formula proposed in section 2.

We distinguish four degrees of link state quality. The most the SNR is great the

most the quality of the link is good. When the quality is not good enough, we assume

that sending a packet of size 1 can cost in real more than 1 unit of resource radio.

According to this model, a packet of size 1 can take either 1, or 2, or 3, or 4 times

more resource radio to ensure its good reception.

If the SNR is very bad, then no packet can be transmitted using this link.

In this model, we assume each node has a capacity of 8000kb/s. This capacity can

be used either for transmit packets or receive some. For example, a node that receives

200kb/s and transmits 100 kb/s has a remaining capacity of 7700kb/s.

At the beginning of the simulation, the network is empty. Then, 2000 requests are

generated and treated one after the other. All requests have the same characteristics:

• An origin node that is randomly chosen.

• A destination node that is randomly chosen.

• A capacity (equal to 1 kb/s)

When a node treats a request, all requests accepted and the reserved resources radio

are known but it is not the case of the next requests.

All decisions are done within the origin node, then after one step all nodes in the

network update their information about link state and remaining capacity.

The goal of these simulations is to compare three heuristics for the reservation of re-

source radio that takes into account interferences. In order to be the most general as pos-

sible, we first compare those heuristics when all nodes have a different frequency

(MESH network) then when all nodes have the same frequency (Ad-Hoc network model.

In order to compare the three heuristics, we focus on the load balancing of the net-

work and the distribution of remaining capacity of each node. Recall that we are in an

on-line context. It means that all past reservations are known but none of the next

requests can be anticipated. Then, a way to ensure a good use of the network is to

maximize the minimum remaining capacity considering all nodes.

396 S. Rousseau et al.

4.2 Evaluation of Performances in Terms of Load Balancing

To compare the three heuristics, we propose to focus on the load balancing in the

network when all requests have been treated. At the end of these simulations all re-

quests have been accepted. Thus, for the same set of requests, we compare the amount

of remaining capacity of each node. Two kinds of curve are presented here.

– In the first one the x coordinate represents the location of nodes and the z

coordinate represents the remaining capacity for each node. With this kind

of curve, we underline the difference between the most loaded node and

the less loaded one. Then we focus on the repartition of the load among all

nodes.

– In the second kind of curve the x coordinate and the y coordinate indicate

the location of nodes in the whole area. We color sub-areas of the network

according to the load of the nodes located in it. When an area is composed

of loaded nodes, this area is black and when the area is composed of

unloaded nodes, it is white. Using this representation, we show where

most loaded nodes are located.

Considering a Mesh Network

We consider all nodes have a different frequency. Then, no interferences appear be-

tween two nodes in this network.

Results of the heuristic based on ETX metric

Results are shown on Figures 1 and 2. If we consider Figure 1, the most loaded node

has about 500 kb/s remaining capacity and the less loaded one has about 5000 kb/s

remaining capacity. If we consider Figure 2, the heuristic based on ETX chooses the

shortest path for all requests. If a node is saturated (i.e. no remaining capacity on this

node) then the heuristic gives another shortest path to connect the origin node and the

destination node. Thus, most of accepted requests go from the origin node to the des-

tination node via the center of the network. When the center of the network is satu-

rated, then next accepted connections go round the center. Thus, most of nodes with

few remaining capacity are located at the center of the network. Outlying nodes have

more remaining capacity.

Fig. 1. Fig. 2.

Interference and Congestion Aware Reservations 397

Results of the heuristic based on remaining capacity

Results are shown in Figure 3 and 4. The most loaded node has 0 kb/s remaining

capacity. Thus, using the heuristic based on remaining capacity, some of the nodes in

the network are saturated. It means, those nodes cannot accept requests anymore. The

less loaded node has about 5000 remaining capacity. Here, we can underline the gap

between the most loaded node and the less loaded one. The distribution of the load

within the network is not equal from a node to another. Let us focus on the location of

loaded nodes in the network. Figure 4 shows the distribution of load in the network

according to the geographic location. Unlike the heuristic based on ETX where the

center of the network tends to be saturated, with the heuristic based on the remaining

capacity, saturated nodes are located around the center. This result is due to the heuristic

that tries to avoid area with a lot saturated nodes. Thus, the first accepted requests are

routed round the center in order to balance the load. But, because this heuristic does not

consider link quality, some of computed paths generate a lot of interferences. Then, all

nodes around the center are saturated and none of the next requests can be connected the

origin node and the destination node via the center. A kind of ring is drawn around the

center and the load of the network is concentrated on it.

Fig. 3. Fig. 4.

Fig. 5. Fig. 6.

Results of the proposed heuristic

Now, we present the results that we obtained with the heuristic we propose in this

article. This heuristic is based not only on the link state quality but also on the remain-

ing capacity of each node. In Figure 5, the curve represents the gap between the most

398 S. Rousseau et al.

loaded node and the less one. The most loaded node has not been saturated yet; its

remaining capacity is about 1000 kb/s. The less loaded node remaining capacity is

about 5000 kb/s. Thus, the distribution of load in the network is quite fair among

nodes. In Figure 6, we present the repartition of the load in the area. A small subset of

loaded nodes is concentrated at the center of the network. Most of the load is well

equitably distributed around the center of the area.

Conclusion on the MESH network

In a MESH network, it is possible to organize nodes and assign different frequency in

order to limit the number of interferences. In the simulation model, we assume that all

nodes have a different frequency. Then, when a node transmits a packet, no interfer-

ence can appear with the other nodes transmissions. However, we still are in a wire-

less network, so each node has to share resource radio with all 1-Hop neighbors for

communications to and from them. This is the main constraint in this model of MESH

network. Considering only this constraint, we compare three heuristic. The heuristic

based only on ETX, has good performances and the one based only on the remaining

capacity is not so good. Combining the two criteria for the choice of the path for each

request, the performances are better than the two others. Indeed, the link state quality

seems to be an important criteria but it is necessary to take into account of the remain-

ing capacity in the path choice.

Considering an Ad-hoc Network

In an Ad-Hoc network, assigning different frequency for each node is not so easy.

Indeed, nodes are mobile and the assignment has to be dynamically done. Obviously,

it is possible to add a signaling protocol in order to do it.

Here, we consider all nodes with the same frequency. However, we assume all

nodes can be considered as static (i.e. nodes are not mobile). This kind of Ad-Hoc

network is often used when a network has to be deployed rapidly but once the net-

work is deployed, nodes don’t move anymore.

In this context, it is very important to take into account the interference model de-

scribed in Section 2. Now, we compare the three heuristics when all nodes have the

same frequency. In Figure 7, 9 and 11, we present the gap between the most loaded

node and the less one. Proposed heuristic is better than the heuristic based on ETX.

Fig. 7. Fig. 8.

Interference and Congestion Aware Reservations 399

The heuristic only based on the remaining capacity, performances are not good.

We obtain results quite similar than those obtained in the MESH network. When we

focus on the distribution of area with high density of loaded nodes, we also obtain

similar results. The heuristic that we proposed here, takes into account two very im-

portant criteria. The first one is the quality of links for transmission, and the second

one is the load balancing in the network.

To conclude, those two criteria have to be considered when we want avoid conges-

tion in a wireless network.

Fig. 9. Fig. 10.

Fig. 11. Fig. 12.

5 Conclusion

Resource reservation in wireless multi-hop networks is a challenging issue. In this

work, we focus on the problem of resource reservation across the network and also

the problem of congestion in the network.

Avoiding congestion consists in maximizing the minimum remaining capacity of

nodes in the network. In this work, we propose a heuristic to avoid interferences and

ensure a good use of the resources in the network. We compare the performances of this

heuristic and two other heuristics by simulations. The proposed heuristic is better than

the two others in the case a MESH network and also in the case of an Ad-Hoc network.

In further work we propose to discuss about the two parameters given in Section 3

in order to improve these results.

400 S. Rousseau et al.

Acknowledgements

The research has been performed in EU FP6 Integrated Project Chorist No. 033685.

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Low-Cost and Accurate Intra-ﬂow

Contention-Based Admission Control for IEEE

802.11 Ad Hoc Networks

AbdelouahidDerhab

Department of Computer Engineering, CERIST, Rue des 3 fr`eres Aissou,

Ben-Aknoun, BP 143 Algiers, 16030 Algeria

Abstract. In this paper, we propose a new admission control method for

IEEE 802.11 ad hoc networks, called Low-cost and Accurate Admission

control (LAAC). The proposed method has two variants: LAAC-Power

and LAAC-CS. LAAC-Power estimates channel bandwidth availability

through high power transmissions and LAAC-CS through passive mon-

itoring of the channel. Due to the shared nature of the wireless medium,

contention occurs among the nodes along a multi-hop path, which leads

to intra-ﬂow contention. LAAC accurately estimates the intra-ﬂow con-

tention. In addition, an analytical study demonstrates that LAAC

achieves optimal results in terms of overhead and delay compared to the

existing intra-ﬂow contention-based admission control methods. LAAC

also utilizes two criteria for accepting ﬂows: one during the route request

phase and the other during the route reply phase, which helps to reduce

message overhead and avoid ﬂooding route requests in hot spots. Sim-

ulation results show that LAAC-CS outperforms LAAC-Power in terms

of packet delivery ratio, throughput, message overhead, and energy

consumption.

1 Introduction

The increasinguseofreal-time applicationssuchas:teleconferencingandon-

demandmultimediaretrieval, as well as the adoption ofIEEE 802.11 technolo-

gies in ad hocnetworks raise the issue ofhow toensure service guarantee in such

environments characterized byunpredictabletopologynetwork,shared wireless

channel, andwhich impose diﬀerentchallenges on supportingreal-time applica-

tionswith appropriate QoS.

The admitted ﬂowsin the network must notexceed the network capacity. To

doso, the wireless channelmust be kept fromreachingthecongestion point.

Thisgoalishardtoachievesince the channelisnotonly shared betweennodes

that cancommunicate with each other directly, but extends toall nodes within

a certain range,called carrier-sensingrange (CSR), through channelaccess con-

tention. Thisrange istypically much larger thanthe transmission range.Nodes

that are within carrier sensingrange detect a transmission but maynotbeable

todecode the packet.Nodes within the sender’stransmission range are consid-

ered its neighbors,andthose which are within the CSRofasender are called its

carrier-sensingneighbors (CSN).

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 401–412, 2008.

Springer-Verlag Berlin Heidelberg 2008

402 A. Derhab

The admission control must ensure that the network shouldhavesuﬃcient

resource before admittingany newﬂow.Moreover,the ﬂow shouldnotdegrade

the QoS ofexistingﬂows.InIEEE 802.11 MACprotocol, all the CSN ofthe

sender are unabletoinitiate a packet transmission whilethesender istransmit-

ting.Due tothe shared nature ofthewireless medium,Anode’stransmission

consumes bandwidth at all nodes within its vicinity(i.e., carrier-sensingrange).

Let us consider a ﬂow fwith a bandwidth requirement,Breq1,goingthrough a

givenroute.Multiplenodes on the route maylocate within the carrier-sensing

range ofagivennode S,andtheyall contendforbandwidth.The number of

these nodes iscalled the contention count oftheroute andisdenoted as CC.To

make admission control decisionsover a multi-hoppath,itisnotenough toonly

consider the bandwidth availableatasinglenode,since the eﬀectivebandwidth

consumed bythe ﬂow at node Sis:(CC ×Breq).

In thispaper,our originalcontributionsarethefollowing.First,wepropose a

newadmission control methodcalled LAAC,andwhich has two variants:LAAC-

Power andLAAC-CS. Second,unlike other intra-ﬂow admission control methods,

LAACguara

ntees both anaccurate estimation ofthecontention andincurs the

lowest cost in terms of message overhead andenergyconsumption. Usingtwo

admission control criteria,the message overhead is reduced.Inaddition, LAAC

does notincur anadditionaldelayover that incurred byregular route discovery

tomake a multi-hopadmission control decision.

The rest of the paper isorganized as follows:InSection 2,wediscuss related

works.Section 3 presents a newadmission control method.InSection 4,we

analyze the performance LAACaswell as other intra-ﬂow contention-based ad-

mission control methods.Section 5 compares the performance ofLAAC-Power

andLAAC-CS. Section 6 concludes the paper.

2 Related Work

CACP[8]is the ﬁrst work tointroduce the concept ofc-neighborhoodavail-

ablebandwidth,which refers tothe availablebandwidth at a node’sCSNs.The

admission control isintegrated with the route discoveryprocedure ofDSRrout-

ingprotocol [4]. To ensure that all nodes aﬀected bythe transmission ofthe

traﬃc ﬂow haveenough availableresources toallow the ﬂow tobe admitted,

CACPproposes two variants:CACP-Power andCACP-CS. In CACP-Power,

anode that receives a Route Reply (RREP)packet,broadcasts usingahigh

power transmission anadmission request message,which carries the full route

oftheﬂow, toits CSNs.Upon reception of the message,nodes calculate their

CC usingtheirknown CSN andthetheidentityofthenodes on the route.In

CACP-CS, channelavailabilityisestimated through passivemonitoringusinga

thresholdcalled the Neighbor-carrier-sensingThreshold,which islower thanthe

Carrier-sensingThreshold.Anode canthenextendits measurementrange to

enclose the carrier-sensingranges ofall its CSNs.It assumes that any transmis-

sion activityinits neighbor-carrier-sensingrange consumes bandwidth at all of

1The equations to derive Breq from the application rate is given in [8].

Low-Cost and Accurate Intra-ﬂow Contention-Based Admission Control 403

its CSNs,which leads that the admission control rejects ﬂowswhose bandwidth

consumptionsarenotbeyond the capacityofthenetwork.However,CACPhas

severaldrawbacks.First,the admission control decision isdelayed at each node

in order toreceivepossiblerejectionsbefore forwardingthereply. Second,CACP

operates only on asource routingprotocol such as DSR[4]that holds the entire

route.Third,itdoes notpropose any strategytohandlemobilityandloss ofQoS

guarantees.Fourth,CACPdoes note

xplain how the bandwidth at the node’s

CSN isreleased whenthe ﬂow isrerouted orterminated.

Sanzgiriet al. [7]describe two methods,PRPandRRT, toobtain the CC,in

which each node records the duration of the received signalstrength correspond-

ingtoapacketin acarrier sensingtable.Although the packet cannotbedecoded,

its size canbe inferred fromits duration. However,PRPandRRTsuﬀer from

some drawbacks.Anode inside the sender’scarrier-sensingrange cannot deter-

mine the bandwidth consumption because itdoes notknow the value ofBreq.

Moreover,the node that ispartoftheﬂow cannotmakeanaccurate admission

control decision because itignores the eﬀects ofcontendingﬂows.Finally, count-

ingsensed packets ofaparticular duration canproduce erroneous results in the

case ofretransmissionsorcollisionsattheMAClayer.

To compute CC,AAC[2]andTAC-AODV [1] consider that the carrier-sense

range ismore thantwice the size ofthetransmission range.Therefore,everynode

on the path generally interferes with,at most,two upstream anddownstream

nodes,which means that the nodes are supposed tohavethesametransmission

range.However,this assumption isnotalwaystruesince a node canincrease or

decrease its transmission power dependingon its own purposes,andhence the

CC calculation as itisproposed bythe protocolsisnot accurate.

MACMAN [5] uses the same method described in CACP[8]tocalculate CC.

Ittries toimprovetheperformance oftheadmission control bymaintaining

multiplepathstothe destination. Thisallowsasource toquickly switch toan

alternate path that cansupport the ﬂow if the currentpathbecomes unusable.

To avoid the accumulation ofstaleroutes that no longer canprovide the required

QoS, MACMAN continuously monitors each alternativeroute in the cache.To

doso, itsends PeriodicRoute CapacityQuery(RCQ)messages alongeachof

the backup paths towards the destination. The disadvantage ofthismethodis

that itgenerates animportantoverhead on monitoringpaththatmight never

be used.

3 Low-Cost and Accurate Admission Control (LAAC)

Our admission control isintegrated with a route discoveryprocedure ofareactive

routingprotocol similar toAODV [6]. In LAAC,each node imaintainstheﬂow

tableFT

ithat stores foreachﬂow fcirculatingin its carrier sensingrange:

(1) the contention countCCi,f ,and(2)the list ofthecarrier-sensingneighbors

which transmittheﬂow f.The admission control isperformed in two phases

ofroute discovery: (1) route request phase and(2)route reply phase.The aim

ofperformingtheadmission control duringtheroute request phase istoreduce

404 A. Derhab

2req

3req

B1,

3req

2req

1,req

(a)

[1]

[1] [1]

[1]

CSR of D

(b)

[2]

[1]

[2]

[2] [2]

[2]

[1]

CSR of C

(c)

[2]

[1]

[3]

[2]

[3]

[2]

[1]

CSR of B

(d)

[2]

[1]

[3]

[4]

[2]

[4]

[3]

[2]

CSR of A

(e)

Fig. 1. Admission control acceptance in LAAC-Power

the overhead caused bypropagating the RREQ in the wholenetwork.Ifthe

availablebandwidth at a givennode issmaller thanthe bandwidth requirement

oftheﬂow, the admission control fails.The Bandwidth reservation isonly carried

out duringtheroute reply phase.

3.1 Admission Control during the Route Request Phase

Whenasource node wants tosendadataﬂow ftoits destination node,it

broadcasts a RREQ packet toits neighbors.The RREQ contains the bandwidth

requirementBreq,f .Each node that receives the RREQ performs anadmission

control tocheck ifenough bandwidth isavailablefortheﬂow. Iftheadmission

control fails,the RREQ packet isdropped.Iftheadmission control succeeds,

the route RREQ packet cancontinue its propagation through the network.The

question that mayarise ishow anode icandetermine the bandwidth required

bythe ﬂow fduring the request phase without knowingthecontention count

CCi,f .Todealwith thisissue,wepropose togivethelower boundofCCi,f .

Thisboundisbasedon the solution proposed in [10].

In IEEE 802.11, nodes cannottransmitand receivedatasimultaneously. For

any packet transmission, itconsumes the same amountofbandwidth resource

at all the carrier sensingneighbors,because theyshouldnotbeabletouse that

periodoftime forother transmissions.Duringroute request phase,each node

idoes notknow its carrier sensingneighbors,itonly knows the previous node

fromwhich it has received the RREQ packet.Italsoknowsits status (i.e., source

node,intermediate node ordestination node). Based on thisknowledge,the

Low-Cost and Accurate Intra-ﬂow Contention-Based Admission Control 405

[2]

[1]

[3]

[4]

[2]

[4]

[3]

[2]

req

M2,req

(a)

[2,1]

[1]

[1,1]

[3,1]

[4,1]

[4]

[2]

[4]

[3]

[2]

[0,1]

CSR of L

(b)

[2,2]

[1]

[1,2]

[3,2]

[4,2]

[4,1]

[2]

[4,1]

[3]

[2,1]

[2]

[0,2]

CSR of J

(c)

[2,3]

[1]

[1,3]

[3,3]

[4,3]

[4,2]

[2]

[4,2]

[3,1]

[2,2]

[2]

[0,2]

CSR of G

(d)

[2,3]

[1]

[1,3]

[3,4]

[3,3]

[4,4]

[4,2] [2]

[4,3]

[3,2]

[2,3]

[2]

[0,2]

CSR of K

(e)

Fig. 2. Admission control rejection in LAAC-Power

lower boundofCCi,f ,denoted byLCCi,f canbe estimated under the following

conditions:

–Ifiisthesource node (e.g,node Ain Figure 1(a)), itrequires Breq,f for

sending the data,andanother Breq,f isconsumed byits next-hopneighbor.

So, LCCi,f =2.

–Ifiis the destination node (e.g,node Ein Figure 1(a)), Breq,f isconsumed

byits previous node.So,LCCi,f =1.

–Ifiisthelast intermediate node (e.g,node Din Figure 1(a)), itrequires

Breq,f forsending the data,andanother Breq,f isconsumed byits previous

node.So,LCCi,f =2.

–Ifiisnotthelast intermediate node (e.g,node BandCin Figure 1(a)), it

requires Breq,f forsending the data,andanother Breq,f isconsumed byit

previous node andits next-hopneighbor.So,LCCi,f =3.

To admitanewﬂowfduring the request phase,the required bandwidth Breq,f

forfmust meet the followingcondition: Bav >LCC

i,f ×Breq,f.

The variableBav in the condition denotes the availablebandwidth.InFigure

1(a), node Awants tointroduce a newtraﬃc ﬂow 1 tonode Erequiring(B

bits/s,such that:Bdenotes the channelcapacity. The route obtained duringthe

route request phase isshown as a sequence ofdirected links,and the respective

minimum bandwidth requirements are shown adjacenttoeach node ofthisroute.

406 A. Derhab

3.2 Admission Control during the Route Reply Phase

Whenthe destination node receives the RREQ packet,itsends a RREPback

toits previous node (i.e., the nexthoptoward the source), denoted bytarget.

Ifmultiplerequestsarrive at the destination, the destination only sends the

RREPalongoneroute.The other routes are cached forashort periodoftime

as backup in case the ﬁrst RREPdoes notreachthesource due to link breakage

oradmission failure.Inthe reply phase,LAACcanuse oneofthetwo variants:

LAAC-Power orLAAC-CS. In LAAC-Power,reply packets are sentusingalarger

transmission power levelthanthe transmission power levelused fornormaldata

transmission. Usingthis approach,the reply packets fromthesender canreach

all ofits c-neighbors.InLAAC-CS, channelavailabilityisestimated in the same

wayas suggested in [8].

LAAC-Power. In LAAC-Power,anode that receives the RREPpacket,exe-

cutes the pseudo-code presented in Algorithm 1.

Ifthereisenough availablebandwidth fortheﬂow f,asoft reservation of

bandwidth issetupin the node and a RREPpacket isforwarded toits previous

node usingahigh power packet transmission. Forexample,inFigure 1(b), nodes

B,C,E,H,I,J,andL,which are CSN ofnode D,set theirCCi,1to1after

receiving a RREPpacket fromnode D.The respectivecontention counts ofthe

ﬂowsareshown adjacenttoeach node.Asthereply packet traverses nodes C,

B,andA,each node ithat receives the high power RREPpacket transmission,

increases its CCi,f by1(See Figures 1(c), 1(d), 1(e)).

In Figure 2,node Kwants tointroduce a newtraﬃc ﬂow 2tonode M

requiringB

7bits/s.After the admission control has succeeded duringtheroute

request phase (See Figure 2(a)), node Mbroadcasts a reply packet with target =

K(See Figures 2(b), 2(c), 2(d)). Upon receivingthereply packet,the source node

Kﬁnds that the totalreserved bandwidth is:(2Breq,1+3Breq,2)=(

7)B.So,it

broadcasts a reply packet usingahigh power packet transmission. Whennode G

receives such a message (See Figure 2(e)), itﬁnds that (4Breq,1+4Breq,2)=(

7)B.

Itconcludes that ﬂow 2will hinder the existingﬂow 1. Then, itsends a Reject

packet toK,which will sendanError packet toM.

To refresh orrelease the bandwidth reservation, we suggest toencapsulate

two bits in the IP option ofeverydata packet,which are:

–BitM(More), itissetto1iftheﬂow containsother packets that need to

be transmitted.Otherwise,Missetto0ifthethepacketisthelast oneof

the ﬂow.

–BitHP (High Power): Itissetto1if the data packet needs tobe transmitted

at high power level.

After a bandwidth alongtheroute isestablished,the source node starts sending

data packets with (M,HP )=(1,0), which indicates that the correspondingﬂow

containsother packets,and the data packet shouldbesenttothe destination

node usinganormalpower packet transmission. To refresh the existingsoft-

reservation at nodes within the carrier sensingrange oftheﬂow, the source

Low-Cost and Accurate Intra-ﬂow Contention-Based Admission Control 407

Algorithm 1. LAAC-Power at node i

When i receives a RREP(target) from j

1: if (B−



g∈FT

(CCi,g ×Breq,g )>B

req,f)then

2: if (fexists in the ﬂow table) then

3: CCi,f := CCi,f +1;

4: else

5: Create a new entry for fin the ﬂow table ;

6: CCi,f := 1;

7: end if

8: if (i=target)then

9: if (i=source node)then

10: target := φ;

11: else

12: target := previous node in the route;

13: end if

14: Broadcast RREP(target) using a high power packet transmission

15: end if

16: else

17: if (i=target)then

18: Send ERROR packet toward the destination using a high power packet trans-

mission;

19: else

20: Send Reject to j using a high power packet transmission;

21: end if

22: end if

node periodically sends a data packet with (M,HP )=(1,1), which meansthat

the packet shouldbesenttothe destination node usingahigh power packet

transmission. The last data packet issentwith (M,HP)=(0,1). Upon receiving

thispacket,each intermediate node releases the bandwidth associated with the

ﬂow f,andsends in turnthe data packet usingahigh power packet transmission.

In thismanner,the bandwidth reserved at nodes within the carrier sensingrange

oftheﬂow isalsoreleased.

LAAC-CS. In LAAC-CS, apassive approach isusedtoobtain c-neighborhood

availablebandwidth.The node that receives the route reply directly estimates

its c-neighborhoodavailablebandwidth using the equation presented in [8]and

compares itwith the bandwidth consumption oftheﬂow tomake admission

decisions.

3.3 Node Mobility

Ifthelinkbetweentwo nodes oftheﬂow route fails,e.g,nodes BandCin

Figure 3(a), the bandwidth reservation along the partialroute [C, E]isreleased.

Moreover,anode decreases its CCi,f by1foreachnode that belongs toboth

the partialroute andthelist ofthecarrier-sensingneighbors which transmit

the ﬂow f(See Figure 3(a)). AsAODV isnotthesource routingprotocol, node

408 A. Derhab

[0]

[1]

[2]

[0]

[2]

(a)

[1]

[0]

[1]

[2]

[3]

[0]

[3]

[2]

[3]

[2]

[1]

CSR of J

(b)

[2]

[0]

[2]

[3]

[4]

[0]

[4]

[3]

[4]

[2]

[1]

CSR of G

(c)

Fig. 3. Flow restoration

Bdoes notneed tonotifythe source about thisevent,itlocally tries toﬁnd

analternativeroute toward the destination, and the bandwidth reservation is

established using the same methodexplained in Section 3 (See Figure 3(b)and

Figure 3(c)). Ifanode suﬀers fromQoS violation due tothe mobilityofsome

nodes,andconsequently theirﬂows,inits vicinity, itwill sendQoS Lost message

toward the source node.Upon reception ofthis message,the source node will

interrupt the generation ofits ﬂow. After a back-oﬀ randomtime,the source

node will generate a newRREQ fortheinterrupted ﬂow in order todiscover a

newroute tofulﬁlits request.

4 Analytical Comparison

In this section, weanalyze the performance of the proposed admission control

methodandcompare itwith CACP, PRP, RRT, AAC,TAC-AODV, andMAC-

MAN. The performance isstudied under the followingmetrics:the number and

size ofcontrol packets,the additionaldelayincurred in makingtheﬂow admis-

sion control decision, the accuracyofCCcalculation, andtheenergycomplexity,

which measures the energyrequired toperform a successfuladmission control.

Note that thisperformance isforasingleﬂow. The results ofcomparison are

shown in Table1. In the table,w

eusethenotationsgivenin[7], which are as

follows:NandMdenote the number ofnodes in the network andthenumber

ofnodes on the path respectively. Q,P,S,IandJdenote the size of RREQ,

RREP, RPRM, RREQ tail in RRT, node ID, andshort integer respectively. D1

andD2are constants used in CACP-Power andPRPrespectively. We assume

that the nodes are randomly distributed in aregion ofareaA.The node density

remainsconstantwhenthe number ofnodes increases,andtheareaAgrows

with N.Since the expected distance oftwo uniformly sampled points within a

square ofsize a×ascales with a[3], itisexpected that the number ofhops

betweentwo randomnodes increases proportionalto√N.Wealsoassume that

the Q,P,andIare proportionaltologN.The energydissipated totransmitK

bits usinganormalpower,andahigh power transmission, are proportionalto

O(K), and(α×K)respectively. IfweholdJ,T,andαas constants,therefore

wegettheenergycomplexities shown in Table1.

Low-Cost and Accurate Intra-ﬂow Contention-Based Admission Control 409

Table 1. Comparison of intra-ﬂow contention-based admission control methods

Metrics CACP-Power CACP-CS RPR RRT

RREQ sent N N N N

RRRP sent M M M M

Other packet sent M(High Power) 0M0

RREQ size Q+M×I Q +M×I Q Q +M×J+T

RREP size P+M×I P +M×I P +J P +M×J

Other packet size M×I0S0

Extra delay M×D10D20

Energy complexity O(N3

2log N)O(N3

2log N)O(Nlog N)O(N3

The accuracy of Ye s N/A No No

CC calculation

Metrics AAC/TAC-AODV MACMAN LAAC-Power LAAC-CS

RREQ sent N N N N

RRRP sent M M M(High Power) M

Other packet sent 0N(High Power) 0 0

RREQ size Q Q +M×I Q Q

RREP size P P +M×I P P

Other packet size 0I0 0

Extra delay 0 0 0 0

Energy complexity O(Nlog N)O(N3

2log N)O(Nlog N)O(Nlog N)

The accuracy of No Yes Yes N/A

CC calculation

In CACPandMACMAN, RREQ and RREPcarrythe IDsofthenodes on

the route.Thus,the control information piggybacked ontothe packets are of

the size ofM×I.AsforPRP, its RREPpacket containsthelength ofthe

probe packet Jsentbythe destination. RREQ in RRTcarries the lengths ofthe

tailsappended bynodes on the path,which causes the packet size toincrease by

M×J.Additionally, the RREQ packet carries the tail appended bythe last node

traversed,which causes a further increase ofTin the packet size.Our method,

AACandTAC-AODV, on the other hand,donotpiggyback any additional

control information ontoRREQ or RREP.

The forwardingof the RREPinCACP-Power isdelayed at each intermediate

node byD1time units.So,the extra delayincurred tomake multi-hopadmission

control decision isM×D1.AsforPRP, the RREPisdelayed D2time units by

the destination. CACP-CS, RRT, AAC,TAC-AODV, MACMAN andour LAAC

all ofwhich require no additionaldelayover that incurred bythe route discovery

procedure.

CACP-Power,MACMAN andLAAC-Power canmake more accurate admis-

sion control decision andCC calculation thanthe other intra-ﬂow contention-

based admission control methods.Forexample,AAC,TAC-AODV assume that

all nodes havethesametransmission andcarrier-sensingrange andhence each

node on the path has,at most,two upstream anddownstream c-neighbornodes.

Thischange isnot true because nodes are abletochange the size oftheirtrans-

mission range.Therefore,AACandTAC-AODV cannotgiveanaccurate esti-

mation ofCC in case of heterogenous ad-hocnetwork.RPRandRRTdonot

giveanaccurate calculation ofCC because ofseveralreasons:First,theyignore

the eﬀects ofcontendingﬂows.Second,inorder tomake a correct admission

410 A. Derhab

control decision, nodes need toknow the resources that a ﬂow will consume if

admitted,RPRandRRTdonotexplain how anode canobtain the value of

Breq.Third,itisnotexplained how anode that senses packets candistinguish

betweenMACcontrol packets that haveﬁxed sizes andother packet,andhence

the assumption that each node transmits packets usingaunique duration isnot

true.

Fromthisstudy, wecanconclude that amongtheintra-ﬂow contention-based

admission methods presented earlier,LAACappearstobe the onethatensures

two properties:(1)itincurs the lowest cost in terms of message overhead,energy

consumption, extra delay, and(2)it accurately estimates CC.

5 Simulation Results

In this section, westudythe performance ofLAAC-Power andLAAC-CSusing

GloMoSimsimulator[9]. Our simulation environmentis characterized by25

nodes movingin the area of1000m×1000m,with randominitialnodes’location.

Nodes moveaccordingtothe waypointmobilitymodel. In thismodel, anode

randomly selects a location andmoves toward itwith a constant speed uniformly

distributed betweenzeroandamaximum speed Vmax,thenitstaysstationary

duringapausetime of1secondbefore movingtoanewrandomlocation. In

the Glomosimimplementation, radio transmission range issetto376mandthe

carrier-sensingrange issetto688m.The bandwidth ofthechannelis2Mbps.

0.2

0.4

0.6

0.8

5 10 15 20 25

Data packet delivery ratio

Vmax

(

m/s

)

LAAC-Power

LAAC-CS

(a)

100000

200000

300000

400000

500000

600000

700000

800000

900000

5 10 15 20 25

Throughput(bits/s)

Vmax

(

m/s

)

LAAC-Power

LAAC-CS

(b)

2000

2500

3000

3500

4000

4500

5000

5500

5 10 15 20 25

Overhead

Vmax

(

m/s

)

LAAC-Power

LAAC-CS

(c)

5620

5640

5660

5680

5700

5720

5740

5 10 15 20 25

Energy consumption (mWhr)

Vmax

(

m/s

)

LAAC-Power

LAAC-CS

(d)

Fig. 4. LAAC Performance

Low-Cost and Accurate Intra-ﬂow Contention-Based Admission Control 411

Six pairs ofnodes are randomly chosentoestablish connectionswith a 512B 100

packets/sCBRtraﬃcsource.The simulation runsfor900 seconds.Weevaluate

the performance ofLAAC-Power andLAAC-CSusingthefollowingfour metrics:

–Data packet delivery ratio: Thisisthefraction of data packets sentbya

source node that reach the destination.

–Message overhead: Itmeasuresthenumber of messages generated bythe

routingprotocol as well as the control admission.

–Throughput: Istheamountof data packet received bydestination nodes.

–Energy consumption: Isthetotalamountofenergyconsumed duringsimu-

lation.

Figures 4 showsthatLAAC-CSoutperforms LAAC-Power in terms ofthefour

metrics.Thisis due tofact that the c-neighborhoodavailablebandwidth estima-

tioninLAAC-CSisconservative,andhence a fewnumber ofﬂows are accepted.

AsLAAC-Power accepts more ﬂowsthanLAAC-CSdoes,ithastogenerate

more control routingpacketstomaintain routes,andhence itconsumes more

energypower.LAAC-Power sends some control and data packets usingahigh

transmission power levelandmayinterfere with more nodes thana message at

the normalpower level. In addition, due tonode mobility, interference between

two ormore accepted ﬂowscanoccur.Thissituation leads that network conges-

tioninLAAC-Power occurs more frequently, andhence itincurs low throughput

andlow data packet deliveryratio thanthat in LAAC-CS.

6Conclusion

In thispaper,wehaveproposed anadmission control method,which canbe inte-

grated with any reactiveroutingprotocol. LAAChastheadvantage that itdoes

notneed tocarryinformation about the entire route like in CACP, PRP, RRT,

andMACMAN. Itcanaccurately estimate the contention countwithout incur-

ringhigh message overhead,energyconsumption, andextra delay. Si mulation

results haveshown that LAAC-CSoutperforms LAAC-Power in terms ofdata

packet deliveryratio, throughput,message overhead,andenergyconsumption.

References

1. Cerveira, C.R., Costa, L.H.M.K.: A time-based admission control mechanism for

ieee 802.11 ad hoc networks. In: 8th IFIP/IEEE International Conference on Mobile

and Wireless Communication Networks (MWCN 2006), pp. 217–228 (August 2006)

2. de Renesse, R., Ghassemian, M., Friderikos, V., Aghvami, A.H.: Adaptive admis-

sion control for ad hoc and sensor networks providing quality of service. Technical

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2005)

3. Dunbar, S.R.: The average distance between points in geometric ﬁgures. College

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ski, T., Korth, H. (eds.) Mobile Computing, ch. 5, pp. 153–181. Kluwer Academic

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quest tail: approaches for calculation of intra-ﬂow contention in multihop wireless

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D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 413–424, 2008.

An Energy-Efficient Query Aggregation Scheme for

Wireless Sensor Networks

Jun-Zhao Sun

Dept. Electrical & Information Engineering, University of Oulu, 90014 Finland

junzhao.sun@ee.oulu.fi

Abstract. This paper presents a novel method for optimizing sliding window

based continuous queries. We deal with two categories of aggregation

operations: stepwise aggregation (e.g. COUNT) and direct aggregation (e.g.

MEDIAN). Our approach is, by using packet merging or compression

techniques, to reduce the data size to the best extent, so that the total

performance is optimal. A QoS weight item is specified together with a query,

in which the importance of the four factors, power, delay, accuracy and error

rate can be expressed. An optimal query plan can be obtained by studying all

the factors simultaneously, leading to the minimum cost. Experiments are

conducted to validate the effectiveness of the proposed method.

1 Introduction

Sensor nodes have very limited supply of energy, and should be available in function

for extremely long time without being re-charged. Therefore, energy conservation

needs to be one key consideration in the design of the system and applications.

Extensive research work has been devoted to address the problem of energy

conservation.

At high level, a sensor network can be modeled with a database view. Continuous

query is commonly used for collecting periodical data from the objects under

monitoring. This query needs to be carefully designed, in order to minimize the power

consumption and maximize the lifetime. Data reduction techniques can be employed

to decrease the size of data to be transferred in the network, and therefore save energy

of sensor nodes.

This paper presents a method for the optimization of continuous query, and in

particular, for the last stage of query processing: query result collection. The key

novelty of the method lies on the careful consideration of QoS issue along with data

gathering. By taking advantage of the QoS constraints on power, delay, accuracy, and

error rate specified with a query, the method can find the optimal combination of

transmitting sensor data to sink.

A query representation scheme is proposed, in which SQL based grammar is

extended with sliding window, QoS constraint weight item, and sample clause. Then,

a sample system model is created to model power consumption and time cost for both

computation (data processing) and communication (data transmission). After that, a

novel method is proposed for the optimization of continuous query with stepwise

414 J.-Z. Sun

aggregation (e.g. MAX, MIN, SUM, COUNT, AVERAGE, etc.). The method is

described in detail including the determination of both sample rate and data

integration. Similar method is presented for the optimization of continuous query with

direct aggregation (e.g. MEDIAN). The similarity and variation of the previous

method are discussed.

2 Query and System Models

A sensor field is like a database with dynamic, distributed, and unreliable data across

geographically dispersed nodes from the environment [1, 2]. Sensor network appli-

cations use queries to retrieve data from the networks. Query processing is employed

to retrieve sensor data from the network [3, 4].

SQL-based query language is commonly accepted in specifying queries for sensor

networks as well. Below are two simple examples query in the form of extended SQL.

// Example query 1

SELECT WINMEDIAN(S.temperature,10min,2min)

FROM sensors AS S

WHERE S.location=Area_C

WHILE delay<10min AND accuracy>0.9 AND error<0.01

WEIGHT (power,time,accuracy,error)=(0.4,0.1,0.3,0.2)

SAMPLE

ON Now + 5 min

RATE min 100

//Example query 2

SELECT WINCOUNT(*,10min,2 min)

FROM sensors AS S

WHERE S.location=Area_C AND S.temperature>4C

WHILE delay<10min AND accuracy>0.9 AND error<0.01

WEIGHT (power,time,accuracy,error)=(0.4,0.1,0.3,0.2)

SAMPLE

ON 00:00:00

RATE min 100

These are two queries to be performed upon streaming data by using a sliding

window. Here, delay in WHILE clause is as the QoS constraint. The WEIGHT clause

gives the weights of the factors in the quality-cost trade-off, by which the query plan

can be optimized. In the two examples above, four factors are considered as the

weight items, power consumption, report delay in time, and the accuracy and error

rate of the result.

Data reduction is to decrease the size of data that is needed in the communication.

Various data reduction techniques exist in this context. Packet merging is a simple

data reduction technique, which combines multiple small packets into a big one,

without considering the correlations between and the semantics within individual

packets. Packet compression is to integrate one or multiple packets into a reduced

packet, by employing suitable data compression algorithms. A number of comp-

ression algorithms have been studied for sensor networks [5-8]. Data aggregation is

used in aggregate query to summarize a set of sensor into a single statistic, like MAX,

An Energy-Efficient Query Aggregation Scheme for Wireless Sensor Networks 415

MIN, AVERAGE, MEDIAN, COUNT, etc. Data fusion refers to more complex

operations above a set of readings and are usually used in multimedia data processing.

The complexity of data aggregation and fusion leads to higher cost in terms of both

energy and time.

This paper concentrates on the optimization of periodical aggregation queries

during result collection. We mainly consider the situation where there are both delay

and accuracy constraints, a weight item, and aggregation operations of average and

count to be performed over collected data in the query. The paper is targeting to

queries that have average/count aggregation operations. In periodical query most

information in packet header (e.g. node ID, query ID, addresses, etc.) is the same

across all the reading, and therefore can be shared. Also, it is reasonable to expect

high spatial-temporal correlation between sample data collected in periodical query

from single node, and therefore the data compression rate can be fairly high. Thus, we

believe packet merging and compression techniques are suitable in this context.

Data reduction ratio, ru can be defined as D’(u) = D(u) (1 – ru), where D(u) is the

data size before reduction, and D’(u) is the size after, D’(u) ≤ D(u). Obviously, a

higher ru is expected. The real value of ru is mostly depending on the

merging/compression algorithms utilized as well as the similarity/correlation between

data samples.

A query plan is executed with two components, computation and communication.

Energy cost resulted from data processing, EP(u) denotes energy consumption for the

data processing at the node u. Energy consumption for single data processing at a

specific node u is fixed, and so can be represented by a constant ESDP(u). Energy cost

for multiple data processing depends on the amount of data to be processed as well as

the algorithms utilized. First the unit processing cost on node u is defined as EPU(u).

Then, the cost for processing the D(u) amount of data at node u is given by EP(u) =

ESDP(u) + EPU(u) D(u). Here D(u) is usually a set of sample result data for one single

or different queries. Similarly, we can define the time for data processing, TP(u) as

TP(u) = TSDP(u) + TPU(u) D(u), where TSDP(u) is the time for single data processing at

node u and TPU(u) is the unit processing time at this node.

The EPU and TPU are relevant to data reduction ratio ru, depending on the

processing algorithm used. Basically, the higher the ru, the higher the EPU/TPU. For

example if a simple packet merge is performed, then ru will be very small, and the

corresponding EPU and TPU will be very low. On the contrary, if some complex data

compression algorithm is utilized, then a much better ru will be reached with fairly

high EPU and TPU.

Transmission cost denotes the cost for transmitting D(u) amount of data (i.e. packet

header plus payload) from node u to node v through link e = (u, v). The cost includes

the energy consumption at both u and v. Unit cost of the link for transmitting data

between two nodes can be abstracted as EU(e), and thus the transmission cost ET(e) is

given by ET (e) = ETU(e) D(u). The unit transmission cost on each edge, ETU(e), can be

instantiated using the first order radio model presented in [9]. According to this

model, the transmission cost for sending one bit from one node to another that is d

distance away is given by

when d < rc, where rc is the maximal

communication radius of a sensor, i.e. if and only if two sensor nodes are within rc,

there exists a communication link between them or an edge in graph G;

and

are

416 J.-Z. Sun

tunable parameters based on the radio propagation, and

denotes energy consumption

per bit on the transmitter circuit and receiver circuit. Similarly, transmission time TT

(e) is given by TT (e) = TTU(e) D(u), where TTU(e) is the unit transmission time, i.e. the

reciprocal of bandwidth, whose value is depended on the condition of the link. We

note that all the cost and time parameters are all defined on link e, because different

link has different conditions e.g. distances, congestion, and reliability.

The model above can be easily extended to the transmission cost and time for a

path, which are the ones utilized in this paper. The cost and time for D(u) from one

node x to another node y through a multihop path x->y can be represented as E(D(x):

x->y) = ∑

>∈ y x-e

TeE )(+

∑

>∈ y x-u

PuE )( and T(D(x): x->y) =

∑

>∈ y x-e

TeT )(+

∑

>∈ y x-u

PuT )(.

3 Query with Stepwise Aggregation

We first study the problem of sliding window based continuous query on data stream

with stepwise aggregation, i.e. the Example query 2 above in Section 2. Stepwise

aggregation includes for example MAX, MIN, SUM, COUNT, AVERAGE. Without

loosing any generality, in this section, we will take COUNT aggregation as an example.

To formalize the problem to be addressed, there are following assumptions.

1) Sliding window: this is a sliding window based continuous query, with window

size (length) of Tw (10 min in the example )and sliding increment Ti (2 min in

the example).

2) Constraints: there is a delay constraint dMAX (maximum allowed delay, 1h in the

example), an accuracy constraint 1-αMIN (minimum confidence interval, 0.9 in

the example), and an error constraint eMAX (maximum packet error rate, 0.01 in

the example) specified in the queries. A minimum sample rate is also specified

as rMIN.(in samples per hour, 100 in the example).

3) Weight: there is a weight item presented in the query denoting the tradeoff

between power consumption and QoS of result report, as (power, time,

accuracy, error) = (Wp, Wt, Wa, We ).

4) MPS: in this paper, we also assume that there exist a constraint on the Max

Packet Size (MPS) of the whole sensor network.

As shown in Figure 1, there are four steps of data processing at each single sensor

node. First, a stream of readings are samples, next a count stream is generated

according to the window size, then the node receives from other nodes their local

results, and finally the node aggregates the results together and conduct data reduction

by using techniques introduced in Section 2.

The criteria of choosing the best query plan lies on the satisfaction of query issuer

to the best extent, by taking all the factors in the weight item (i.e. power, time delay,

accuracy, and error probability) in to account. Moreover, there are two obvious

constraints affecting the decision making. First, size of the integrated data packet

should be less than MPS. Second, the delay constraint specified with the query should

be obeyed.

An Energy-Efficient Query Aggregation Scheme for Wireless Sensor Networks 417

5 3 -1 0 3 6 5 5 2 0 3 7 4 6 3 2 5 7 2 0

3 3 3 2 3

time

5 7Header 4 5

1.Readings

4. Aggregation &

Reduction

2. Counts

2 4Header 1 3 3. Received from

other nodes

Fig. 1. Data processing in a node

Therefore, the problem under study can be formalized as two questions:

Question 1: how to find the best number of samples, ns in one window size (i.e.

sample frequency, see step 1 in Figure 1), and

Question 2: how to find the maximal number of sample data (can be 1), ni to be

integrated (step 4 in Figure 1),

so that trade-off denoted by the weight item leads to optimal result.

The answer of Question 1 has nothing to do with data transmission, but only data

processing. This means only power consumption and accuracy need to be considered,

without taking delay and error rate into account. Therefore, following node cost

function can be defined as

C1(ns)= )n(A

)n(E

p⋅

+⋅

+ (1)

where Wp and Wa are the weights assigned to factors power and accuracy respe-

ctively, and )n(E s

Pand )n(A s

Rare normalized energy consumption of data proce-

ssing and accuracy reciprocal respectively. The cost function denotes the total energy

and accuracy costs of one specific window size, the less the better. Normalization of

power consumption and accuracy reciprocal needs more study. First, since power

consumption results only from data processing, the energy cost is given by EP(ns) = ns

(ES + ECU DRU), where ES is sample energy, ECU is unit energy for Count operation,

and DRU is the size of one reading data. To perform the formalization, we need to find

out the maximum possible number of sample in the sliding window, ns-MAX.

Obviously, we can simply assume that the maximum sample rate occurs in the case

the node samples each time when the node wakes up. However in practice, the real

maximum sample rate must be much lower than the case. This is because the lifetime

goal of a sensor network is often explicitly defined. In [2] the maximum sample rate

(in samples per hour) is estimated according to the remaining battery capacity of the

node, the specified lifetime of the sensor network, and the energy to collect and

transmit samples. Taking advantage of this estimation, the formalization of the energy

cost is given by

)n(E

MAXsP

−

=. (2)

418 J.-Z. Sun

The accuracy of the result is represented by the reciprocal of the length of the

confidence interval, and thus is relies on the estimation method. The Boolean result of

whether an attribution is larger than a threshold (S.temperature > 4 C in the example)

is a random variable whose probability distribution is (0 – 1), i.e. P (ValueOfAttribute

> Threshold) = p. Query is used to estimate this probability, p by p = Count / ns. As

to (0 – 1) distribution, its expectation is p and variance is p(1-p). According to Central

Limit Theorem, when number of samples is big, the distribution of )p(pn

pnCount

−

1 is

approximately N (0, 1). Therefore, the accuracy of the estimation with ns samples is

given by

)n(A

⋅σ

=, where σ is the variance and zα/2 is the α quantile of

standard normal distribution. The minimum accuracy can be easily obtained by

MINs

MIN

)n(A

−

−⋅σ

=, where ns-MIN is given by ns-MIN = rMIN Tw.

The normalized accuracy reciprocal )n(A s

R is given by

)n(A

MINs

−

=. (3)

Note that even the variance is unknown, the normalization can still be performed.

By using formula (2) and (3) to (1), we can obtain '

n = arg min ns (C1(ns)). Thus,

the answer of Question 1 is given by

ns = (ns-MIN < '

n< ns-MAX, '

n, ( '

n>ns-MAX: ns-MAX, ns-MIN)). (4)

The answer of Question 2 concerns both local data processing (step 2 to 4 in Figure 1)

and data transmission. Suppose a data integration technique is to be utilized above a

stream of results (local counts or counts received from other nodes), the algorithm

focuses on finding the maximal number of samples, ni that optimizes trade-off items

of the query. According to the MPS, delay, and error constraints, we have the

following three arguments. For any selected node u, first, ni1(u)= arg maxni (D’(u) <

MPS), where size of data after data reduction D’(u) = D(u) (1-ru) = (Header_Size + ni

DCU)(1-ru), with DCU the size of one count result (most probably attached with a

sequence number of time stamp). Second, ni2(u)= arg maxni (dW(u) < dMAX), where dW

(u) = (ni – 1) Ti + T(D’(u): u->s) denotes the time of waiting and sending the

integrated packet. Third, ni3(u)= arg maxni (ep(ni) < eMAX), where ep(ni) = 1 – (1 –

eb(u))D’(u) is the packet error rate and eb is the bit error rate of the link from local node

to its parent node. The eb is affected by both the data transmission rate and the signal

power margin, and can be obtained from empirical estimation.

Finally, a global cost function, C2 can be defined as

C2(ni)= )n(e

)n(d

)n(E

edp

p⋅+⋅+⋅

(5)

An Energy-Efficient Query Aggregation Scheme for Wireless Sensor Networks 419

where Wp+d+e= Wp+Wd+We, and E’, d’ and e’ are formalized energy consumption,

time delay and packet error rate respectively. The cost function denotes the total costs

of one specific query plan, the less the better. Normalization of power consumption,

time delay and error rate can be performed as follows.

∑

∀

+>−+⋅

>−

uCUi

TP )su:)Size_HeaderD((En

)su:)u('D(E

)n(E

selected

(6)

MAX

TP d

))su:)Size_HeaderD((Tdw(

)n(d MAX >−+−

=∀

selected (7)

MAX

)u(D

))u(e((

)n(e

MAX −−

=∀

related (8)

Here the energy consumption and time delay concerns both data processing (as

depicted in Figure 1) and data transmission during the entire path from local node to

sink. According to the cost function in formular (5), we have ni4 = arg minni C2(ni).

And finally, the number of samples is given by

ni = min (ni1, ni2, ni3, ni4) (9)

4 Query with Direct Aggregation

Direct aggregation is different from stepwise aggregation in the sense that, direct

aggregation cannot be performed until all the aggregation data is available. In other

words, it cannot be executed upon partial data. In this section, without loosing any

generality, we simple take MEDIAN as an example. Figure 2 illustrated the basic idea

and key processes of this sort of query.

5 3 2 4 3 2 4 2 4 5 3 5 4 6 3 3 4 2 4 4

3 3 4 4

time

3 3Header 4 4

1.Readings

4. Reduction

3. Median

2. Transmission

4 2 0 1 3 6 2 1 2 4 6 2 6 6 2 7 2 3 4 3

5 3 -1 0 2 4 3 3 0 0 3 7 4 3 3 2 5 7 2 0

3 2 4 5 5 4 5 5 5 3 7 3 5 4 6 2 5 7 2 5

Fig. 2. Data transmission and processing

The most crucial difference the sliding window based continuous MEDIAN query

(query example 1) with the one in Section 3 (COUNT query over stream data, query

420 J.-Z. Sun

example 2) is that in query 2 COUNT is a monotonic and summary aggregate which

means its value can only get larger as more values are aggregated, while on the other

hand allows partial aggregation with other count values (as step 4 in Figure 1). Instead

as for query 1, MEDIAN is an exemplary aggregate computing some property over

the entire set of values, and therefore does not allow partial aggregation. In other

words, the aggregation cannot be performed until all the concerned data is available.

This means in query 1 there will be more data transmission.

The query is executed with two steps. First, all the readings are sent to a node who

is the common ancestor of all the concerned nodes for MEDIAN aggregation. Next, a

stream of median aggregation results is sent to the sink. In the second step, the

problem is simple and the problem of data reduction (i.e. find out the best ni) can be

directly solved with the method introduced in Section 3, by simply assuming ns=1.

Therefore without losing any generality, here we assume that the common ancestor

node is exactly the sink node.

As to query 2 in the previous section, the answers of the two questions (i.e. to find

out ns and ni) are independent. While in query 1 the key is still to find the answers for

the same questions, they are actually correlated due to the time reason and therefore

should be jointly considered. Also, in answering Question 1, the main difference of

query 1 with query 2 is that in query 2, we need to simply concentrate on one local

node, to decide the window size for it which is actually common to all the rest

concerned sensor nodes. Instead, in query 1 we have to first find out the total

population of samples for all the selected sensor nodes (hereafter suppose the number

is m) according to the WHILE clause (S.location = Area_C as the condition in the

example above), and after that uniformly assign to each node a number of samples for

one window size.

After the discussions above, a global cost function for query 1 can be defined as

)n,n(dW)n(EW)n,n(C is

TPdi

TPpis ++ += )n(eW)n(AW i

pes

Ra ++ (5’)

All the formula (6) to (9) in previous section are applicable here for query 1, unless

the Ti for getting dW should now be replaced by sample interval Tw/ns.

Another difference is, instead of (0, 1) distribution as in query 2, here for

MEDIAN aggregation, the distribution of the concerned random variable is usually

assumed as either normal distribution or uniform distribution. To normal distribution

the derivation is the same as previous section. As to uniform distribution, by using the

same approximating method of Central Limit Theorem, method in previous section is

still applicable.

5 Experiments

In this section, we validate the effectiveness of the proposed algorithm. We assume

that all the sensor nodes are homogeneous. Table 1 shows the system and query

parameters values used in the performance analysis. We assume an average TTU(e) is

available and thus we can define a number of hops (noh) to represent the distance

An Energy-Efficient Query Aggregation Scheme for Wireless Sensor Networks 421

from the end node to sink (10 in this paper). We study three data reduction scenarios.

The first one is based on packet merging (PM), in which the ru can be derived by

ru = )DSph(n

DnSph

RUi

+⋅

⋅+

−=− 11 . (10)

where Sph is header size (15 bytes in this paper). The second scenario is to employ

packet compression (ru1) with ru = 0.3 (ru2), and for the third ru = 0.8 (ru3). We

study the example query 2 with two weight item settings: (Wp, Wt, Wa, We) = (0.6,

0.1, 0.1, 0.2) and (0.1, 0.1, 0.5, 0.3). The target sensor network is simplified so that

there is only one selected node which is of 10 hops to sink.

Table 1. Parameters values used in performance analysis

System parameters

parameter value parameter value

100 pJ/bit/m2 Es 10 nJ/bit

2 ru PM, 0.3, 0.8

90 nJ/bit Header Size 15 bytes

d 10 m DRU 2 bytes

EPU 20 nJ/bit MPS 2k bytes

TPU 0 ns/bit noh 10

ETU 100 nJ/bit ns-MAX. 1 / ms

TTU 0.02 ms/bit

Query parameters

parameter value parameter value

dMAX 1 h Tw 10 min

1-αMIN 0.9 Ti 2 min

eMAX 0.01 rMIN 100

er 10 E-5

(Wp, Wt, Wa, We ) w1: (0.7, 0.0, 0.1, 0.2)

w2: (0.1, 0.0, 0.6, 0.3)

Two experiments are designed to valid the methods for answering Questing 1 and 2

respectively. Figure 3 shows the result of experiment 1. The figure clearly demo-

nstrates the effect of the weight item. In case of w1, power consumption is deemed

more important than accuracy (0.7 vs. 0.1), therefore a relatively small ns (204) is

obtained than the case of w2 (ns=2455) in which accuracy is emphasized more than

energy (0.6 vs. 0.1).

Figure 4 – 8 illustrate the results of experiment 2, in which the number of data

integration ni is being found. In Figure 4, ni1 is found via data size. Obviously, ru and

MPS play key roles for this calculation. In Figure 5, ni2 is found via waiting time. In

our setting the maximum delay allowed is large, and so the time for data processing

and transmission is tiny. The resulted number thus is depended mostly on sliding

increment vs. delay. This is why the three scenarios of ru1-3 all return the same

result. Figure 6 depicts the result of finding ni3 via packet error rate. Again D’(u) is

the key factor influencing the results.

422 J.-Z. Sun

Fig. 3. Finding sample rate ns Fig. 4. Finding integration number ni1

Fig. 5. Finding integration number ni2 Fig. 6. Finding integration number ni3

Fig. 7. Finding number ni4 for w1 case Fig. 8. Finding number ni4 for w2 case

An Energy-Efficient Query Aggregation Scheme for Wireless Sensor Networks 423

Figure 7 and 8 are more interesting, illustrating the trade-offs between error rate

and power consumption. The effect of time delay is neglected because the setting is

large (1 hour) and therefore the item in the weight is set to 0 for both w1 and w2.

When n is small, the cost is relatively high. Then cost decreases with increasing n.

This is the benefit gaining from energy saving due to data reduction. From some point

of n, the cost starts to increase again. This is because the increase in packet size leads

to the increase of packet error rate. This effect is much clearer in case of w2, if

comparing the two figures. This is due to the fact that w2 considers error rate more

than power consumption. Finally, it is easy to understand that large ru always

performs better.

6 Conclusions

A novel method is proposed to optimize the execution of periodical queries with

COUNT and AVERAGE aggregations, by jointly considering four QoS factors

including energy consumption, time delay, result accuracy and packet error rate.

Algorithm is described in detail. Experiments are conducted to validate the method.

Results show that the proposed method can achieve the goal of query optimization.

Future work includes to study the effectiveness of adaptive sampling rate, smart

sampling (not with fixed interval), and sample dropping schemes.

Acknowledgment. Financial support by Academy of Finland (Project No.: 209570) is

gratefully acknowledged.

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2. Madden, S.R., Franklin, M.J., Hellerstein, J.M., Hong, W.: TinyDB: An Acquisitional

Query Processing System for Sensor Networks. ACM Transactions on Database

Systems 30(1), 122–173 (2005)

3. Madden, S., Franklin, M.J., Hellerstien, J.M., Hong, W.: The design of an acquisitional

query processor for sensor networks. In: Proceedings ACM SIGMOD, San Diego, CA,

USA, June 2003, pp. 491–502 (2003)

4. Gehrke, J., Madden, S.: Query processing in sensor networks. IEEE Pervasive

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Computing Systems and Applications (RTCSA 2005), pp. 394–399 (2005)

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System Sciences (January 2000)

Novel Algorithms for the Network Lifetime

Problem in Wireless Settings

MichaelElkin1,,YuvalLando2,ZeevNutov3,MichaelSegal2,,

andHananShpungin1, 

1Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva

84105, Israel

2Department of Communication Systems Engineering, Ben-Gurion University of the

Negev, Beer-Sheva 84105, Israel

3Computer Science Division, The Open University of Israel, Raanana 43107, Israel

Abstract. A wireless ad-hoc network is a collection of transceivers po-

sitioned in the plane. Each transceiver is equipped with a limited, non-

replenishable battery charge. The battery charge is then reduced after

each transmission, depending on the transmission distance. One of the

major problems in wireless network design is to route network traﬃc

eﬃciently so as to maximize the network lifetime, i.e., the number of

successful transmissions. This problem is known to be NP-Hard for a

variety of network operations. In this paper we are interested in two

fundamental types of transmissions, broadcast and data gathering.

We provide polynomial time approximation algorithms, with guaran-

teed performance bounds, for the maximum lifetime problem under two

communication models, omnidirectional and unidirectional antennas. We

also consider an extended variant of the maximum lifetime problem,

which simultaneously satisﬁes additional constraints, such as bounded

hop-diameter and degree of the routing tree, and minimizing the total

energy used in a single transmission.

1 Introduction

Wireless ad-hocnetworks gained much appreciation in recentyears due tomas-

siveusein alarge varietyofdomains,fromlife threateningsituations,such as

battleﬁeldor rescue operations,tomore civil applications,like environmental

data gatheringforforecast prediction. The network iscomposed ofnumerous

transceivers (nodes)located in the plane,communicatingbyradio. A transmis-

sion betweentwo nodes ispossibleif the receiver iswithin the transmission range

ofthetransmitter.The underlyingphysicaltopologyofthenetwork isdependent

on the distribution ofthewireless nodes (location) as well as the transmission

power (range)assignmentofeachnode.Since the nodes haveonly alimited,non-

replenishableinitialpower charge (battery), energyeﬃciencybecomes a crucial

factorin wireless networks design.

Supported by the Israeli Academy of Science, grant 483/06.

 Supported by REMON (4G networking) consortium.

 Supported in part by the Lynn and William Frankel Center for Computer Science.

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 425–438, 2008.

Springer-Verlag Berlin Heidelberg 2008

426 M. Elkin et al.

The transmission range rvofnode vis determined bythe power assigned

tothat node,denoted byp(v). Itiscustomarytoassume that the minimal

transmission power required totransmittodistance disdα,where the distance-

power gradient αisusually takentobe in the interval[2,4](see [1]). Thus,

node vreceives transmissionsfromuifp(u)≥d(u, v)α,where d(u, v)isthe

Euclideandistance betweenuandv.There are two possiblemodels:symmetric

andasymmetric.Inthe symmetricmodel, alsoreferred toas the undirected

model, there isanundirected communication linkbetweentwo nodes u, v ∈T,

ifp(u)≥d(u, v)αandp(v)≥d(v, u)α,that isifuandvcanreach each other.

The asymmetricvariantallowsdirected (oneway) communication links between

two nodes.Krumke et al. [2]argued that the asymmetricversion is harder than

the symmetricone.This paper addresses the asymmetricmodel.

RamanathanandHain [3] initiated the formalstudyofcontrollingthenet-

work topologybyadjustingthetransmission range ofthenodes.Intuitively, an

increase tothe transmission range assignmentallowsmore distantnodes tore-

ceivetransmissions.But at the same time,itcausesaquicker batteryexhaustion,

which results in ashorter network lifetime.Weareinterested in maximizingthe

network lifetime under two basictransmission protocols,data broadcastingand

data gathering.Data broadcasting,orin short broadcast,isanetwork task

whenasource node swishes totransmit a message toall the other nodes in

the network.Data gathering -aless popular,nevertheless importantnetwork

task,isalsoknown as convergecast.Opposite tobroadcast,there isadestination

node d,andall the other nodes wish totransmit a message toit.Weconsider

data gatheringwith aggregation.

Each node v,has aninitialbatterycharge b(v). The batterycharge decreases

with each transmission. The network lifetime isthetime fromnetwork initial-

ization tothe ﬁrst node failure due tobatterydepletion. Itispossibletolook

at two formulationsofthemaximum network lifetime problem.Inthe discrete

version, node vcantransmitatmost b(v)/dαtimes todistance d.Whereas,the

fractional variant states that a transmission fromnode vtodistance disvalid

forb/dαtime units.Forexample,forb(v) = 15, d=2,andα=2,the discrete

version of the problem wouldallow 15/4=3separate transmissions,whilethe

fractionalformulation determines that node vcanhaveavalidtransmission for

15/4=3

.75time units.Most of the current research addresses the fractional

formulation. The discrete version was introduced bySahni andPark [4]. They

provided a number ofheuristics without guaranteed performance bounds.This

paper studies the discrete version, which seems tobe more problematic.

An additionalconsideration in wireless networks design, isthetype ofthe

antennausedforcommunication. In thispaperweconsider two types ofcom-

munication antennas,omnidirectional andunidirectional.Foranode u∈V

equiped with anomnidirectionalantenna,asingle message transmission tothe

most distantnode in asetofnodes Xissuﬃcientsothat all the nodes in X

receive the message.While,ifuuses a unidirectionalantenna,thenithasto

transmittoeach ofthenodes in Xseparately.

Novel Algorithms for the Network Lifetime Problem 427

The paper isorganized as follows.Inthe rest of the section, weintroduce our

model, discuss previous work andoutlineour contribution. In Sections2and3

wepresentour results fortheunidirectionalandomnidirecitonalantennatypes,

respectively.

1.1 The Model

Graph Preliminaries. Here wepr

ovide some graph theoryrelated deﬁnitions

used in thispaper.

–Forany graph H,let V(H)andE(H)be the node andedgesetsofH,

respectively.

–In adirected graph H,let δH(v)be the set ofoutgoingedgesfromvin V(H).

–Foraweighted graph H,with a weight function w,wealternately use the

notation w(e)andw(u, v), tospecifythe weight ofedgee=(u, v)∈E(H).

The weight ofHisgivenbyC(H)=e∈E(H)w(e).

–The weight function wofgraphHissaidtobe uniform,if∀e∈E(H),w(e)=

w0,forsome non-negativevalue w0.

–The cube ofgraphH,denoted H3,containsanedge (u, v)ifthereisapath

fromutovin Hwith at most 3edges.

–AHamiltoniancircuith=(u1,u

2,...,u

n+1 =u1)ingraph H,where ui∈

V(H)for1≤i≤n,is a graph cyclethatvisits each node in V(G)exactly

once andalsoreturnstothe startingnode.The weight ofhisgivenby

C(h)=n

i=1 w(ui,u

i+1), where wistheweight function ofH.

–Givenanundirected graph H,let MST(H)be a minimum spanningtree

ofH.

Network Model. Wehavenwireless nodes Vpositioned in aEuclideanplane.

The wireless network isthenmodeled byacomplete,weighted,andundirected

graph GVwith a weight function w:V×V →IR,w(u, v)=d(u, v)α.It

iseasytoverifythat the weight function obeystheweak triangleinequal-

itywith coeﬃcient2

α−1,i.e., forany u, v, w ∈V,w(u, w)≤2α−1(w(u, v)+

w(v, w)).

Both types of messages,broadcast orconvergecast,are propagated byusing

adirected spanningtreeofGV,called a transmission tree.Abroadcast message,

originatingin s∈V,ispropagated byanarborescence Tsrooted at s,alsocalled

abroadcast tree.Inthe case ofaconvergecast tod∈V,the messages fromall

nodes are propagated byareversed arborescence Tdrooted at d,alsocalled a

convergecast tree.Inthe case ofabroadcast message,anode maybe required

totransmittomultiplerecipients (its childreninthe broadcast tree), while

aconvergecast message istransmitted once tothe parentin the convergecast

tree.1

1We consider data gathering with aggregation, which means that each node vcombines

the messages sent by the nodes in a subtree rooted at vinto one message, and then

propagates it to its parent.

428 M. Elkin et al.

Everynode v∈Vhas aninitialbatterycharge b(v). After each message

propagation, its residualenergydecreases.The energydecrease depends on the

recipientnodes location, as well as the antennatype used,either omnidirec-

tionalorunidirectional. Formally, the power consumption ofv∈Vdue toa

transmission tree Tis,

βT(v)=⎧

⎪

⎨

⎪

⎩

max

e∈δT(v)w(e),omnidirectional,



e∈δT(v)

w(e),unidirectional.

Note that the reverse ofabroadcast tree isaconvergecast tree.Due tothis

symmetryproperty, andin anattempt tokeep the deﬁnitionssimple,fromthis

point,we refer tothe broadcast transmission protocol only. Although there is

symmetryindeﬁnitions,nevertheless notall the results work well forboth cases.

Weprovide explicit statements whenever the results are relevantforconvergecast

as well. In thispaperwe assume α=2forsimplicity, though our results canbe

easily extended toany constantvalue ofα.

Problems Deﬁnition. The generalmaximum lifetime broadcast (MLB) prob-

lem isdeﬁned as follows.The input tothe MLB problem isgraphGV,ini-

tialbatterycharges b:V→IR,andasequence ofmsource nodes S=

{s1,s

2,...,s

m},where si∈V,for1≤i≤m.Each ofthesource nodes has

onebroadcast message totransmittoall the other nodes.The output isa

sequence ofbroadcast trees TB={T1,T

2,...,T

k},where Tiisrooted at si,for

1≤i≤m,sothat forall v∈V,k

i=1 βTi(v)≤b(v). Our objective isto

maximize k.Intuitively, givenasequence ofsource nodes,wewish tomaximize

the number of successfulbroadcast message propagations,whilesatisfyingthe

batteryconstraint.That is,all the nodes haveenough batterycharge tosupport

message propagation in aseque

nce ofbroadcast trees.

There are two possiblerelaxationsofthegeneralmaximum lifetime broadcast

problem.The ﬁrst relaxation istoset si=s,forall si∈S,that isonesource

node sgenerates all broadcast messages.The second relaxation istorequire

that all the broadcast trees wouldbeanorientation ofoneundirected tree.In

thispaperweconsider the following three problems.

Problem 1. [SingleSource Maximum Lifetime Broadcast (SSMLB)]

Input: Graph GV,initialbatterycharges b:V→IR,andasource node s∈V.

Output: Asequence ofbroadcast trees TB={T1,T

2,...,T

k},sothat Tiis

rooted at s,andforall v∈V,k

i=1 βTi(v)≤b(v).

Objective: Maximize k.

Problem 2. [SingleSource/TopologyMaximum Lifetime Broadcast (SSTMLB)]

Input: Graph GV,initialbatterycharges b:V→IR,andasource node s∈V.

Output: Adirected spanningtreeTofGVrooted at s,andaninteger k,1≤

k≤m,sothat forall v∈V,kβT(v)≤b(v).

Objective: Maximize k.

Novel Algorithms for the Network Lifetime Problem 429

Problem 3. [SingleTopologyMaximum Lifetime Broadcast (STMLB)]

Input: Graph GV,initialbatterycharges b:V→IR,andasequence ofmsource

nodes S={s1,s

2,...,s

m},where si∈V.

Output: An undirected spanningtreeTofGVandaninteger k,1≤k≤m,so

that forall v∈V,k

i=1 βTi(v)≤b(v), where Ti,1≤i≤k,isabroadcast tree

rooted at si,andisobtained byorientingtheedgesofT.

Objective: Maximize k.

The analogous problems forconvergecast, SSMLC, SSTMLC,andSTMLC

are deﬁned in asimilar way.

1.2 Previous Work

Numerous studies were conducted in the area ofmaximizingthenetwork lifetime

under various transmission protocols.Inaddition tobroadcast andconverge-

cast,itiscommon toﬁnd references tomulticast andunicast2as well. Diﬀerent

formulationsofthemaximum lifetime problem are due tothe single/multiple

source/topologyrelaxations.These relaxations,mixed together with the antenna

type,haveimpact on the complexityof the problem.

Asmentioned previously, tothe best ofour knowledge,there isno reference to

the discrete version ofthemaximum lifetime problem,except for[4]. Instead,we

surveythe state of currentresults forthefractionalcase,grouped in accordance

tothe communication modelused.

Omnidirectional Model. Orda andYassour [5] gavepolynomial-time algo-

rithms forbroadcast,multicast andunicast in the case ofsingle source/single

topology,which improved previous results by[6].Segal[7]improved the running

time oftheMLB problem for the broadcast protocol andalsoshowed anopti-

malpolynomial-time algorithm forconvergecast with aggregation. Additional

results maybe foundin [6,8]. By allowingsingle source/multiple topology,

the broadcast andmulticast become NP-Hard [5], whileconvergecast anduni-

cast havepolynomial-time optimalsolutions.In[5],the authors establish an

O(logn)andO(kε)approximation algorithms forbroadcast andmulticast,re-

spectively, where kisthesize ofthemulticast destination set andεisany

positiveconstant.The same paper showsanoptimalsolution fortheunicast

case byusinglinear programmingandmax-ﬂow algorithms.LiangandLiu[9]

prove that the convergecast problem without aggregation isNP-Complete for

generalcosts.Aneasier version, with aggregation, does haveapolynomialsolu-

tion [10] in O(n15 logn)time.Tocounter the slowness ofthealgorithm,Stan-

ford andTongngam [11] proposed a (1 −ε)-approximation in O(n31

εlog1+εn)

time based on Garg andK¨onemann [12]algorithm forpackinglinear programs.

Theyalsopropose severalheuristics andevaluate theirperformance bysimula-

tion. Generally, acommon approach tosolvingthefractionalproblem istouse

2Multicast is a more general case of broadcast. A source node is required to transmit

to a set of nodes; unicast is more speciﬁc, a source node is required to transmit to a

single node.

430 M. Elkin et al.

Table 1 . Current results for the fractional case

Single Source - Omnidirectional Model

Topology Broadcast Convergecast (with agg.)

Single OPT [5,6,7] OPT [7]

Multiple 6(1 −ε) approx. (follows from [11] and [16]) OPT [10]

Single Source - Unidirectional Model

Topology Broadcast Convergecast (with agg.)

Single NP-Hard [5] OPT [7]

Multiple OPT [5] OPT [10]

various LP formulations that reduce the problem tooneofﬁndingthemaximum

multicommodityﬂowinanetwork.See also[13,14,15].

Unidirectional Model. The authors in [5] show that forbroadcast,the problem

isNP-Hard in the case ofsingle source/single topology andhasapolynomial

solution in the case ofsingle source/multiple topology.Theyalsoshow

that itisNP-Hard in both of these cases formulticast.Tothe best ofour

knowledge,thisistheonly paper toaddress the unidirectionalcommunication

model. Note that forconvergecast there isno diﬀerence betweenthe two models

(omnidirectionalandunidirectional), as the node isrequired totransmittoits

parentin the convergecast tree only. Therefore,the results from[7]and[10] hold.

Asummaryoftheresults forthefractionalcase under the omnidirectional

modelisgiveninTable1(OPT represents that the problem canbe solved opti-

mally). The resultforsinglesource/multipletopologyincase ofbroadcast isde-

rived fromthesimplefactthatwhenthe Garg-K¨onemann (1 −ε)-approximation

algorithm uses λ-approximation minimum length columnsitproduces a λ(1 −ε)

approximation tothe packingLP deﬁned by[11]ifusedforbroadcasting.Wecan

choose a 6-approximation byAmb¨uhl[16]as the λ-approximation algorithm for

the minimum energybroadcast problem.The 6-approximation canbe improved

byusingtheresultin [17].

1.3 Our Contribution

Westudythe discrete version ofthemaximum lifetime problem under broad-

cast/convergecast transmissions.Weprovide polynomialtime approximation

algorithms,with guaranteed performance bounds,forthemaximum lifetime

problem under two communication models,omnidirectionalandunidirectional

antennas.Wealsoconsider anextended variantofthemaximum lifetime prob-

lem,which simultaneously satisﬁes additionalconstraints.Inparticular,our main

contributionsare:

1. Under the unidirectionalmodel, we state the NP-Hardness oftheSSMLB and

SSTMLB problems.Weprovide anO(logn)-approximation tothe SSTMLB

problem.Then, fortheSSMLB problem weﬁndasequence ofbroadcast

trees ofoptimallength k∗,sothat the batteryconstraintisviolated byat

Novel Algorithms for the Network Lifetime Problem 431

Table 2 . Our contribution in the discrete case

Single Source - Unidirectional Model

Topology Approx. Remark s

Single O(log n)

Multiple 1battery violation by O(log(nk∗)), k∗is OPT

Multiple Source - Omnidirectional Model

Topology Approx. Remark s

Single 2with additional bi-criteria

Multiple O(ρ2)with n/ρ +logρhop-diameter, and additional bi-criteria

most O(log(nk∗)) times.That is,the energyconsumed bynode visatmost

O(log(nk∗))b(v).

2.Under the omnidirectionalmodel, wedeveloptwo approximation algorithms

fortheSTMLB problem.We assume uniform initialbatterycharges and

presenta2-approximation algorithm byusingtheMST(G)as the broadcast

tree.Thisimmediately yields constantbounds forthetotalenergyconsumed

in asingletransmission andthemaximum degree.Wethenconstruct a

broadcast tree which isaO(ρ2)-approximation tothe problem.Inaddition,

ithasabounded hop-diameter n/ρ +logρ,where 1≤ρ≤n,aconstant

maximum degree,andtheenergyconsumed in asingletransmission isat

most ρtimes the optimum forabroadcast transmission. We argue that the

tradeoﬀ betweenthe maximum lifetime andthehop-diameter isoptimal.

That is,our multi-criteria approximation istight.

3. Finally, weshow that the results fortheSTMLB problem,canbe applied

fortheSTMLCproblem as well.

To the best ofour knowledge,these are the ﬁrst theoreticresults forthediscrete

formulation of the problem.Our results are summarized in Table2.

2 Unidirectional Communication Model

The unidirectionalmodelimplies that each node ischargedforeveryoutgoing

edge in the transmission tree.The power consumption ofv∈Vdue toasingle

message transmission, in adirected tree T,isβT(v)=e∈δT(v)w(e).

In this section weconsider two variants oftheMLB problem under the sin-

glesource relaxation. First the more generalcase is addressed,where multiple

topologies are allowed,which istheSSMLB problem.Then, weshow that by

doingslight modiﬁcationstothe proposed algorithms,weestablish a similar

resultin the case ofsingletopologyrelaxation, namely the SSTMLB problem.

Weslightly modifythe originalproblems,byallowingaviolation of the battery

constraintbyγ.That is,werequire that the energyconsumption ofeveryv∈V

isatmost γb(v).

432 M. Elkin et al.

AssumingP=NP, both the singleandthemultipletopologycases cannot

achievea1/γ-approximation algorithm forany constantγ>0, since deciding

whether evenonetranmission ispossibleisequivalenttothe socalled Degree

Constrained Arborescence problem.Thisimplicates that the SSMLB and

SSTMLB problems are NP-Hard (take γ=1).

Note that in the singletopologycase,ktransmissionswith initialbattery

charges {γb(v):v∈V}imply k/γtransmissionsforinitialbatterycharges

{b(v):v∈V}.Indeed,since weareusingthesamearborescence,the power

consumption ofeverynode in everymessage propagation isidenticalandthere

are kmessage propagations,thenfortheoriginalcharges {b(v):v∈V}the

number ofpropagationsisatleast b(v)/(γb(v)/k)=k/γ.Unfortunately, for

the multipletopologycase,wedonothaveamethodtoconvert the battery

violation toastandard approximation.

Although the input tothe SSMLB problem,isaweighted,undirected graph

GV,wecanalternatively lookatthedirected version G

V,i.e., foreveryedge

e=(u, v )∈E(GV), create the instances (u, v),(v, u)inE(G

V). The weight

ofthedirectionaledge isthesameasoftheoriginalone.Inthe rest ofthe

section weprovethenexttheorem,which summarizes our main results forthe

unidirectionalmodel.

Theorem 1. Given a weighted, directed graph G

Vand a source node s∈V,

let k∗

1and k∗

2be the number of successful message propagations in the optimal

solutions of the SSTMLB and SSMLB problems, respectively. Then, (i) there

exists a broadcast tree Trooted at s, so that for al l v∈V,(k∗

1/logn)βT(v)≤b(v);

(ii) there exists a sequence of broadcast trees TB={T1,T

2,...,T

k∗

2},eachrooted

at s,andforallv∈V,k∗

i=1 βTi(v)≤(log(nk∗

2))b(v).

2.1 Weight Scaling Reduction

Westartbyshowingasimplescalingofweights,which allowsustomanipulate

the input graph G

V.Ifforsome node v∈Vandconstantc>0, wesetb(v)←

b(v)/c andforeveryoutgoingedgee∈δG

V(v),set w(e)←w(e)/c,weobtain a

similar instance toour problem.Note that aninstance with uniform weights3is

easily transformed intoaninstance with unit weights (all weights being1), by

applyingtheweight scaling reduction described above.

2.2 The SSMLB Problem

Westartwith the multipletopologycase oftheMLB problem under the single

source relaxation andprovepart(ii) ofTheorem 1.

Adirected graph Hisk-edge-outconnected from sifitcontainsk-edge disjoint

paths fromstoany other node.ByEdmond’sTheorem [18], agraphisk-

edge-outconnected fromsif,andonly if,itcontainskedge-disjointspanning

arborescences rooted at s.Let us introduce the followingdecision problem.

3Though graph G

Vdoes not necessarily has uniform weights, nevertheless we use this

scaling in future developments.

Novel Algorithms for the Network Lifetime Problem 433

Problem 4 (Bound Constrained k-Outconnected Subgraph (BCkOS)).

Input: Adirected graph Gwith a weight function w,bounds b:V(G)→IR,a

source node s∈V(G), andapositiveinteger k.

Question: Does Ghaveak-edge-outconnected spanning subgraph H,sothat

forall v∈V(G), βH(v)≤b(v).

Givenapositiveinteger k,the problem ofﬁndingasequence ofbroadcast trees

oflength kin G

Vcanbe reduced tothe BCkOSproblem as follows.Asanedge

in E(G

V)maybe used severaltimes,weaddk−1copies ofeachedgetothe

graph.4Call thisgraphGk

V.ThenwesolvetheBCkOSproblem forGk

To solvetheSSMLB problem,weneed tosearch forthemaximum value ofk,

forwhich the BCkOSreturnsapositiveanswer givenGk

V.Thiscanbe donebya

simplebinarysearch in the range {1,...,K},where K=maxe∈δGV(s)b(s)/w(e).

The upper boundis due tothe source node batteryconstraint.The BCkOS

problem isNP-hard evenforuniform weights andk=1.Wetherefore consider

the optimization problem that seeks tominimize the factoroftheweight-degree

bounds violation.

Problem 5 (Weighted-Degree Constrained k-Out conn ected Subgraph (WDCk

OS)).

Input: Adirected graph Gwith a weight function w,bounds b:V(G)→IR,

asource node s∈V(G), andapositiveinteger k.Graph Ghas a k-edge-

outconnected spanning subgraph H∗satisfying,forall v∈V(G), βH∗(v)≤b(v).

Output: Findak-edge-outconnected spanning subgraph HofG,sothat forall

v∈V(G), βH(v)≤γ·b(v).

Objective: Minimize γ.

Clearly, guaranteeingafactorofγfortheWDCkOSproblem alsoguarantees a

γviolation in our case.Let the Degree Constrained k-Outconnected Subgraph

(DCkOS) problem be the restriction ofWDCkOSproblem toinstances with

unit(oruniform)weights;inthiscasethebounds b(v)are just the degree con-

straints,andthusassumedtobe integral. The following statementfollowsfrom

Theorems 1and4in [19] (dH(v)istheoutdegree ofvin H).

Theorem 2 ([19]). There exists a polynomial time algorithm that given an

instance of DCkOS ﬁnds a k-edge-outconnected spanning subgraph Hof Gso

that dH(v)≤b(v)+2if k=1and dH(v)≤b(v)+4if k≥2.

Itiseasytoverifythat DCkOSadmits a 3-approximation algorithm fork=1

anda5-approximation algorithm fork≥2.Foreverynode vwith b(v)=0,

removefromGthe edges leavingv,andthencompute a k-edge-outconnected

fromsspanning subgraph HofGusingthealgorithm as in Theorem 2.Then

4Instead of adding k−1 copies of an edge, we may assign to every edge capacity

k, and consider the corresponding ”capacited” problems; this will give a polynomial

algorithm, rather than a pseudo-polynomial one. For simplicity of exposition, we will

present the algorithm in terms of multigraphs, but it can be easily adjusted to the

terms of capacitated graphs.

434 M. Elkin et al.

dH(v)=0foreveryv∈V(G)with b(v)=0.Foreveryv∈Vwith b(v)≥1we

havedH(v)≤b(v)+2≤3b(v)ifk=1,anddH(v)≤b(v)+4≤5b(v)ifk≥2.

The followinglemma (proofisomitted due tolack ofspace), in conjunction

with the O(1)-approximation toDCkOS, proves part (ii) ofTheorem 1.

Lemma 1. An α-approximation algorithm for the DCkOS problem implies an

α·O(log(kn))-approximation algorithm for the WDCkOS problem.

2.3 The SSTMLB Problem

The singletopologycase oftheMLB under the singlesource relaxation istoﬁnd

aspanningarborescence TofGVrooted at s,sothat the number oftransmissions

ismaximized under the batteryconstraints.The problem canbe reduced,similar

tothe multipletopologycase,tothat ofﬁndinga1-edge-outconnected froms

(namely, anarborescence rooted at s)spanning subgraph HofG,satisfyingthe

constraints k·βH(v)≤b(v)forall v∈V.BysettingB(v)←b(v)/k,weobtain

the weighted-degree constraints βH(v)≤B(v). Thisdeﬁnes aninstance ofthe

WDCkOSproblem with k=1.Thus,wecancompute in polynomialtime a

1-outconnected fromsspanning subgraph HofGsothat foreveryv∈V(G)

wehaveβH(v)≤γ·B(v)=b(v)/k,namely, k·βH(v)≤γ·b(v). Thismeans

that wecanguarantee ktransmissionsusingHwith batterycapacities γ·b(v).

Consequently, wecanguarantee k/γtransmissionswith the originalbattery

capacities b(v), which proves part (i) ofTheorem 1.

3 Omnidirectional Communication Model

In this section weconsider the omnidirectionalmodel. Thismodeldeﬁnes that

the transmission ofsome node v∈Vis received byall the nodes within the

transmission range ofv.Therefore,the power consumption ofnode v∈Vdue to

asingle message transmission, in adirected tree T,isβT(v)=maxe∈δT(v)w(e).

We assume uniform initialbatterycharges,that isforall v∈V,b(v)=B.

Without loss ofgeneralitywemayassume B=1.

Recall the STMLB problem.WelookforaspanningtreeTofGV,sothat the

number ofbroadcast messages routed byusingits orientationsismaximized.We

call Tthe broadcast backbone.Inthis section weshow two diﬀerentconstructions

ofT,each satisfyingadditionalmulti-criteriaconstraints.Inthe end,we state

that Tcanbe used forconvergecast (the STMLCproblem)as well.

Wearegivenaweighted,undirected graph GV,andasequence Sofmsource

nodes.Let T∗,k

∗be anoptimalsolution fortheSSMLB problem.Westartby

derivinganupper boundon k∗.

Lemma 2. Let e∗=(u, v)be the longest edge in T∗.Thenk∗≤2/w(e∗).

Proof. Let Ti,1≤i≤k∗,be a broadcast tree rooted at si,andobtained by

orientingtheedgesofT∗.Note that either utransmits tov((u, v)∈E(Ti)) orv

transmits tou((v, u)∈E(Ti)), but notboth.Out ofthek∗broadcast trees,let

Novel Algorithms for the Network Lifetime Problem 435

kube the number of trees in which utransmits tov.Without loss ofgenerality, let

ku≥k∗/2(otherwise wetakev). Since e∗isthelongest edge in T∗,wecanlower

boundthetotalpower consumption ofu,k∗

i=1 βTi(u)≥kuw(e∗)≥w(e∗)k∗/2.

Due tothe power consumption constraint,k∗

i=1 βTi(u)≤B=1.Asaresult,

k∗≤2/w(e∗). !"

3.1 Multi-criteria Broadcast Backbone

In this section weshow that ifwetakeTtobe MST(GV), thenweobtain a

2-approximation algorithm fortheSTMLB problem,as well as additionalmulti-

criteria.

Lemma 3. Let kbe the maximum value, so that for all v∈V,k

i=1 βTi(v)≤

b(v),whereTi,1≤i≤k, is a broadcast tree rooted at si, and is obtained by

orienting the edges of MST(GV).Thenk≥k∗/2.

Proof. Let e=(u,v

)be the longest edge in MST(GV). Since the longest

edge in any minimum spanningtreeisnotgreaterthanthe longest edge ofany

spanningtree,w(e)≤w(e∗). Clearly, nodes u,v

havethelargest possiblepower

consumption w(e)inany broadcast tree Ti,1≤i≤k.Therefore,k>1/w(e).

FromLemma 2,k∗≤2/w(e∗). Weconclude k≥k∗/2.!"

Note that usingMST(GV)as the broadcast backbone,alsoprovides some ad-

ditionalvaluablemulti-criteriaguarantees,as concluded in the nexttheorem.

Theorem 3. Given a weighted, undirected graph GV, and a sequence of m

source nodes S. Setting T=MST(GV); (i) provides us with ksuccessful broad-

cast message propagations, where k≥k∗/2; (ii) Thas a bounded degree of 6;

(iii) the total energy consumption in one broadcast tree is at most ctimes of the

optimum, where 6≤c≤12.

Proof. (i) FromLemma 3, k≥k∗/2; (ii) the maximum degree ofMST(GV)is

at most 6, since the minimum spanningtreeofGVisidenticaltothe Euclidean

minimum spanningtreeon the node set V,andthelatter has a bounded degree

of6; (iii) in [20] the authors provethatforany node set in the plane,the totalen-

ergyrequired bybroadcastingfromany node isatleast 1

ce∈E(MST(GV)) w(e),

where 6≤c≤12.Therefore the totalenergyconsumption in onebroadcast tree

isofaconstantfactorfromthebestpossible.

3.2 Bounded Hop-Diameter Multi-criteria Broadcast Backbone

Our construction isbasedon aHamiltoniancircuit.Sekanina[21] showed that

the cube ofany tree,with at least 3vertices,isHamiltonian. Andrea andBandelt

[22]givealinear time algorithm fortheconstruction oftheHamiltoniancircuitin

T3,givenT.Theyalsoshow that the weight oftheHamiltoniancircuitisatmost

2τ2+1

2τ)times the weight ofthetree,where τistheweak triangleinequality

parameter (under our assumption that α=2,τ=2α−1=2). Moreover,itcan

be shown that the longest edge in the Hamiltoniancircuitisatmost O(1) times

the longest edge in T.The followingtheorem applies the abovetoMST(GV).

436 M. Elkin et al.

u1u2u3u4u5u6u7u8u9u10 u11 u12 u13 u14

B1B2

Fig. 1. Bounded hop-diameter broadcast backbone for h=(u1,u

2,...,u

14)andρ=7.

There are 14/2 = 7 node sequences U1={u1,u

2,...,u

7}and U2={u8,u

2,...,u

14}.

The center nodes of U1and U2are u4and u11, respectively. Each of the trees B1,B

spans the corresponding nodes in U1and U2, respectively.

Theorem 4 ([22]). Let h=(u1,u

2,...,u

n+1 =u1),whereui∈Vfor 1≤i≤

n, be the Hamiltonian circuit as a result of applying the construction in [22] on

MST(GV). Deﬁne e∗

MST and e∗

hto be the longest edges in MST(GV)and h,

respectively. Then C(h)=O(C(MST(GV)) and w(e∗

h)=O(w(e∗

MST )).

Next,we describe the construction of the broadcast backboneTh,based on the

Hamiltoniancircuith=(u1,u

2,...,u

n+1 =u1)fromTheorem 4.Let ρbe an

integer parameter,1≤ρ≤n.The node set ofThisV.Wedivide the sequence

ofnodes Uh={u1,u

2,...,u

n}inton/ρ consecutivesequences Uiwith ρnodes

each,sothat Ui={uρ(i−1)+1,u

ρ(i−1)+2,...,u

ρi},1≤i≤n/ρ.

The center node ofasequence U={x1,x

2,...,x

j},denoted c(U), istheme-

diannode with anindexj+1

2.There are two types ofedgesin Th,E(Th)=

E1∪E2.The ﬁrst type ofedgesconnects the center nodes ofeverytwo adja-

centnode sequences,E1={(c(Ui),c(Ui+1))}n/ρ−1

i=1 .The secondtype ofedges,

E2,induces n/ρ complete binarytrees B1,...,B

n/ρ.Each tree Bi,1≤i≤n/ρ

spansthenodes in Uiandisrooted at c(Ui). The tree Biisconstructed re-

cursively. The childrenofc(Ui)are the center nodes in subsequences U1

{vρ(i−1)+1,...,v

ρ(i−1)+ ρ−1

2}andU2

i={vρ(i−1)+ ρ+3

2,...,v

ρi}.Wethencontinue

toconstruct a complete binarytree in each of the subsequences,U1

i,U2

i,ina

similar way. Note that each tree Bihas logρlevels(see examplein Figure 1).

Denote bye∗

Thande∗

hthe longest edges in Thandh,respectively. The next

lemma showssome valuablebounds forTh(the proofisomitted due tolack of

space).

Lemma 4. The graph This a spanning tree of GVand has a bounded hop-

diameter of O(n/ρ+logρ), a bounded degree of 4, and it holds C(Th)=O(ρC(h))

and w(e∗

Th)=O(ρ2w(e∗

h)).

Note that the tradeoﬀ betweenthe approximation ofthelongest edge andthe

hop-diameter boundpresented in Lemma 4 isoptimal. Consider the unweighted

n-path:any tree ofhop-diameter at most Dforit,containsanedge with an

intervallength ofatleast (n−1)/D,andsoits squared length isatleast (n−

1)2/D2.Since the longest edge ofthen-path has a squared length of1, wegetan

increase ofthelongest edge byafactorofatleast Ω(n2/D2). Finally, substitute

D=n/ρ toobtain Ω(ρ2).

Novel Algorithms for the Network Lifetime Problem 437

Similar tothe ﬁrst construction, the broadcast backboneThsatisﬁes multiple

constraints accordingtoLemma 4.Wecantherefore derivethenexttheorem.

Theorem 5. Given a weighted, undirected graph GV, and a sequence of m

source nodes S. Setting T=Th; (i) provides us with ksuccessful broadcast

message propagations, where k≥k∗/2ρ2; (ii) Thas a bounded hop-diameter of

n/ρ +logρ; (iii) Thas a bounded degree of 4; (iv) the total energy consumption

in one broadcast tree is at most O(ρ)times of the optimum.

Proof. Conditions(ii) and(iii) are immediate fromLemma 4.Fromthesame

lemma in conjunction with Theorem 4,w(e∗

Th)=O(ρ2w(e∗

MST )). By follow-

ingsimilar arguments as in the proofofLemma 3, weobtain (i). Combining

Theorem 4 andLemma 4 alsoyields the boundC(Th)=O(ρC(MST(GV))).

Following the same arguments as in Theorem 3condition (iv) follows.!"

3.3 Applicability to the STMLC Problem

The two constructionsfor the broadcast backbonemaybe used forconverge-

cast,which will resultin similar asymptoticbounds.The similarityfollowsfrom

Lemma 2,which canbe applied forconvergecast transmissions,since itdoes not

rely on any broadcast speciﬁc characteristics.Thisresults in the same approxima-

tion ratiosforthenetwork lifetime (number of successfulmessage propagations).

The hop-diameter anddegreebounds follow immediately fromtheconstructions.

Finally, wehavetoshow that the totalpower consumption boundalsoholds.

In [23], the authors showed that the totalpower consumption needed forone

convergecast propagation isatleast C(MST).

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Message Quality for Ambient System Security

Ciar´anBryce

INRIA-Rennes, France

Ciaran.Bryce@inria.fr

Abstract. In ambient systems, a principal may be a physical object

whose identity does not convey useful information for taking security

decisions. Thus, establishing a trusted channel with a device depends

more on the device being able to demonstrate what is does, rather than

who it is. This paper proposes a security model that allows a principal

to establish the intent of an adversary and to make the adversary prove

its trustworthiness by furnishing proof of current and past behavior.

1 Introduction

The technologicalcombination ofportabledevices (e.g., smart phones,PDAs),

wireless networkingandprocessor cards embedded in everydaydevices has led

tothe emergence ofambientcomputingsystems.Ambientsystems are employed

forprocess control andperson-centricapplicationslike mobilehealth [7], do-

motics [11] andpayment[8]. Securityisamajorconcernforthesesystems,

especially with personaldevices containingprivate information andincreasingly

sensitiveapplications.The major securityrisks faced include device theft,virus

infectionsandspam.

Ambientsystems pose a challenge forinformation securityenforcement.Com-

municatingdevices canbe unknown toeach other,andsince the network might

use short-range radio, itmight notpossess a trusted third partythat canact

as a certiﬁcate authority[14]or reputation server [16] that facilitates the es-

tablishmentoftrustedchannelsbetweendevices.Solutionsfor securityneed to

be scalable.Thismeansthatwhentwo peers wanttoestablish a trusted chan-

nel, thenthere shouldbesuﬃcientinformation on theirdevices toestablish the

channel, andthusminimize reliance on third parties.

The goalofthispaperistoexamine the securityrequirements forambient

systems andtopropose a securitymodel. Thismodelisentitled message quality

since its roleistoexamine each message that a device receives fromapartner

device,andtodetermineif that message isconsequenttoa securityattack on,

orby, the partner device.The model’simplementation leverages the support

oftheTrusted Platform Module (TPM) [17]–ageneralpurpose hardware chip

designed for secure computingthatisusedbyaplatform todemonstrate that

its software has notbeentampered with.

Akeyfeature of the securitymodelis the deprecated roleofprincipalidentity:

itcanbe more importantforadevice toprovewhat it does thanitistoprove

who it is.Forinstance,whenauserPDA interacts with a soda vendingmachine,

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 439–450, 2008.

Springer-Verlag Berlin Heidelberg 2008

440 C. Bryce

itismore usefulforthePDA toestablish that the machinereturnssodas in

returnforpaymentthanitistoknow the vendingmachine’sserialnumber.This

approach requires that a securitymodelvalidates the software runningon the

device,whereas traditionalsecuritymodelsaredesigned tovalidate the identity

ofaprincipal. A secondaimthemodelistoenableprincipalstoestimate the

trustworthiness ofapartner principal, bybeingabletodetermineiftheirpartner

has behaved in atrustworthywayinthe past.

Thispaperisorganized as follows.Section 2presents the securitychallenges

ofambientcomputingsystems that the paper addresses.The securitymodelis

presented in Section 3, andwecommenton its strengths andweaknesses.In

Section 4,the modelisintegrated intoaprogrammingmodelthat isoftenused

in ambientcomputing–the tuplespacemodel[5].Anexampleof the security

modelinuse ispresented.Related work ispresented in Section 5 which concludes

the paper.

2 Security Challenges

Viruses remain oneofthemost common andmost costly source of security

attacks.Handhelddevices are notimmunetoviruses,the Cabirvirus forinstance

being the ﬁrst majorvirus on the Symbianoperatingsystem andtheDuts virus

infectingPocketPCs1.Amobiledevice virus ispotentially more pernicious than

anInternet virus since a device canbe engaged in acommunication without the

owner beingaware.(Onecanalwaysdisconnect a wired communication linkand

thus be sure that the computer isnotengaged in hiddencommunication).

Asecondmajor securityconcernintoday’sinformation systems isinforma-

tion misuse [4]. Thisis the problem ofinformation beingexposed ordestroyed

through ineﬀective access controlstophysicalandinformation resources.Acon-

crete exampleforhandhelds istheft:the French interiorministryreports that

up to200 000 mobilephones are stoleninFrance each year2.

Afurther risk forambientsystems isspam–awell known problem forthe

Internet,with up to70% ofe-mail traﬃc consistingofunsolicited messages [9].

Spam is attractivefor attackers (spamers)due tothe low cost ofsendingmes-

sages.Asimilar situation canarise in ambientsystems,where devices cansend

information toothers at no cost –apart fromtheenergyconsumed bythe de-

vice’s battery. An examplespamscenario isonewhere a user passes near a

supermarket andpicks up unwanted messages fromitems on sale.

Wechoose in thispapertoconcentrate on the aboverisks since theyare

relatively novel. There are ofcourse other risks,like network blocking attacks,

as well as traditionalriskssuchascracking the trusted hardware on devices and

PIN theft.

There are a number ofchallenges toimplementing a securityinfrastructure:

–There isapotentially huge number of peers without centralized management.

No peer knowsall others,andmost peers know fewothers.Strictly speaking,

1http://www.virusthreatcenter.com/

2http://www.afom.fr/v3/TEMPLATES/acces elus l2.php?rubrique ID=115

Message Quality for Ambient System Security 441

peer Alice knows Bobifshecan linkBob’sidentitytohisexpected behavior.

Thislack ofknowledge wouldnormally imply the use oftrustedthird parties

such as recommendation servers and certiﬁcate authorities.However,given

the potentialsize ofsystems andweak connectivityofwireless networks,

these solutionsmustbeminimized in favorof decentralized scalableones.In

a decentralized solution, whenAlice sends a message MtoBob,thenthe

peers and message Mcontain suﬃcientdataforBobtoverifythat itissafe

toact upon the message.

–Personalcomputingdevices need tominimize physicalresources like energy,

andthusoptimize network communicationsand securityprocessing,as well

as memoryspace.

–Each device owner isautonomous andhascomplete control over hisdevice.

Hecanin

stall any software on hisdevice and access any service.Hecan

manipulate information on the device in any way, unless that data isstored

on atrustedzone,possibly with the support of trusted hardware.Adevice

maybe stolenandthenused ormisused byanon-owner.Itiscrucialthat the

manipulationsmadebyausertohisdevice be bounded topreventspooﬁng

attacks.These are a high risk in ambientsystems ifusersareabletogenerate

(false)identities.

–Systems in practice degrade over time through ware ofhardware andsoftware

(as patches are applied for upgrades andvirus/bug ﬁxes). Thus,ahitherto

trusted principalcanstart behavingbadly, soa securityinfrastructure must

be abletodetect this.

3 Message Quality Security

3.1 Approach

There are two cornerstones toour securitymodel. The ﬁrst is that a principal

must provewhat it does rather thanwho it is (i.e., its identity). A principal’s

identitymight notchange,but its abilitytoservice a request –what itdoes –can

change as newfunctionalityis added,viruses spread,etc.The secondcornerstone

is decentralization. That is,as suggested in Figure 1, the securityframework on

aprincipal’sdevice decides on the securityof each message.If the message

is acceptable,thenitispasseduptohigher application layers forprocessing.

Otherwise,the message gets rejected without the application beinginformed.For

decentralization, theremustbesuﬃcientinformation in the message andpre-

distributed toBobtotake thisdecision. Thisisnecessarytoallow adecision to

be takenwithout real-time recourse toa(perhaps absentfromnetwork)trusted

third party.

Consider a message MsentfromAlice toBob,c.f., Figure 1. There are three

properties ofMthat deﬁneits security:

1. Mis plausible.Thisis the propertythat Mis a message that Alice islikely

toutter,giventhe behavioralproﬁleofPrincipalAlice.Forinstance,ifAlice

isafrequenttaxi passenger,thenthe messages she islikely toutter include

requests forataxi.

442 C. Bryce

Fig. 1. Message Quality

2.Mis trustworthy.Thisis the propertythat permits Bobtobelievethat

the contents of message Mare true.Forexample,ifAlice sends a message

askingforataxi, thenBob–the taxi driver –canstopthetaxi with suﬃcient

conﬁdence that there is a passenger waitingtomount.Trustworthiness is

notanabsolute value of a message.Rather,itisafeaturewherebyAlice

cancomplement a message with proof that the contents of the message are

trustworthy. This aspect leverages work donein trust-based frameworks,

e.g., [16,18]. In Figure 1, the proofisrepresented in the plea object.

3. Mis useful.Thisis the propertythat Bobisinterested in M.The message

isrejected as spam byBob’sdevice ifitdoes notcorrespondtothe class of

messages that Bobwishes toreceive.

These properties are collectively known as message quality and,as islater argued,

are crucialtoaddressingtherisks outlined.Note how the onus ison the message

sender toconvince the receiver ofthequalityofits message.

3.2 Management of Message Quality

The elements needed toimplement message qualityare proﬁles,policies and

pleas.Allare ﬁrst-class objects in the message qualitymodel.

Aproﬁledeﬁnes the expected behaviorofaprincipal. A policyisanelement

of the receiver andisevaluated whenever it receives a message.It determines ifa

message istrustworthy, plausibleandusefulfrom the receiver’spointofview. A

plea isacopyofthesender’sproﬁleinformation andhistoryinformation that a

sender includes in a message in order toargue forquality. Both proﬁleandpolicy

objects are declarative;theyare downloaded with anapplication andinstalled

on adevice.Installation isPIN-protected.

Principals. The roleofidentityforprincipalsis deprecated in the message

qualitymodel. Whilemost principalsdonotneed tofurnish orevenpossess an

identity, there isasmall population ofidentities that are well-known. Forin-

stance,software providers (e.g., application andOSproviders), service providers

(e.g., ataxi company where passengers use theirPDAstogain access tothe

service)canbe considered well-known since all passengers must interact with

them at some stage,e.g., todownload the software orrenewtheir subscription.

Another class ofwell-known principals are hardware providers.

The roleofthewell-known principalsistodeﬁneprograms andpolicies for

devices since many users might notbein aposition todeﬁnetheseforthemselves.

Message Quality for Ambient System Security 443

Proﬁles. Principalbehaviorisdeﬁned in aproﬁle.Aproﬁleisqualiﬁed by

the set ofinstalled programs.Aprogram,inturn, isqualiﬁed bythe following

information:

–The actions of the program.These are expressed as the set of messages that

the program sends and receives.

–Acertiﬁcation of the program origin that describes where orbywhomthe

program was developed.(The createdBy certiﬁcate).

–Acertiﬁcation of the program installation describingwhoinstalled the pro-

gram on the device.(The installedBy certiﬁcate).

–Any other application orservice speciﬁc certiﬁcationsthatareconsidered

usefulinanapplication context,e.g., inspectedBy.

The certiﬁcates in the proﬁle are termed proﬁle certiﬁcates.The roleof a certiﬁ-

cate istobind a publickeytoaproﬁle,which are keysbelongingtowell-known

principals.Weconjecture that the number of certiﬁcates isnonetheless mini-

mized since theycertifybehavior,andnotidentity. Forinstance,there canbe

millionsoftaxi clients forasingletaxi clientbehavioralproﬁle.Further,since

the number ofwell-known principalsissmall, certiﬁcates canbe pre-distributed,

e.g., duringsoftware installation.

Policies. WhenBob receives a message,its securitykernelrejects the message

ifitdoes notconform tothe proﬁleofAlice.Further,forutility, Bo bcanspecify

apolicy on the acceptableproﬁleofthesender.Asender whose message does

notconform with thispolicyhas its message automatically rejected.The two

elements ofthepolicyare i) the evidence –a message historythat the sender

must demonstrate fortrustworthiness,andii) the required proﬁle certiﬁcates –

speciﬁed as the role(i.e., createdBy,installedBy,etc.) andidentityofwell-known

principals.Like programs,policies canbe downloaded andinstalled on the device

(since ordinaryPDAusers are notexpected tounderstandtheintricate details).

Platform. The structure ofaambientdevice platform using the message quality

modelisillustrated in Figure 2.The OSorruntime environmentrunsalongside

Fig. 2. Ambient device environment

444 C. Bryce

asoftware layer called the trusted zone.Thiszonestores proﬁles,policies and

historydata.The proﬁleandpolicycanonlybe set byfurnishingaPIN that

supposedly, only the owner oftheplatform knows.Oneof the programs running

on the device isadevice agent ;itis a trusted program that interacts with well-

known principalsfordownloadingprograms andproﬁles.

Verifying Message Quality. Aproﬁleisusedtoconstruct a plea foreach

message sent.The other componentofaplea isahistory of messages sentand

received byaprincipal. A plea sentalongwith a message MfromAlice toBob

isusedin the followingwaybyBob’strustedzonetoverifymessage quality.

–Plausibilityisveriﬁed byi):ensuringtheMbelongs toAlice’sproﬁle; ii)

validatingany proﬁle certiﬁcates in the proﬁle.

–Trustworthiness isveriﬁed byensuringthatAlice’sh

istoryof messages

matches a series of messages that Bobspeciﬁes as required evidence.

–Utilityisveriﬁed byensuringthatMbelongs toBob’sproﬁle.

4 Model Implementation

4.1 Prototype

The programmingmodelchoseninthispaperisbasedon the Linda tuplespace

model[5].Our implementation isbasedon the Lanasystem [2], each principal

has its own tuplespacein which it publishes its tuples.The tuples in aprin-

cipal’stuple space canbe read byall other principalsin its network vicinity;

see Figure 3. Many systems designed forambientenvironments employ Linda’s

tuplespacemodelforthereasonscited above,e.g., Lime [12], Spread [3].

The tuplespacerd operation returnsatuplematching the patternargument

fromthetuplespaceofany device in the neighborhoodof the device issuing

the request.The out operation publishes a tuplein the space of the current

principal. The tuple space primitives donotcontain explicit reference tothe

message qualitymodel, soweconsider its implementation in the programming

modelas transparent.

Akeyrequirementfor the message qualitymodelis that a trusted zone

be presenton each device participatingin the model. One approach tobuild-

ingtrustedzones istouse software protection techniques,nowpossibleusing

strongly typed languages like Java[6]. Another approach istorely on the Trusted

Fig. 3. Each device has its own tuple space

Message Quality for Ambient System Security 445

Platform Module(TPM) toenableaplatform todemonstrate that the software

itisrunninghasnotbeentampered with.ATPMisahardware device whose

functionalityisspeciﬁed bythe Trusted ComputingGroup [17]. The TPM isbe-

comingcommodityhardware,with 200 million TPM-enabled PCs havingbeen

shipped bythe endof2007.

ATPMisusedtostore measures ofthesoftware in the form of secure code

and data hashes internally in its Platform Conﬁguration Registers (PCRs). To

verifythat a device isrunningcorrect (non-modiﬁed)software,its TPM canbe

challenged toproduce its stored PCR values signed usinganAttestation Identity

Key(AiK).ThisiscreatedbyaTPM and certiﬁed byawell-known principal

(orprivacyauthority). The privacyauthoritythat certiﬁes the AiKscanbe

the application software provider.Oncontacting the provider,the clientdevice

downloads the correct digest values.Asillustrated in Figure 4,whenAlice sends

a message mtoBob,thisisin fact in reply toatuple space queryfromBobanda

challenge toAlice’sTPM. BobcanverifyAlice’sPCRs (andsoftware)usinghis

copyofthedigest that he gotwhendownloadingthesoftware.Trust isthusbuilt

in atransitivefashion: the digest permits Bobtobelievethatacorrect version

of the trusted zoneisrunningon Alice’sdevice,andthentrust in Alice’strusted

zoneprovider issuﬃcientforBobtobelievethatAlice iscorrectly implementing

the message qualitymodel.

Fig. 4. Message quality in tuple space model

4.2 Example

The exampleillustrates a shuttleservice that peoplecancall usingtheirPDAs.

There are two classes ofservice:the fast service enables clients tocall taxis

fromany location, the secondrequires them togotoashuttledepotwhere

theytake the shuttle.The principalinteractionsareillustrated in Figure 5. The

ﬁrst three messages,forcallingashuttle,are only forfastshuttles;the ﬁnaltwo

message exchanges occur in all shuttles at the endofthetrip.Tocall ashuttle,a

customer sends a message –“Please”–with the desired destination. The shuttle

replies with a fare quote,which the customer canaccept bysendinga“Stop”

446 C. Bryce

Fig. 5. Shuttle scenario

message.Attheendofatrip,the shuttlesends an“Arrived”message tothe

customer,which isacknowledged by“Bye”.

There are two keysecurityrequirements that wewanttoimplementin this

application. Oneisplausibilityforshuttles –customers canbe sure that theyare

communicatingwith realshuttles,rather thanwith rogue devices masquerading

as shuttles.The secondrequirementiscustomer trustworthiness:shuttles that

receiverequestsneed tobelieve that the request comes fromacustomer who

wants totake a shuttle,rather thanfromsomeoneplayingcustomer messages

“forfun”. To increase trustworthiness,fast shuttles require that potentialcus-

tomers furnish evidence ofprevious shuttlerides.The taxi service assumes here

that someonewhohas previously takenataxi isless likely tolieabout wanting

totake the service again. The only inconvenience forcustomers is that theirﬁrst

ride viatheservice ison aslow shuttle.

The ﬁrst extract showshow the message exchange part ofaproﬁle(which

isdenoted protocol)canbe simply deﬁned.Thisis the proﬁleof a fast shuttle

andfor the part oftakingacustomer.Recall, the principalisunabletosend

messages that donotcorrespondtoits proﬁlesince theyget rejected byreceiving

principals due tomessage qualityfailure.

// Take a client protocol

TupleSequence.ExchangedTuple inc1, outc, inc2;

TupleSequence clientSeq = new TupleSequence();

inc1 = new InTuple(new Tuple(

new Entry[]{new Entry.String("Please"),

Entry.Type.Strings}));

outc = new OutTuple(new Tuple(

new Entry[]{Entry.Type.Strings, Entry.Type.Ints}));

inc2 = new InTuple(new Tuple(

new Entry[]{new Entry.String("Stop"),

Message Quality for Ambient System Security 447

Entry.Type.Strings, Entry.Type.Ints}));

clientSeq = new TupleSequence(

new TupleSequence.ExchangedTuple[]{inc1, outc, inc2});

fastTaxiProtocol.append(clientSeq);

Whenoperating,the fast service shuttle accepts requests.Its ﬁrst task isto

deﬁnetheevidence forservicingclients.

// Set up stuff -- in main()

TrustedZone tz = TrustedZone.getTrustedZone();

PIN pin = new PIN(111);

tz.setProfile(pin, TaxiProtocol.getFastTaxiProtocol());

tz.setRequiredEvidence(pin, TaxiProtocol.getEvidence());

tz.addRequiredCertificate(pin, Role.installedBy,

Shuttle.pubKey);

while ( true ) {

String destination = takeClient();

handleReceipt(destination);

}

private static String takeClient() {

String destination;

// Detect passenger

Entry te1, te2; Tuple t1;

te1 = new Entry.String("Please");

te2 = Entry.Type.Strings;

t1 = TupleSpace.rd(new Tuple( new Entry[]{te1, te2} ));

destination = ((Entry.String)t1.get(1)).extractString();

// Give fare

Entry te3, te4;

te3 = new Entry.String(destination);

te4 = new Entry.Int(30);

TupleSpace.out(new Tuple(new Entry[]{te3, te4}));

// Get OK from passenger

Entry te5 = new Entry.String("Stop");

TupleSpace.rd(new Tuple(new Entry[]{te5, te3, te4}));

return destination;

}

private static void handleReceipt(String destination) {

Entry te1, te2; Tuple t1, t2;

te1 = new Entry.String("Arrived");

te2 = new Entry.String(destination);

t1 = new Tuple(new Entry[] { te1, te2 } );

TupleSpace.out(t1);

t2 = TupleSpace.rd(new Tuple(new Entry[]{ Entry.Any }));

The program starts bysetting the proﬁleof the principal. Thiscanonlybe

donebyfurnishingthecorrect PIN (which issomethingthatathief presumedly

448 C. Bryce

cannotknow). The remainder ofthecode simply implements the protocol with

the passenger.The call setRequiredCertiﬁcates speciﬁes a proﬁle certiﬁcate that

must be presentin the plea.This certiﬁcate attests that the shuttleprogram

was installed bythe shuttlecompany. Thispermits the clienttodistinguish a

realshuttlefromsomeonepretendingtobe onebyinstalling the same program.

The keyused in this certiﬁcate is the publickeyof the shuttlecompany: thisis

loaded on the principalwhenthe customer program isinstalled.

4.3 Analysis of Model

Message qualityisusefulinaddressingtherisks outlined in Section 2.With

respect totheft,whilethisrisk cannever be eliminated,the goalof a security

framework istoreduce the beneﬁt toathief.Forinstance,employingPINsto

access a device andhavingtheowners re-enter hisPIN at the start ofeachsession,

reduces beneﬁt tothieves.Forthisreason, PINs are part ofour securitysolution.

Further,the plausibilityfeature of message qualityensures that ifCharliesteals

Alice’sdevice andsends a message toBob,thenBobcandetect that the device is

stoleniftherequestdoes notcorrespondtoa message that Alice wouldnormally

send.The thief canonlyuse the device foractions(behavior)that Alice speciﬁed,

andonly in the time window that exists before the principalown

er isrequired

tore-enter a PIN.

Similarly, viruses exhibittheirpresence on adevice through behaviorthatis

nottypicaloftheowner of the device.Malware that manifests itselfin thisway

is detected through violationsofplausibilitysince messages are sentthatare

incompatiblewith the device’sproﬁle.Thus,evenifvalidly installed programs

get corrupted viastacksmashingorbuﬀer overﬂow, theirinvalidbehaviorgets

detected.Finally, the usefulness andtrustworthiness properties tacklespam.

In the model, the historyisstored in the trusted zone.Aprincipalmaychoose

toremovepartsofits historyfrom the trusted zone–forinstance toeconomize

space ortoeliminate redundancy–but itmaynot add messages explicitly. We

contendthatmost scenariosonly need torecord a small part oftheirhistory. The

shuttleservice was anexamplewhere a principal’shistoryisusedasevidence to

argue for a message’squality. Another approach toeliminatingthehistorylog

isforaprincipaltoask a well-known authorityprincipaltosignaproﬁle certiﬁ-

cate (with a rolehistoryValidatedBy)fortherequestingprincipal. The requestor

only needs topresentits historylogin exchange for the proﬁle certiﬁcate.The

principalcantransmitthisproﬁle certiﬁcate in pleas.

5 Conclusions and Related Work

Thispaperhaspresented a securitymodelforambientinformation systems.

The modelconcentrates on the propertyof message quality, w hich isthecorner-

stoneforimplementingother securityprotocols.The framework has the advan-

tage ofnotundermining the attractivepr

operties ofambientsystems,notably,

anonymityandspontaneityofcommunication. The modelisprototyped in Java

Message Quality for Ambient System Security 449

and the prototype’simplementation uses the TPM. A longer version ofthispaper

isfoundin [1].

Property-based attestation [13] looks at how the TPM canbe used toenable

devices todeliver proofs that speciﬁc securityproperties hold.The work does

notspecifyhow properties are derived from the measures takenbythe TPM.

Nonetheless,itshows that the TPM canbe used formore elaborate security

guarantees thanbinary(code)attestation.

The plausibilityaspect of message qualityissimilar in concept toproof-

carryingcode [10] whose main aimistoprotect a platform fromuntrustworthy

code.Inthis approach,adownloaded program isaccompanied byaproofofthe

program’s(good)behavior.The host environmentcanverifythe proofmechani-

cally, andifthis passes,canthentrust the program torunsecurely. An example

of the properties that canbe proveninthis approach isthesequence ofsystem

callsmadebythe program,e.g., [15] where the host environmentveriﬁes that

the program does notleak platform information. The message qualitymodelis

nonetheless computationally less expensivethanthe veriﬁcation mechanisms of

proof-carryingcode.

Acknowledgments. Thiswork ispartly conducted in the contextofthe

PRIAM (PrivacyinAmbientSystems)project -anINRIA ﬁnanced collabora-

tion examining the representation ofprivacylegislation in moderninformation

systems.

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August 01(2004)

Request Satisfaction Problem in Synchronous

Radio Networks

BenoˆıtDarties,Sylvain Durand,andJ´erˆome Palaysi

LIRMM, Universit´e Montpellier II

161 rue Ada, 34392 Montpellier Cedex 5 - France

{benoit.darties,sylvain.durand,jerome.palaysi}@lirmm.fr

Abstract. We study two algorithmical problems inspired from rout-

ing constraints in a multihop synchronous radio network. Our objec-

tive is to satisfy a given set of communication requests in the following

model: nodes send omnidirectional radio transmissions in synchronous

slots; during a given slot, a node can receive a message from an adja-

cent node if and only if no other neighbour is transmitting - otherwise,

radio interferences may occur if two or more neighbors transmit in the

same slot -. The objective is to minimize the number of slots used. The

two problems diﬀer in that the routing policy may be imposed (DAWN-

path), or not (DAWN-request). In this second case, a path must be

assigned for each request, to deﬁne the nodes to use to reach the destina-

tion from the source. We present some complexity results, in particular

showing that both problems are NP-hard when the network is restricted

to a tree. We also present a polynomial algorithm in O(n2K) when the

number of requests is bounded (by above) by a constant K.

Keywords: Radio Network, Request Satisfaction, Complexity.

1 Introduction

Aradio network isacollection oftransmitter-receiver stations(ornodes)com-

municatingwith oneanother viamultihopwireless links.The use oftheradio

medium implies some restrictionsandproperties:whenever a node transmits,all

the nodes in its communication range mayreceivethetransmission. Incoming

messages havetobe forwarded toreach nodes which are located more thanone

hopawayfromthesource.Since all nodes share the same frequencychannel, a

collision mayoccur iftwo ormore neighbors transmitsimultaneously, preventing

correct reception of the message.

In thispaper,westudytwo communication problems inspired fromrouting

constraints in thiskindofnetwork.Weconsider the followingsimpliﬁed commu-

nication model, which has beenwidely used for the broadcast problem[1, 4–6,

10, 12, 13] or the gatheringproblem [2,3] in multihopradio networks :nodes

send messages in synchronous slots;duringeachsloteachnode acts either as a

transmitter or a receiver.Anode actingasatransmitter sends a message which

canpotentially reach the nodes that are in its communication range.Anode

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 451–462, 2008.

Springer-Verlag Berlin Heidelberg 2008

452 B. Darties, S. Durand, and J. Palaysi

acting as a receiver successfully receives a message fromatransmitter node if

no other neighbortransmits in thisslot.Iftwo ormore neighbors of a receiver

node utransmitsimultaneously in agivenslot,thenthe messages mayinterfere

with each others (collide)and the messages are nottransmitted successfully to

u.Wenote that two neighbors uandvmaysuccessfully transmitin the same

slottouandv,ifwe assume that uandvare notadjacent,and respectively

vandu:the node uactingastransmitter simply ignores the transmission of

vandreciprocally. Such a network is characterized as a ∆-port transmission, 1-

port reception, half-duplex, synchronous network.We suppose that the network

topologyisﬁxed,at least duringthetime the problem must be solved.Allthose

properties specifythe modelweusein thiswork.

In thiscontext,weconsider the problem ofsatisfyingasetofcommunication

requests within aminimum timeframe,byindicatingforeachnode the slots

on which ithastorelaytransitingpackets.Arequest isacoupleofsource-

destination nodes representingthestartingandendingnodes ofagivenmessage.

The second section ofthispaperdetailsthemodelandintroduces the DAWN-

path andDAWN-request problems.Generalcomplexityresults are discussed

in athird section where wewill show that these problems are quite diﬃcult

evenforparticular cases.However wepresentin the fourth section apolynomial

algorithm whenthe number ofrequestsisbounded byaconstantK.

2 Describing the Model and Expressing the Problem

2.1 The Model

The network isrepresented as anundirected graph Gwhere the set V(G)ofver-

tices corresponds tothe set ofnodes ofthenetwork.Anedge e={u, v}∈E(G)

denotes that ucandirectly communicate tov(no additionalnode isrequired to

relaythe message)andreciprocally1.

Arequest risacouple(s, t)|s, t ∈V(G), where srepresents the source andt

the destination oftherequest.

Apath oflength kin agraphGisanordered list (v0,v

1,...,v

k), where

vi∈V(G)forany i∈[0,k], and such that the edge (vi,v

i+1)exists in E(G)for

any i∈[0,k−1], andall the edges are diﬀerent.Throughout the paper all the

considered paths are simplepaths,that is,paths which visitavertexat most

once.Paths are used here torepresentacommunication road in the network.

GivenagraphGandacollection ofcommunication requests R,let Pbe a

routing function on Rwhich associates toeach r=(s, t)∈RapathP(r)inG,

(alsodenoted byPr), beginningwith sandendingwith t.

GivenagraphG,acollection ofrequestsR,andaroutingfunction P,

wedeﬁneadate assignment dtobe a function which takes two arguments r

andx,with r=(s, t)∈R,x∈Prandx=t,andreturnsaninteger d(r, x).

1We consider that if xcan directly communicate with ythen ycan directly commu-

nicate with x. We can deduce that the graph is symmetrically directed, and will be

represented by an undirected graph.

Request Satisfaction Problem in Synchronous Radio Networks 453

Thisinteger corresponds toaslot,such that xtransmits the message ofrto

the nexthop duringthisslot.Multiplexingisnotallowed,thisimplies that each

transmission only containsasingle message.Adate assignmentdissaidtobe

valid ifandonly iff

oreachrequestr=(x0,x

k)with Pr=(x0,x

1, ..., xk)the

proposition d(r, x0)<d(r, x1)< ... < d(r, xk−1)istrue.Moreover wesaythat a

validassignmentisconﬂict-free ifandonly ifforeachd(r, xi)=d(r,y

j)where

r=r,the followingholds :

1. xi=yj:prevents multiplexing

2.xi+1 =yj∧yj+1 =xi:anode cannot receiveandtransmitsimultaneously

3. {xi,y

j+1}/∈E(G)∧{yj,x

i+1}/∈E(G): ∆-port-transmission, 1-port-

reception.

Wenote max(d)=maxr∈R,x∈V(G)d(r, x)the cost ofd,i.e.the number ofslots

used byadateassignmentd.

2.2 The DAWN Problem

Givenasetofrequeststosatisfyinasynchronous radio network andamaximum

number ofslots,the problem DAWN (Date Assignment in Wireless Network)

consists in ﬁndingaconﬂict-free date assignmentalongcommunication paths.

Accordingtowhether the paths are given(e.g.bythe routingfunction) ornot,

wedistinct two main problems:DAWN-paths andDAWN-request.

The DAWN-path problem is stated as follows:

INPUT: An undirected graph G,acollection ofrequestsR=.ri=(si,t

i)|1≤

i≤K/,aroutingfunction Pon Rwhich associates toeach request riapath

P(ri) linkingthevertices ofri,anaturalinteger D.

QUESTION: Does a validandconﬂict-free date assignmentexist in such a man-

ner that the number ofrequired slots islower thanorequaltoD?

Let min-DAWN-path be the optimization version ofDAWN-path.Foreachnat-

uralinteger DwedeﬁnetheD-DAWN-path problem as the subclass ofDAWN-

path where the maximum number ofallowed slots isD.Note that Disbounded

byaboveby|V(G)|×|R|otherwise the answer isobviously “yes”. Figure 1

presents aninstance ofDAWN-path (1(a)) andasolution (conﬂict-free assign-

ment)toit(1(b)).

Weobserve that there isno optimalﬁxed routingfortheDAWN-path prob-

lem [8,page 97]. Thisleads us topropose the DAWN-request problem:

INPUT: An undirected graph G,acollection ofrequestsR=.ri=(si,t

i)|1≤

i≤K/,anaturalinteger D.

QUESTION: Does a validandconﬂict-free date assignmentexist in such a man-

ner that the number ofrequired slots islower thanorequaltoD?

454 B. Darties, S. Durand, and J. Palaysi

ABCD

GHIJK

(a)

ABCD

GHIJK

(b)

Fig. 1. An instance (G, R, P ) of min-DAWN-path containing 2 requests r1=(a, f ),

r2=(g, k), P(r1)=(a, b, c, d, e, f)andP(r2)=(g, h,i, j, k) (sub-ﬁg. a). A valid and

conﬂict-free date assignment and within a minimum number of slots (sub-ﬁg. b).

As stated before,wecall min-DAWN-request the optimization version ofDAWN-

request,andD-DAWN-request the subclass ofDAWN-request where Disthe

maximum number ofallowed slots.

3 Complexity Results

Weadopt the terminologyof[7]: aproblem isnot approximablewithin aconstant

factorifno polynomialapproximation algorithm with a constantperformance

guarantee exists.Moreover anapproximation algorithm has a constantperfor-

mance guarantee ofρifforeachinstance Iofaproblem itﬁnds a solution the

cost ofwhich isatmost ρtimes the cost oftheoptimalsolution forinstance I.

In the following subsection weshow that in generalmin-DAWN-path and

min-DAWN-request are NP-hard andnot approximablewithin aconstantfact

or.

These results are based on the complexityofcoloringproblems on graphs.The D-

COLORINGproblem [11] consists in assigningacolor(represented byanumber

bounded byabovebyD)toeach vertexassumingthattwo adjacentvertices

are assigned diﬀerentc

olors.Itisknown that D-COLORINGisNP-complete

forany constantD≥3, and that the correspondingminimization problem min-

COLORINGisNP-hard andnot approximablewithin aconstantfactor.

In asecond subsection weshow these problems remain NP-hard evenwhen

the network isatree,but here the reduction does notenableustoprovethe

inapproximability(within some constant). In the third subsection welocate the

boundaries betweenpolynomialityandNP-completeness forD-DAWN-path and

D-DAWN-request whenonlyDvaries.

3.1 Two Diﬃcult Problems

The ﬁrst theorem proves the NP-completeness ofboth problems in general.

Theorem 1. Problems min-DAWN-path and min-DAWN-requests are NP-hard

and not approximable within some constant factor. For any D≥3, decision

problems D-DAWN-path and D-DAWN-request are NP-complete.

Proof. WeﬁrstprovetheNP-completeness ofD-DAWN-request bya reduction

toD-COLORING.

Request Satisfaction Problem in Synchronous Radio Networks 455

D-DAWN-request isin NP : givenaroutingfunction Pandadateassignment

das a solution ofaninstance,onecancheck in apolynomialtime ifPenables

each message toreach theirdestination, andifdisavalidconﬂict-free date

assignmentusingfewer thanDslots.

Let IC=(GC)be aninstance ofD-COLORING,andlet us note n=|V(GC)|.

FromICwedeﬁneaninstance I=(G, R)ofD-DAWN-request,where Gisa

graph such that V(G)={sx,t

x|x∈V(GC)}andE(G)=.{sx,t

x}|x∈V(GC)/

∪.{sx,t

y}|{x, y}∈E(GC)/∪.{tx,t

y}|x, y ∈V(GC)/.WedeﬁnethesetR=

rx=(sx,t

x)|x∈V(GC)ofncommunication requests.Clearly, the instance

Icanbe constructed in apolynomialtime.Figure 2(b)gives anexampleofa

graph Gconstructed from the graph GCofﬁgure2(a).

(a) A graph GC

clique

(b) The resulting graph G

Fig. 2. Construction of Gfrom Gc

Weshow that,ifthereexists a validconﬂict-free date assignmentforIusing

k≤Dslots,thenthere exists a solution tothe instance ICofD-COLORING

with cost k≤Dandreciprocally.

Let S=(P, d)be a solution ofI=(G, R)where Pisaroutingfunction

forRanddavalidandconﬂict-free date assignmentfor(G, R, P )with cost

k=max(d)≤D.Let us suppose there exists a request ri=(si,t

i)inSsuch

that the message isnotdirectly emitted fromsitoti,but requires at least one

relaynode tj|j=i.Iftjtransmits in slotu,thennoother node slmaytransmit

in thesameslot,while∪i≤ntiisaclique.Thenwecanextract a solution S

fromSwith cost z≤zin which sitransmits directly totiat slotu.Thus

fromany solution Swith cost k,wecompute a proper solution S=(P,d

)

with cost k∗≤k≤Dsuch that each message isdirectly transmitted fromits

source toits destination. Clearly P(ri)=(si,t

i)∀ri∈R.Let cbe the function

which assignstoeach vertexx∈V(Gc)the colord(rx,s

x). Let us note that

max(d)=max(c)≤D.The resultingcoloringisvalid because ifxandyare

adjacentin Gcthenbyconstruction the edges {rx,t

y}and{ry,t

x}exist in G

andimply that d(rx,s

x)=d(ry,s

y).

Reciprocally, let cbe a vertexcoloringofGcwith cost k≤D.Let Pthe

routingfunction such that P(ri)=(si,t

i)∀ri∈R,anddbe the date assignment

which associates the date c(x)toeach couple(rx,s

x). Thendisavalidconﬂict-

free date assignment such that max(c)=max(d).

To conclude,weclaimthattoany vertexcoloringcofICcorresponds a

solution toIcomposed ofaroutingfunction Pavalidandconﬂict-free date

456 B. Darties, S. Durand, and J. Palaysi

assignmentdof(G, R)such that max(c)=max(d), andreciprocally. Since D-

COLORINGisNP-complete forany D≥3 [11] andD-DAWN-request belongs

toNP,thenD-DAWN-request isalsoNP-complete forany D≥3. Thisproofcan

be extended toprovetheNP-completeness ofD-DAWN-path forany D≥3, by

addingtothe instance Ithe routingfunction Psuch that P(ri)=(si,t

i)∀ri∈R.

By adaptingthisprooftothe optimization versionsof these problems weshow

that min-DAWN-path andmin-DAWN-request are NP-hard bya reduction to

min-COLORING.Therefore the reduction preserves the inapproximabilityof

min-COLORING,which isNP-hard andnot approximablewithin some constant

factor.Thisallowstoconclude.

Wenow show that DAWN-path andDAWN-request are still NP-complete even

ifthenetwork isatree.Thisresolves anopenquestion suggested in [9]. The

proofcanbe extended tobinarytree orUnitDisk Graph (intersection graph of

disks with equaldiameters). UDGareoftenused tomodelthe topologyofad-hoc

wireless communication networks.Let us introduce the followingpropositions:

Lemma 1. Let I=(G, R, P, D)be an instance of DAWN-path, let xa vertex

from V(G)and ian integer. Then there exists an instance I=(G,R

,P,D)

of the same problem with V(G)⊆V(G),R⊆R, such that :

–each valid and conﬂict-free date assignment don Irequires exactly Dslots,

and is also a valid and conﬂict-free date assignment on I,

–for each valid and conﬂict-free date assignment don Iand each request

r∈Rwe have d(r, x)=i,

–the instance Ican be constructed in a polynomial time.

Proof. Let us consider the followingitems:

–aninstance I=(G, R, P , D)ofDAWN-path,

–arequestr∈Rsuch that P(r)=(s,...,x,y,...,t),

–achain C={c1,c

2,c

3,...,c

D+1}oflength D+1,with V(G)∩V(C)=∅,

–arequestr=(c1,c

D+1),

–anaturalinteger i∈[1,D].

Wenote H=(V(G)∪V(C),E(G)∪E(C)∪{{y, ci}})anddeﬁneP(r)=

(c1,c

2,c

3,...,c

D+1). Note that ifGisatree,thenHisalsoatree.Figure 3

schematically illustrates such a construction. Weclaimthefollowing:

1. The instance I=(H, R ∪{r},P,D)canbe constructed in polynomialtime

fromI=(G, R, P, D),

2.let dbe a validandconﬂict-free date assignmentforI,thenwehave

d(r,c

i)=i, d(r, x)=i,anddisavaliddateassignmentforI.

Thisconstruction presented in the proofoflemma 1 will be used in the proof

oftheorem 2 topreventsome nodes fromtransmitting during certain slots.In

the following,wesaythat arequestr=(s, t)starts at slottifthes

ource node

sproceeds tothe transmission of the message ofrduringthetth time slot.

Request Satisfaction Problem in Synchronous Radio Networks 457

i-1 i+1

D+11 i+2i

STG

Fig. 3. Howtopreventanodexfrom transmitting in slot i

Let uandDbe two naturalintegers such that D≥6. Wedeﬁneatight (u, D)

DAWN-path instance as the DAWN-path instance (C[1,D+7u],R,P,D)where

C[1,D+7u]isachain havingD+(7u)vertices {1,2,...,D+7u}andtheedges

{i, i+1}|∀0≤i≤D+7u−1. Risthesetof2urequests {r1,¯r1,r

2,¯r2,...,r

u,¯ru}

with ri={(7i−5,7i+D−9)}and¯ri={(7i−6,7i+D−8)}|∀i≤u.

Lemma 2. Let us consider a tight (u, D)instance for some integer uand D.

Let us suppose dis a valid and conﬂict-free date assignment, and i∈[1,u].We

make the following observations:

1. (d(ri,7i−5),d(¯ri,7i−6)) ∈{(5,1),(1,3)},

2. d(ri,j+1)=d(ri,j)+1,∀j∈P(ri)−{7i+D−9},

3. d(¯ri,j +1)=d(¯ri,j)+1,∀j∈P(¯ri)−{7i+D−8}.

Given two natural integers i∈[1,u]and j∈P(ri):

1. if d(ri,7i−5) = 1 then d(ri,j)=j−7i+6 and d(¯ri,j)=j−7i+9

2. if d(ri,7i−5) = 5 then d(ri,j)=j−7i+10 and d(¯ri,j)=j−7i+7

Proof. Thisobvious proofisleft tothe reader.

Theorem 2. DAWN-path and DAWN-request remain NP-complete even if the

graph representing the network topology is a tree.

Proof. The proofisbasedon apolynomialreduction ofany instance of3-SAT

problem [11] toaninstance (G, R, P, D)ofDAWN-path where Gisatree.

Let ISAT =(U, W )be aninstance of3-SAT, composed ofasetofvariables

U={x1,x

2, ..., xn}andasetofclauses of3literalsW={c1,c

2, ..., cm}.We

note n=|U|,m=|W|,andsetD=m+7n+3.

Let us consider the tight (n, D)instance (G1,R

1,P,D). The main idea ofthe

proofconsists in assigningtwo requests riand¯ritoeach variablexi∈W.Thus

forthesakeofclaritywenote rxithe request riandr¯xithe request ¯ri.

Let G2be the tree such that V(G2)=V(G1)∪(ci,1),(ci,2)|i∈[1,m]and

E(G2)=E(G1)∪.{(ci,1),(ci,2)},{7n+i, cs

i}|i∈[1,m]/.Inthe followingwe

note cs

ithe couple(ci,1) andct

ithe couple(ci,2)forany integer i.Let R2

be the set ofrequests{rci=(cs

i,c

i)|i∈[1,m]}.Now,consider the instance

(G2,R

1∪R2,P,D)(see Figure 4 foranexample).

By applyingtheconstruction oflemma 3.1 severaltimes,wecreateaninstance

I=(G, R, P, D)byaddingelements to(G2,R

1∪R2,P,D)as follows:foreach

458 B. Darties, S. Durand, and J. Palaysi

2915 16 21 24 25 31 32 3839

r1 r1’ r2 r2’ r3 r3’

47...

Fig. 4. AgraphG2and a set of requests R1∪R2constructed from an instance ISAT =

(U, W )whereU={x1,x

2,x

3}and W={c1,c

2}.HereD= 26.

request rci=(cs

i,c

i)wepreventcs

ifromtransmittingtoct

ithe message ofrequest

rciduringeachslott≤D,except for3speciﬁc ones which are deﬁned from

the literalsoftheclause ci:ifcicontainsthepositive(resp.negative)literal

associated tothe variablexj|j≤n,thencs

iisallowed totransmitin slot7n+

i−7j+6(resp. 7n+i−7j+8).Since G2isatree,Gisalsoatreeandthe

routingfunction isstill obvious.

The size ofIispolynomialinthe size ofISAT ,anditcanbe constructed in

apolynomialtime.Weclaimthatifthereisasolution in Dslots toI,thenwe

candeduce a solution tothe instance ISAT andreciprocally.

Let us consider a validandconﬂict-free date assignmentdon the instance I.

Accordingtolemma 2 andforeachinteger i∈[1,n], onerequestof{rxi,r

¯xi}

must start at slot1, andtheother as soon as possible,andonce a request has been

started,its progression cannotbestopped.Moreover each request rci|i∈[1,m]

isclearly satisﬁed byd.The slotwhich has beenassigned to(rci,c

i)isoneof

the three allowablevalues deﬁned fromtheliteralsofclause ci.Our construction

implies that there exists jsuch that d(rci,c

i)isoftheform 7n+i−7j+6

or7n+i−7j+8,accordingtoxjisapositiveoranegativeliteral. Ifxjisa

positiveliteral, thenthe source ofrxjislocated on vertex7j−5, i.e.at distance

7n+i7j+5 fromthevertex7n+jwhich isadjacenttocs

i.Thenrxjnecessarily

starts at slot1-andwehaved(rxj,7n+i)=d(rci,c

i)-otherwise messages

wouldcollide.Weadopt a similar reasoningwhenxjisanegativeliteral. Then

foreachclause ci,there exists at least one(positiveornegative)literall∈ci,

such that the request rlstarts before r¯

l.Byaﬀectingthevalue “True”toall

variables xiwhere rxihas beenstarted at slot1(i.e.before r¯xi)and“False”

otherwise,weobtain asolution tothe instance ISAT .

Reciprocally wecandeduce a solution tothe instance Ifromasolution to

ISAT :foreachvariablexiwe start the request rxibefore r¯xiifandonly ifxihas

the value “True”. Foreachclause ci,westartrciat the ﬁrst validandavailable

slot(thisslotexists since the clause ciissatisﬁed byat least oneliteral).

To conclude wepointout that 3-SAT isNP-complete andthatDAWN-path

belongs toNP.Thenthe DAWN-path isNP-complete evenifthenetwork is

atree.Thisimplies the NP-completeness ofDAWN-request,since there isone

unique path linkingeachsource toits destination whenthe network in atree.

Request Satisfaction Problem in Synchronous Radio Networks 459

3.2 Locating the Boundaries between Polynomiality and

NP-Completeness

Wehaveshown that DAWN-path andDAWN-request are NP-complete even

whenthe network topologyisveryrestrictive.Inthe following subsection, we

focus our interest on the inﬂuence ofthemaximum number ofslots Don the

complexityof these problems.

Theorem 1alreadyaﬃrms that D-DAWN-path andD-DAWN-request are NP-

complete whenD≥3. By the waywhenD=1onecanverifyinpolynomial

time ifaninstance canbe satisﬁed:foreachrequestr=(s, t), smust be adjacent

tot,andcanonlyemits at the ﬁrst slot.Hence tcannotbeadjacenttoanother

source node s2,andsmust be a source only fort.The nexttheorem states that

onecancheck in apolynomialtime ifthereisasolution toaD-DAWN-path

instance whenD≤2.

Theorem 3. The 2-DAWN-path decision problem is polynomial

Proof. Let I=(G, R, P )aninstance of2-DAWN-path.Onecansuppose that

foreachrequestr=(s, t)the path P(r)containsatmost onevertexlbetween

sandt,otherwise the instance isclearly insolvable.Wepropose analgorithm in

three steps :

–Dates are forced fortransmitters belongingtotwo-hoprequests.

–Therefore dates 1(resp.2)are spread toeverytransmitter which cannot

transmit duringthesecond(resp.ﬁrst)slot.

–Remaining dates are computed usinga2-SAT-like algorithm.

Theorems 1and3show that D-DAWN-path ispolynomialwhenthe maximum

number ofslots Dislower thanorequalto2,andbecomes NP-complete when

D≥3. Theorem 4 proves that D-DAWN-request isNP-complete forD=2.

Theorem 4. The 2-DAWN-request decision problem is NP-complete

Proof. Let ISAT =(U, W )be aninstance of3-SAT where U={x1,...,x

denotes a set ofvariables andW={c1,...,c

m}asetofclauses.Foreach

variablexi∈Ulet Hxi=(X, Y , E)be the complete bipartite graph K3,2

such that X={(1,x

i),(1,¯xi)}andY={(2,x

i),(2,¯xi}.Foreachclause ci=

{l1,l

2,l

3}∈W,let Fci=(X, Y, E )be the complete bipartite graph K3,2such

that X={(1,c

i),(2,c

i)}andY={(ci,l

1),(ci,l

2),(ci,l

3)}.Note that l1tol3can

be positiveornegativeliterals,each literalcorrespondingtoavariablexi∈U.

Let I=(G, R)be a 2-DAWN-request instance with V(G)=.{xi∈UV(Hxi)}∪

{ci∈WV(Fci)}/andE(G)=.{xi∈UE(Hxi)}∪{ci∈WE(Fci)}∪{(ci,l),(2,

l)|ci∈W, l ∈ci}/.Figure 5presents anexampleofgraphGconstructed from

a3-SAT instance ISAT =(U, W ). The requests collection Rcontainsexactly all

the requests oftheform ((1,c

i),(2,c

i))|ci∈W,and((1,l),(2,l)) where lisa

literalcorrespondingtoavariablexi∈U.

Let dbe validdateassignmentdforIusingonly 2slots.Weassigntoany

literallthe value “True”ifandonly if(1,l)emits at slot1,and“False”oth-

erwise.Givenaclause ci∈W,exactly onenode oftheform (ci,l)emits at

460 B. Darties, S. Durand, and J. Palaysi

xA yAb

x1 x1b

x2 x2b

zBb

xB yBb

y1 y1b

y2 y2b

z1 z1b

z2 z2b

zCbxCbyC

Fig. 5. graph constructed from ISAT =(U, W )withU={x1,x

2,x

3}and W=

{c1,c

2,c

3}with c1={x1,¯x2,x

3},c

2={x1,¯x2,¯x3}and c3={¯x1,x

2,¯x3}

slot2.Thisnode isadjacenttoanode (2,l), which could receive the message of

the request ((1,l),(2,l)) at slot1only.Thus (1,l)istrueandcissatisﬁed.

Reciprocally, suppose that ISAT admits a solution. Foreachliterallﬁxed at

“True”, let us assignthe date 1tovertex(1,l)and the date 2 to(2,¬l).Let ci

be a clause fromW.Date 1isassigned tovertex(1,c

i). Date 2 must be assigned

toexactly oneadjacentvertexof(1,c

i). Wecanchoose any couplewith the

correspondingliterallﬁxed at “True”. Thisdateisavailablesince (ci,l)isonly

adjacentto(2,c

i)(the destination) and(2,l), which has alreadyreceived the

message at slot1. Since 3-SAT isNP-complete and2-DAWN-request isin NP,

2-DAWN-request isindeed a NP-complete problem.

Thus wehaveshown that knowledge oftheroutingpolicyplaysarolein the

complexityofboth problems,since the limitbetweenpolynomialityandNP-

completeness islocated between2and3forDAWN-path,but between1and2

forDAWN-request.

4 Solving Instances with a Bounded Number of Requests

Wegiveapolynomialalgorithm formin-DAWN-path problem andmin-DAWN-

request problem whenthe number ofrequestsisbounded byabovebyaconstant

K.The followingnotation anddeﬁnition will be used :

–Fori∈[1,n], let πi(t)denotes the ith elementofan-tuplet=(x1,x

2, ..., xn).

–The contracted form of a tu ple (x1,x2,...,x

n)isthetuple(xi)(i∈[1,n ])∧(xi=xi−1).

Wepropose a polynomialalgorithm tosolveinstances Iwith a number of

requests bounded byK.Webuildastategraph,where each vertexdescribes a

possible state ofthenetwork at a givenslot.Anedge links XandYifandonly

ifonecangofrom state Xtostate Yorreciprocally in only oneslot.Foragiven

min-DAWN-path instance I=(G, R =(r1,r

2, ..., rk),P)with |R|≤Kthe state

graph S(I)isdeﬁned as follows:

–the vertexset is the cartesianproduct P(r1)×P(r2)···×P(rK). A vertex

X=(x1,x

2,...,x

K)indicates that foreachi≤K,the message ofrequest

rihas reached the node πi(X)=xi∈V(G).

Request Satisfaction Problem in Synchronous Radio Networks 461

–there isanedge betweenX=(x1,x

2,...,x

K)andY=(y1,y

2,...y

K)of

S(I)ifandonly ifthesimultaneous emission ofnodes {xi|xi=yi,1≤i≤K}

allowstodeliver each message fromxi=yitoyiin oneslotonly. Formally,

forX=(x1,x

2,...,x

K)andY=(y1,y

2,...y

k), (X, Y )∈E(S(I)) ifwe

have,foreachisuch that xi=yi:

•xiandyiare immediately consecutivein P(ri),

•there isno j=i,such that xj=yjand{xj,y

i}∈E(G),

•foreachj=isuch that xj=yj,wehave|xi,y

i,x

j,y

j|=4.

The state graph S(I) ofamin-DAWN-request instance Iisconstructed according

tothe same method,exceptthatthesetofvertices isthesetV(G)×V(G)×

···×V(G)=V(G)K.These state graphs canbe constructed in apolynomial

time,since Kisaconstant.Wecandistinguish two vertices in S(I): the source

(s1,s

2,...,s

K)andthesink (t1,t

2,...,t

K)where siandtiare respectively the

source andthetargetoftherequestriforany i∈[1,K].

Weconclude the section with thistheorem:

Theorem 5. min-DAWN-path and min-DAWN-request can be solved by a poly-

nomial-time algorithm with complexity O(n2K)when the number of requests is

bounded by above by a constant K.

Proof. (sketch of the proof)Consider I=(G, R =(r1,r

2,...,r

K),P)amin-

DAWN-path instance with |R|≤K,andlet us construct the state graph S(I).

Onemaycheck that a shortest path betweenthe source andthesinkin S(I)

canbe associated with anoptimalconﬂict-free date assignmentandreciprocally.

Such a path canbe foundwith a O(n2K)complexityalgorithm.

5 Conclusion and Perspectives

Wehavestudied the complexityoftherequestsatisfaction problem in asyn-

chronous radio network.Table1summarises the results ofthispaper.

Wehave suggested other results [8]onparticular cases i.e.ondynamicnet-

work,orwhenrequests cannotbepausedassoon as theyhavestarted.Possible

perspectiveforth

is research work consist in studyingthecomplexityofDAWN-

path andDAWN-request on speciﬁc topologies,inorder todiscover polynomial

cases evenwhenthe number ofrequestsisunbounded.Particularly the complex-

itywhenthe network isachain isanopenquestion (however forthiscase,we

Table 1.

DAWN-path: Complexity: DAWN-request:

Min-DAWN-path NP-hard (even in trees),

not approximable within

some constant factor.

Min-DAWN-request

D-DAWN-path D≤2Polynomial D≤1D-DAWN-request

D≥3NP-complete D≥2

min-DAWN-path, |R|≤KPolynomial : O(n2K)min-DAWN-request, |R|≤K

462 B. Darties, S. Durand, and J. Palaysi

haveaconstantfactor approximation algorithm). Moreover,ﬁndingheuristics

with performance guarantee fordiﬃcultinstances constitutes a naturalextension

ofthiswork.

References

1. Alon, N., Bar-Noy, A., Linial, N., Peleg, D.: A lower bound for radio broadcast. J.

Comput. Syst. Sci. 43(2), 290–298 (1991)

2. Bermond, J.-C., Galtier, J., Klasing, R., Morales, N., P´erennes, S.: Hardness and

approximation of gathering in static radio networks. In: FAWN 2006, Pisa, Italy

(2006)

3. Bermond, J.-C., Peters, J.: Eﬃcient gathering in radio grids with interfer-

ence. In: Septi`emes Rencontres Francophones sur les Aspects Algorithmiques des

T´el´ecommunications (AlgoTel 2005), May 2005, pp. 103–106 (2005)

4. Chelius, G.: Architectures et Communications dans les r´eseaux spontan´es sans ﬁl.

PhD thesis, INSA de Lyon, INRIA Rhˆone Alpes, France (April 2004)

5. Chlamtac, I., Kutten, S.: On broadcasting in radio networks - problem analysis

and protocol design. IEEE Transactions on Communications 33, 1240–1246 (1985)

6. Chlamtac, I., Weinstein, O.: The wave expansion approach to broadcasting in mul-

tihop radio network. IEEE Transaction Communication (39), 426–433 (1991)

7. Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms, 2nd

edn. Dunod (2001)

8. Darties, B.: Probl´emes algorithmiques et de complexit´edanslesr´eseaux sans ﬁl.

PhD thesis, LIRMM, Universit´e Montpellier 2, France (December 2007)

9. Darties, B., Palaysi, J.: Satisfaction de requˆetes par aﬀectation de dates d’´emissions

dans les r´eseaux radios. In: Rencontres francophones du Parall´elisme (RenPar’17),

pp. 157–163 (2006)

10. Fraigniaud, P., Lazard, E.: Methods and problems of communication in usual net-

works. In: Proceedings of the international workshop on Broadcasting and gossip-

ing, pp. 79–133. Elsevier North-Holland, Inc. (1994)

11. Garey, M.R., Johnson, D.S.: Computers and Intractability: A guide to the theory

of NP-completeness. W.H. Freeman, New York (1979)

12. Hedetniemi, S.M., Hedetniemi, S.T., Liestman, A.L.: A survey of gossiping and

broadcasting in communication networks. Networks 18, 319–349 (1986)

13. Kowalski, D.R., Pelc, A.: Centralized deterministic broadcasting in undirected

multi-hop radio networks. In: APPROX-RANDOM, pp. 171–182 (2004)

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 463–474, 2008.

A Novel Mobility Model from a Heterogeneous Military

MANET Trace

Xiaofeng Lu1,3, Yung-chih Chen2, Ian Leung1, Zhang Xiong3, and Pietro Liò1

1 Computer Laboratory ,University of Cambridge,

15 JJ Thomson Avenue, Cambridge CB3 0FD

{firstname.lastname}@cl.cam.ac.uk

2 Department of Computer Science

University of Massachusetts at Amherst

140 Governors Drive, Amherst, MA 01003-9264

yungchih@cs.umass.edu

3 College of Computer Science

Beijing University of Aeronautics and Astronautics

XueYuan Road, Beijing 100083

xiongz@buaa.edu.cn

Abstract. In this paper we describe our analysis of a real trace and propose a

mobility model. The trace data we used for this study was collected from a

military experiment carried out in Lakehurst, N.J., U.S.A. The structure of these

entities in the trace is novel, say layered and heterogeneous—some nodes

moved on the ground whilst some hovered in the sky. Evaluation results show

our mobility model well and truly captures some aspects of the spatial and

temporal characteristics of the real traces. This mobility model can be used to

generate synthetic traces with different travel schedules. Such experiments are

costly to be realized in real world scenarios

1 Introduction

Mobility models are important in simulation-based studies of wireless Ad hoc

networks. However, the majority of models have little relevance to real-world

movements, such as Random Waypoint. In order to thoroughly analyze the

performance of network protocols of Ad hoc networks, it is imperative to capture the

gist of the movements by providing a realistic mobility model [1, 2, 6].

Many mobility models have been developed to simulate the movements of real life

systems. There are two types of mobility models used in the simulation of networks:

traces and synthetic models [2, 5]. Traces log the movements of individuals in real

life systems. If number of entities in the traces is large and the period time is long

enough, they can provide real and accurate information of mobility pattern. An

increasing number of researchers extract the mobility characteristics from actual

traces to build more realistic mobility models [7, 11-14, 16-18].

In this paper, we analyze a novel set of mobility traces from an actual military

training trace. Suppose a number of soldiers navigate through a highly hostile terrain

where they are highly susceptible to adversities such as an ambush and traps. In the

464 X. Lu et al.

hope of maximizing the security, a common practice is to traverse through the area

along the same path one squad after another. These squads depart along the same path

only when the frontal squad arrives somewhere of confirmed security. And the frontal

squads may also have to rest and wait for the following squads for supply and back

up. During the movement, if a squad is in danger, squads nearby would immediately

move to (or, of course, near if it is unsafe) the scene for assistance. Such mobility

patterns are common in military settings, and are also highly applicable in scenarios

such as large-scale survivor search and even planetary explorations.

At a high level of abstraction, a mobility model consists of a set of rules that

defines the spatial and temporal characteristics of the mobile nodes. Spatial

characteristics dictate the choice of a new direction or a new destination. Temporal

characteristics define how fast a node should travel to its destination or when a node

should depart or stop if required [3, 10]. Structural characteristics are also an

important part of a mobility model, which is often neglected by researchers. In a

network in which nodes move separately, the structure of these nodes is not so

important as they are disordered and unsystematic. In an organized network, however,

the structure of the network depends on the motion of nodes. Only when both the

mobility and structural characteristics are clearly known can we define a realistic

mobility model.

This paper is organized as follows. Section 2 is a survey of related research in the

area of mobility modeling. The structural, spatial and temporal characteristics we

extracted from the traces are described in Section 3, 4 and 5. We introduce our

mobility model in Section 6. We conclude the work in Section 7.

2 Related Work

The beginning stage of mobility model research saw numerous influential synthetic

models when real movement traces were difficult to obtain [1, 2, 5]. Some widely

used synthetic mobility models are Random Walk, Random Way Point, Random

Direction Walk, etc. Random Walk Mobility Model [5] was developed to simulate

erratic movements. In this model, a node moves from one location to a new location

by randomly choosing a direction and speed. Random Direction model in [4] is a

modified version of the random mobility model. Another widely used random

mobility models is the Random Waypoint model [1]. In this model, a node selects its

destination randomly and the speed from a velocity range. When it reaches its

destination, it pauses for some time and then selects a new destination and speed and

continue to move.

Recent years also saw an increasing number of researches on mobility models with

emphasis on real mobility traces [7, 8]. Tuduce and Gross proposed a WLAN mobility

model from a WLAN trace [8]. The trace was gathered from a campus wireless network

consisted of 166 APs. They presented a framework to extract the mobility parameters to

build the WLAN model. But the spatial parameters and temporal parameters in the

model are independent of each other. The study in [10] suggests that there exists a

strong correlation between the space and time dimension. Treating space and time

independently is not adequate. Kim et al. collected a campus Wi-Fi network trace at

Dartmouth College from nearly 10,000 users [7]. The space and time dimension in this

A Novel Mobility Model from a Heterogeneous Military MANET Trace 465

model is therefore correlative. The users in their traces traveled separately. Students

usually go to somewhere by themselves, they do not move in organized groups, which is

a significant difference from the entities in our trace.

Some researchers studied application dependent traces. Aschenbruck et al. studied

a disaster scenario trace in which there were 150 communication devices [16]. Their

model shows specific characteristics like heterogeneous node density, because in

disaster area scenarios, nodes move in a structured way based on civil protection tactics.

Zhang et al. looked into a bus mobility trace taken from UMass DieseNet which

consisted of 40 buses [14]. They found the inter-meeting time between buses was not

constant but random because of traffic conditions whereas the inter-contract time of

buses was indeed periodic. The periodicity in buses traces exists because they always

travel along a closed route. It is fundamentally different from node behavior in our trace.

3 Structual Characteristic

The trace data we used for this study was collected from a MANET consists of 64

jeep vehicles and four Unmanned Aerial Vehicles (UAVs). These vehicles traveled

over an area of approximately 240 square kilometers near Lakehurst, New Jersey,

USA for 180 minutes. The system logged every vehicle’s ID, GPS location and

communicational pathloss data throughout the period per second time. We believe the

structure of the network in our traces differs from those of the usual traces [7, 9, 11,

12]. For instance, the nodes in [7

9, 11, 12] move individually, the motion of one

user having no relation to the others. Nodes in military scenarios do not move

individually; instead they often form groups to accomplish a task cooperatively.

We say that two nodes are out of communication when the pathloss between the

two nodes is higher than a threshold 130dB, which is a known minimum requirement

of radio communication. With this threshold, we are able to investigate the nodes’

mobility and their interaction with each other.

A node is said to belong to a specific group when it within the communication

range of any member in that group ( ie., pathloss smaller than 130dB). In Figure 1, we

Fig. 1. The number of disconnected components with pathloss threshold 130 dB

466 X. Lu et al.

show that the number of disconnected groups of the network varies from 1 to 9. When

we keep track of those nodes belonging to specific groups, we discover that the 64

vehicles are of nine groups. Nodes of the same group always move as a unit group.

They move in the same direction, with relatively the same speed, and exhibit identical

mobility behavior.

The clustering coefficient of a vertex in a graph quantifies how close the vertex and

its neighbors are from being a complete graph. We study the clustering coefficient to

know how stable the cluster structure is. Denote the graph by G = (V, E). Let Ni =

{j∈ V: (i,j) ∈ E} and ki = |Ni|. The clustering coefficient of the graph, C, is given by

∑

∈

C1 (1)

Where )1(

|)},{(|

−

∑

∈

Nkj

ikk

Ci.

Fig. 2. Clustering coefficient change with different pathloss thresholds

Figure 2 shows the clustering coefficient over time for different pathloss

thresholds. Not surprisingly, the clustering coefficient is close to one, reflecting the

very strong clustering behavior associated with the nine groups of vehicles.

4 Spatial Characteristic

The mobile nodes in the traces were heterogeneous. The vehicles were organized in

teams which moved on the ground whilst the UAVs hovered above them. Since

UAVs travelled with much greater flexibility than the vehicles, the movement

behavior of former were different from that of the latter. Figure 3 displays the layered

heterogeneous structure of the mobile Ad hoc network.

A Novel Mobility Model from a Heterogeneous Military MANET Trace 467

Fig. 3. Heterogeneous nodes

In this section, we discuss the spatial characteristics of our traces. We begin by

analysing the direction characteristics. Direction characteristic describes a node’s

direction of travel. We employ the relative direction angle as the metric of direction

change. We define the relative direction angle

to be the angular distance between

the new direction BC and the former direction AB as illustrated in Figure 4 (a). Since

the traces do not contain direction information, we employ equation (2) to compute

the absolute angular change in direction,

(a) (b)

Fig. 4. (a) Direction vector and Relative direction angle. (b) Coordinate transform.

⎟

⎠

⎞

⎜

⎝

⎛

⋅

BCAB

Arc cos

(2)

Since

does not tell us whether the vehicle turned left or right, we obtain this

information by coordinate transform. In the original coordinate system, the angular

distance between last direction vector AB and the X axis is

. In coordinate

transform, we define the direction of the last direction vector AB as the positive

direction of X axis in the new coordinate system as Figure 4 (b) shows. Then we

calculate the new coordinates of point C (x’, y’) in the new coordinate system using

equation (3). If this vehicle’s new coordinate y’ in the new coordinate system is

positive, it means that the vehicle turns left, otherwise the vehicle turns right, and we

reverse

−.

468 X. Lu et al.

⎟

⎠

⎞

⎜

⎝

⎛−

⋅=

αα

cossin

sincos

),()','( yxyx (3)

Figure 5 shows the trajectories of UAVs and ground vehicles when they were moving

in the 180 minutes. In this Figure, the circle and triangle paths are the trajectories of

the two UAVs respectively and two solid lines are the track of jeeps. As the Figure

shows, the UAV turned to left and right with larger relative direction angle.

Fig. 5. The trajectories of UAVs and ground vehicles

Table 1 depicts the distribution of absolute relative direction angle during the

whole 180 minutes. From the statistics we can simply conclude that a mobile node

does not select its new direction randomly from a uniform distribution (0o, 180o).

Most of the absolute relative direction angles are smaller than 30o. Compared with

vehicles, UAVs move with much greater flexibility, there is about 30.5% of the

absolute relative direction angle being in the range of (30o, 90o).

Table 1. Distribution of absolute relative direction angle of UAV and vehicle

Angle(degree) 0-30 30-60 60-90 90-120 120-150 150-180

UAV 67.4% 19.8% 10.7% 1.5% 0.3% 0.3 %

Vehicle 93.08% 3.9% 1.73% 0.43% 0.43% 0.43%

5 Temporal Characteristics

Travel duration and pause duration characterize vehicles’ temporal behavior. We

analyse the distance a vehicle covered during two sampled time to estimate vehicle’s

motion phase. If the distance a vehicle covered between two sampled positions is too

short, we assume that the vehicle was not in motion during that interval of time. In

our traces, we sample the positions of a vehicle at 10 second intervals to determine its

A Novel Mobility Model from a Heterogeneous Military MANET Trace 469

movement. As the ground vehicles in the traces were jeeps, their speeds ranged from

30 km per hour to 120 km per hour; hence we set the threshold to be 10 meters for

deciding whether or not the vehicle is moving.

We define the pause duration to be the length of time from when a vehicle stopped

to when it started off again. Plotting the change in position at 10 seconds intervals

effectively yields a speed time graph as depicted in Figure6. As this figure shows, the

vehicle would travel from one place to another place at an average speed of about

16m per second, which roughly translates to 57 km/h. The speed tends to increase and

drop quite sharply at the start and stop of node movement.

Fig. 6. The distance between time intervals

Fig. 7. The travel schedule of three groups

470 X. Lu et al.

Figure 7 illustrates the variation of motion phase of three groups along the same

path. It shows that all three different groups had 6 travel phases even though they did

not start off at the same time. Since all three groups traveled along same path but

paused at different times, we deduce that when vehicle groups arrived at a checkpoint,

they would stop and pause for some time. We observe that the six pause durations

from each group were not exactly the same length, but the travel durations from

checkpoint i to checkpoint i+1 of the three groups are roughly equal. The length of

travel duration depends on the distance from a checkpoint to the next checkpoint and

vehicle’s speed. This means different groups proceeded at roughly equal velocities.

As discussed, vehicle groups departed from the start point at different times with

different travel and pause durations. Some groups converged and separated

periodically such as groups (a) and (b) in Figure 7, while others never met each other

as groups (a) and (c) in Figure 7.

6 Mobility Model

6.1 Mobility Model

Here we employ the various studied characteristics of our traces to develop a mobility

model. As we have mentioned above, mobility model consists of a set of rules that

defines the movement characteristics of the mobile nodes.

(1) Structural rules set:

• Our model assumes that nodes are organized into groups and nodes within a

group have the same travel duration and pause duration.

• Within a group, nodes can be heterogeneous and have different mobility

flexibility, e.g. mobility radius.

• Each group has a FIFO destination queue to save the location of destinations.

• Groups start off at different times and have heterogeneous travel schedules.

• Nodes of a group start at the same place in the beginning.

(2) Mobility rules for a group:

Step 1: All nodes of a group pause for a certain time, given by the pause duration.

Step 2: After the pause duration, if the destination queue is empty, go to Step 3,

otherwise go to Step 5.

Step 3: Generate a group destination with relative direction angle being in the

range (-30o, 30o). Broadcast this new destination and put into all groups' destination

queues.

Step 4: Calculate the group’s travel duration according to the distance to this

destination and the average group velocity.

Step 5: Pop a destination from the group's queue. Every node of this group

calculates its destination around the group destination randomly in a circle region

whose radius depends on the type of node. Heterogeneous nodes have different

mobility radius. For example, the radius of UAV is about 2 or 3 times of that of

vehicle as Figure 8 shows.

Step 6: Every node of this group starts off to its destination.

A Novel Mobility Model from a Heterogeneous Military MANET Trace 471

Fig. 8. The movements of different types of node

Note that we do not add the end restrict in the model. We can use different restricts

to end the program, such as program running time or cycle times.

In this model, if a group which is behind of some groups departs from a place, it

does not need to calculate its next destination. Its destination queue has at least one

destination, because it passes by fewer destinations than the frontal groups. To those

groups in front of all other groups, when one of them wants to depart ahead of others,

it checks its destination queue firstly. If its destination queue is empty, actually its

destination queue should be empty because no other groups depart ahead of it, this

group will calculate the newest destination and put it into all other groups’ destination

queues. Hence, all these groups have a common new destination.

Those groups which start off from the start point behind of others still have the

opportunity to catch up with and exceed the frontal groups, if they have shorter pause

durations. We can assign different travel schedules to different groups to study the

structural and spatial variations between these groups.

6.2 Evaluation

We divided the data set into two sets: a training set and a test set. Firstly, we analyzed

the mobility characteristics of training set. Then we make the mobility model to

generate synthetic data according to the values of these mobility characteristics. We

compare the spatial and temporal characteristics of the synthetic data our model

generated with the real mobility characteristics of the traces to evaluate our model

[12]. To acquire a more accurate quantity of the difference between the synthetic

values and the data set, we use the relative error to estimate the model. We calculate

the relative error using the equation (4)

∑

−

errorrelative

(4)

where ri is the value of testing data and si is the simulation data, and n is the number

of performance time

472 X. Lu et al.

Firstly, we evaluate the spatial characteristic of our model. The vehicles changed

their directions according to the terrain and traffic situation in real world, but our

model do not consider these kinds of conditions now, so we could not compare the

directions between the test set and that in model directly. We compare the

distributions of relative direction angle of test set with that of synthetic data as Figure

9 and 10 shows. The relative error of the distribution of relative direction angle of the

vehicle is as low as 1.7%, and that of the UAV is about 2.1%.

Fig. 9. Vehicle’s distributions of relative direction angle of testing data and simulation data

Fig. 10. UAV’s distributions of relative direction angle of testing data and simulation data

A Novel Mobility Model from a Heterogeneous Military MANET Trace 473

Secondly, we evaluate the temporal characteristics: the travel schedule. We use the

training set to get the values of the travel duration and pause duration and use these

values in our model. The relative error of travel schedule is 4.3%. This value is rather

low and indicates our model matches the temporal characteristics of the real system.

With this mobility model, we can study the distances between any two groups, the

network connectivity and the performance of routing protocols with different travel

schedules. We can also understand what combinations of travel schedules allow the

nodes to attain maximum average network connectivity or the shortest average inter

group distance, which is important in military scenarios.

7 Conclusion

In this paper, we propose a novel mobility model based on the mobility characteristics

extracted from a layered heterogeneous military MANET trace collected from

Lakehurst, New Jersey. In the model, nodes are divided into many groups and these

groups travel along the same route but with different time schedules. When a group

reaches its current destination, it pauses for some time and then departs again to the

next destination. If there is no destination in the group’s destination queue, it will

generate a new destination and notify all other groups. All the nodes of a group have

the same travel schedule, but they select themselves destinations around its group’s

destination randomly with different mobility radiuses.

Evaluation results show our mobility model well and truly captures some aspects

of the spatial and temporal characteristics of the real traces. The mean relative error of

distribution of relative direction angle is 1.9%, and the mean relative error of travel

schedule is 4.3%. Both of the spatial and temporal relative error is very low.

Therefore, this mobility model can be employed to generate synthetic data for a long

time to do some searches, such as the longest average network connectivity or the

shortest average group distance, with different travel schedules. Such kinds of

experiments are costly to be realized in real world.

For future work, we intend to further study the motions of these nodes not only in

common condition but also in some accidental scenarios.

Acknowledgments

We would like to make a grateful acknowledgement for Don Towsley. Don gave

many suggestions on this research. Research was sponsored by the U.S. Army

Research Laboratory and the U.K. Ministry of Defence.

References

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[6] Song, L., Kotz, D., Jain, R., He, X.: Evaluating location predictors with extensive Wi-Fi

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[9] Schwab, D., Bunt, R.: Characterising the Use of a Campus Wireless Network. In: Proc.

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[10] Burgess, J., Gallagher, B., Jensen, D., Levine, B.N.: MaxProp: Routing for Vehicle-Based

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[13] Garetto, M., Leonardi, E.: Analysis of Random Mobility Models with PDE’s. In: Proc.

IEEE MobiHoc 2006 (May 2006)

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Measuring Energy-Time Eﬃciency of Protocol

Performance in Mobile Ad Hoc Networks

Ida Pu1, Yuji Shen2, and Jinguk Kim1

1Department of Computing, Goldsmiths

University of London, London SE14 6NW, UK

2School of Medicine, University of Birmingham

Birmingham B15 2TT, UK

Abstract. This paper introduces two new metrics for assessment of mo-

bile ad hoc network performance in terms of energy-time eﬃciency. The

combined eﬀect of both energy and time consumption is considered and

represented in mathematical terms. The measures have demonstrated a

number of advantages over the conventional ones in which the energy

and time were often considered separately. The proposed new metrics

are simple, generic and ﬂexible. As an application, we have compared

the energy-time eﬃciency of Blocking Expanding Ring Search (BERS)

and Expanding Ring Search (ERS), two similar Time to Live (TTL)-

based expanding ring search algorithms using our new metrics. The re-

sults show that the new metrics can be applied eﬃciently in assessment

of diﬀerent protocols.

Keywords: Energy-time, eﬃciency, metric, algorithm.

1 Introduction

Energy eﬃciency is one of the fundamental issues for Mobile ad hoc networks

(MANETs) and has drawn attentions of researchers in recent years [1,2]. Many

research papers are concentrated on design of energy eﬃcient protocols [1,2,3]

and others dedicated to the energy eﬃciency analysis [4,5,6]. Characteristics of

certain aspects of energy waste have been identiﬁed. It is known, for example,

that the communication between nodes consumes substantial amount of energy

in wireless networks [7]. Many challenges, however, are still ahead due to high

dependency on the cooperative ad hoc environment, the variety of the physi-

cal elements involved in MANETs and the complex requirements to diﬀerent

network layers and interfaces.

One interesting phenomenon is that the energy saving does not come for free.

It is often a tradeoﬀ between the amount of energy saved for completion of a

task and the extra time it may take. The saving is usually achieved on the cost

of taking a longer time [6,8].

Despite importance, few dedicated measures are used in MANETs to describe

the energy-time tradeoﬀ in a directly quantitative means. Most discussions ad-

dress the issues of energy saving and time latency separately. The combined ef-

fect, however, has not been explicitly addressed. This often causes inconvenience

D. Coudert et al. (Eds.): ADHOC-NOW 2008, LNCS 5198, pp. 475–486, 2008.

Springer-Verlag Berlin Heidelberg 2008

476 I. Pu, Y. Shen, and J. Kim

in assessment of diﬀerent protocols or for exploring the insight of a speciﬁc ap-

proach on energy-time eﬃciency. Consider a simple example of comparison of

two systems. Suppose that system A achieves ‘energy saving of 40% with 15%

time delay’, while system B ‘35% saving with 5% time delay’. Which one is better

in terms of the energy-time eﬃciency and how much better?

The energy consumption of a real MANET can be far more complicated to

determine than this question. Nodes in MANETs consist of various mobile com-

puter devices. They may come from diﬀerent manufacture in diﬀerent decades,

equipped with diﬀerent operating systems, under diﬀerent energy management

schemes, yet they need to cooperate to forward packets and to maintain a live

network as long as possible. This means that neither the amount of energy sav-

ing nor the length of the time taken alone is suﬃcient for assessment purpose.

In real time applications, time factor may play a more important role than the

energy, and vice versa in energy constraint applications. In order to address the

energy eﬃciency issues, we need to ﬁnd a combined measure that takes into con-

sideration of both the energy consumption and the time required, and it should

be scalable, genetic, simple, and allow a better understanding of the energy

consumption problems in MANETs.

In this paper, we consider the energy consumption problems from a new angle

by considering a combined eﬀect, described as cost, to capture the tradeoﬀ nature

of the amount of energy consumption and the time required to complete a task.

Two simple metrics are proposed: one is referred to as product models and the

other trade model, both including entities of the energy and time. We deﬁne the

models and explain the mathematical and physical meanings in adoption of these

measures in Sections 4 and 5. We brieﬂy review Blocking Expanding Ring Search

(BERS) and Expanding Ring Search (ERS), two Time to Live (TTL)-based

ERS algorithms [8,9,11] for commonly used reactive route discovery protocols for

MANETs in Section 2. We discuss the goal and experiment settings in Section 6.

We demonstrate the advantages of the new metrics by presenting the analytical

results for BERS and ERS in Section 7. The metrics we proposed are in fact

not only simple but also genetic and ﬂexible. We describe brieﬂy how to extend

the measures to a number of variations which can measure diverse and complex

systems in Sections 4.2 and 4.3. We conclude ﬁnally that these new metrics can

be a useful tool for exploring the energy eﬃciency issues and for assessment of

diﬀerent protocols of MANETs in Section 8.

2 Background and Related Work

A communication channel in MANETs can be established between two nodes

consisting of a source,adestination and possibly a number of intermediate nodes

without any ﬁxed base station. Intermediate nodes need to cooperate to forward

packets upon requests.

The route discovery process in MANETs, among many necessary activities,

has been found to consume signiﬁcant amount of energy [12]. The process starts

from the moment when a source node broadcasts the ﬁrst RREQ (Route

Measuring Energy-Time Eﬃciency of Protocol Performance 477

Request) packet until the source node receives the RREP (Route Reply) or

the ﬂooding terminates, whichever the latest.

We adopt two models in the route discovery process, namely one-to-all [13]

multicast for broadcast and one-to-one unicast for transmission RREP, and as-

sume a route cache on each mobile node. A node in MANETs broadcasts a

RREQ and its one-hop neighbour nodes within the broadcast range cooperate

the route discovery process by checking their own route caches for requested

route information and maintaining an updated list of known routes.

An intermediate node who has the requested route information towards the

destination is deﬁned as a rou te node in this paper. If the route information is

found in its route cache, the route node would stop rebroadcasting the RREQ

and sends a RREP to the source node with the complete route information

consisting of the cached route in itself and the accumulated route record in the

RREQ. In this way, the route may be established more quickly and the total

amount of delivery time and energy consumption can be reduced.

2.1 TTL-Based Expanding Ring Search

Reactive routing protocols such as DSR [10] and AODV [11] are often supported

by a so-called ERS scheme. The goal of the ERS is to ﬁnd nodes who have the

valid route information to the destination node in their route cache by propa-

gating RREQs in a controlled ﬂooding manner.

To control the ﬂooding in MANETs, a TTL [10] sequence is used with ERS.

A pre-deﬁned TTL number is issued with a RREQ which deﬁnes a maximum ra-

dium of a searching area by ﬂooding. Each time when TTL is run out, the source

node restarts a second-round ﬂooding process by rebroadcasting the RREQ with

an increased TTL number to allow the new RREQ to reach the nodes in further

distance. There is no optimal TTL incremental sequence. The common values

of the incremental TTL are 1 [14,15], and 2 [16]. For simplicity of discussion,

we assume the increment of TTL value is 1, but other increments can be easily

applied with similar approach.

ERS wastes energy by rebroadcast RREQs redundantly. Flooding analysis

shows that rebroadcast could provide at most 60% additional coverage and only

41% on average over that already covered by the previous attempt [13].

2.2 Blocking Expanding Ring Search

The BERS is a modiﬁed ERS which achieves substantial amount of energy sav-

ing in the worst case [8]. BERS integrates, instead of TTL sequences, a newly

adopted control packet, stop instruction and hop number (H) to reduce the

energy consumption during route discovery process.

The basic route discovery structure of BERS is similar to that of conventional

TTL-based ERS. The source node, however, passes the right of reissuing RREQs

to intermediate nodes on subsequent rings. Since the source node only issues a

single RREQ, BERS does not resume its second round ﬂooding from the source

node when TTL fails. The new RREQs can be initialised by any appropriate

478 I. Pu, Y. Shen, and J. Kim

intermediate nodes in a synchronised fashion. Intermediate nodes that perform

a rebroadcast on behalf of the source node or the nodes on previous ring act as

an agent node. In this way, the energy saving is achieved.

The energy saving gained, however, does not come for free. Like in most energy

eﬃcient protocols, the energy saving is achieved on the cost of time delay.

3 Our Contribution

From next section, we introduce our cost and trade models and demonstrate how

these models can be used to evaluate the energy-time eﬃciency of a protocol.

As an application, we investigate the performance diﬀerence between BERS and

ERS using the new metrics. We demonstrate our simulation results and discuss

the characteristics of BERS and ERS in terms of energy-time eﬃciency.

Our main contribution in this paper includes: (i) introducing two simple and

abstract metrics, namely cost and trade models for MANETs with justiﬁcation,

(ii) analysing the energy-time eﬃciency of BERS and ERS applying our mod-

els, (iii) demonstrating the behaviours of BERS and ERS under various node

distributions.

4CostModels

Our initial goal is to describe the tradeoﬀ nature of two independent but related

entities, i.e. energy and time in most route discovery protocols. The new com-

bined measure, described as cost, should be simple, abstract and generic. Our

ﬁrst metric is referred to as a product model.

4.1 Product Model

A cost function based on the product of the energy and time can be deﬁned as

C(n)=E(n)T(n)(1)

where nrepresents the size of the input data, which is task-oriented and can

be, for example, the number of expanding rings, or the number of nodes. E(n)

represents the energy consumed and T(n) the time it takes to complete a task.

The cost function C(n) takes two arguments E(n)andT(n). Obviously, the

smaller the C(n) is, the more energy-time eﬃcient is the system.

The intuition of this model comes from the moment principle of leverage in

physics as demonstrated in Figure 1. The principle of the lever tells us, in order

to achieve a load balance state (the static equilibrium), with all forces balancing,

the moment, i.e. the product of the weight and the distance between the load

point and the fulcrum (lever pivot), on either side of the fulcrum must be equal

in value. Consider an instance that two Approaches A and B are carried out

to complete a task involving a number of nodes. Suppose it takes T1time for

Measuring Energy-Time Eﬃciency of Protocol Performance 479

E1 E2

T1 T2

Fig. 1. Product model

Approach A to complete the task and consumes energy E1,andT2time for

Approach B and consumes energy E2.

To quantify the performance of A and B, we imagine the following scenario:

We weight the energy consumptions E1and E2on a balance scale as shown in

Figure 1, where the distances from the hanging positions on the left, and right, to

the fulcrum, i.e. the two moment arms, correspond to T1and T2respectively. If

the moments E1T1and E2T2are equal in value, the scale will show the balance.

This means that the performances of Approach A and B are equally good (or

bad) in terms of energy-time eﬃciency. There may be two possibilities: (a) If

E1=E2,thenT1=T2;(b)IfE1=E2,thenT1=T2.

If, however, the moments are diﬀerent, i.e. E1T1<E

2T2(or E1T1>E

2T2),

it is possible to be one of the following four cases:

1. E1<E

2(or E1>E

2), and T1=T2,

this means that Approach A (or B) is more energy eﬃcient than Approach

B(orA).

2. E1=E2,andT1<T

2(or T1>T

2),

this means that Approach A (or B) is more time eﬃcient than Approach B

(or A).

3. E1<E

2(or E1>E

2), and T1<T

2(or T1>T

2),

this means that Approach A (or B) is more eﬃcient in both of energy and

time than Approach B (or A).

4. E1<E

2(E2<E

1), and T1>T

2(or T2>T

1),

this means that Approach A (or B) is more energy eﬃcient but not time

eﬃcient than Approach B (or A).

The ﬁrst case reﬂects the situation where one side is lighter in weight than the

other side but both moment arms remain the same length, the scale will show

imbalance and E1(or E2), one side will be moving up.

The second case corresponds to the situation where the loads on both sides

are of equal weight, but the moment arm (T1) of one side is shorter than the

other side, the scale will then show the imbalance, and one side (E1) will be

moving up.

The third case represents the situation where both the weight and the moment

arm of one side are less than the other side in value, the scale will show the

imbalance again, and E1side will be moving up.

The fourth case represents the situation where the weight of one side is lighter

but the moment arm is longer than the other side, the scale will show balance or

480 I. Pu, Y. Shen, and J. Kim

imbalance depending on the moment values on both sides, i.e. whether E1T1=

E2T2or E1T1=E2T2.

Note that both energy Eand time Tare a function of the input size nof

an algorithm. This is because, in general, the larger the input size n,themore

energy will be consumed and it would usually take longer to complete a task.

This energy-time measuring model is simple but eﬃcient, and can be gener-

alised as given in the next section.

4.2 General Product Model

The cost function proposed in Eq.(1) is not ﬂexible for situations where one

aspect, either the energy or the time, is considered as more important than the

other. For example, there may be situations where the energy is the only criteria

to be measured, or time aspect is considered as more signiﬁcant than the energy.

We therefore modify the cost function in Eq.(1) by adding a parameter αas the

power of the time factor:

C(n)=E(n)Tα(n), where α≥0(2)

Here αis a positive real number. As we can see, the general cost function (2)

becomes our linear cost function (1) when α= 1. In other words, the linear cost

function (1) is a special case of the general cost function (2) when α=1.

Similarly, when 0 ≤α<1, the weight of the time factor is reduced, and

the energy factor weights more. When α>1, the weight of the time factor is

increased, and the energy factor weights less.

4.3 Extended General Product Model

For a more complex system, we can also consider extending Eto a vector space

E=(E1,E

2,···,E

m)andT=(Tα

1,Tα

2,···,Tα

m), where mis the number of

subsystems and αis a weight parameter for emphasis on Tj(j=1,2,···,m).

So the cost function (1) becomes

C(E,T)=E−1T(3)

We have the extended general model as follows:

C(E,T)=⎛

⎜

⎝

⎞

⎟

⎠(Tα

1,Tα

2,···,Tα

m)(4)

This is equivalent to the same scenario to that for our general model except

where we hang a number of objects at diﬀerent positions on either side of the

equilibrium.

Measuring Energy-Time Eﬃciency of Protocol Performance 481

In theory, the cost function can be tailored to suit various situations in measur-

ing tradeoﬀs and to apply to diﬀerent layers and diﬀerent systems. For example,

on the Medium Access Control (MAC) layer, energy eﬃcient algorithm design

needs to consider a number of attributes such as collision, idle listening, over-

hearing, radio controlling. With extended cost function (4), the comparisons of

the energy eﬃciency can be made across the layers and diﬀerent systems.

5 Trade Model

The cost models in the previous section can be used to measure the amount of

energy-time tradeoﬀ. In this section, we introduce another simple metric called

trade model which can indicate the level of energy-time tradeoﬀ.

The trade model captures the amount of energy saving in exchange of unit

time latency. This is a normalised measure and is deﬁned as ∆E/∆T ,where

∆T = 0. It describes the amount of energy saving that is traded oﬀ by a unit time

of latency. Given two protocols with diﬀerent amounts of energy consumption

E1and E2and the diﬀerent lengths of time required T1and T2, the amount of

energy saving traded by the time latency can be calculated by

∆E

∆T =E2−E1

T1−T2

We assume that the ﬁrst system consumes less energy but takes longer time as

the cost, i.e. E1<E

2but T1>T

2. However, as we shall see later, this condition

is not essential since the equation can capture other cases such as E1>E

2and

T1>T

6 Energy Eﬃciency of BERS and ERS

In this section, we compare the results in two cases. In the ﬁrst case, we use

the conventional separate measures for the energy saving and time latency. In

the second case, we use our cost functions to demonstrate the advantages of the

measures.

6.1 Separate Measures

We demonstrate here how the energy consumption and the time latency, despite

being dependent on one to another, are measured and discussed separately.

Energy Consumption: The energy consumption can be described in the fol-

lowing mathematical expressions [8]. For convenience of discussion, we adopt

the unit of the energy (in UnitEnergy) as the amount of energy consumed

by a node for broadcasting an RREQ. Similarly, we deﬁne the unit of the

time (in UnitTime) as the the amount of time for each node to wait before

482 I. Pu, Y. Shen, and J. Kim

rebroadcasting RREQ. The total energy consumed in BERS route discovery

process can be described as:

EBERS =21+

Hr−1



i=1

ni+ERREP (UnitEnergy)

where ERREP is the amount of energy consumed for unicasting the RREP.

The total energy consumed in ERS is:

EERS =Hr+

Hr−1



i=1



j=1

nj+ERREP (UnitEnergy)

The energy saving by using BERS is therefore:

∆E =EERS −EBERS =Hr−2+

Hr−1



i=1  i



j=1

nj−2ni(UnitEnergy)

Time-Delay: Again we adopt the analytical results from [8].

The total time required for BERS is:

TBERS =3Hr+2



i=1

i=H2

r+4Hr(UnitTime)

Similarly, the total time for ERS route discovery process is:

TERS =2



i=1

i=H2

r+Hr(UnitTime)

The time latency for BERS is 3Hr, i.e.

∆T =TBERS −TERS =3Hr(UnitTime)

where Hris the hop number of the ﬁrst node that returns the RREP to the

source node.

6.2 Comparing BERS and ERS

We now apply our models developed in previous sections and take the route

discovery of the MANETs as an example to demonstrate how our cost models and

trade model can be used to explore the energy-time eﬃciency of two algorithms:

one is the conventional TTL-based ERS and the other is the BERS.

We have conducted a number of analytical simulation based on the above the-

oretical results and implemented in IDL 6.0 (Research Systems, Boulder, CO,

USA). Our main goal is to investigate the diﬀerence between the performance

of BERS and ERS in terms of energy-time eﬃciency. In order to gain the in-

sight of the two algorithms, we investigate their behaviours under various node

distributions as follows:

Measuring Energy-Time Eﬃciency of Protocol Performance 483

1. Uniform Distribution

A total of 1000 nodes are placed uniformly in a geographic area covering a

region with Hrof 10.

2. Pseudo-Normal Distribution

A total of 1000 nodes are within a geographic area covering a region with

Hrof 10. For each Hrcovered area, 100 nodes are placed uniformly. That

is: the given area is divided by 10 rings Hr=1,2,···,10, there are 100

nodes uniformly distributed within each area, i.e. 100 nodes in areaHr<=1,

another 100 in area1<Hr<=2, ..., another 100 nodes in area9<Hr<=10 .The

node density is gradually reduced from the centre along the radius to the

outest ring.

We experiment with the settings for BERS and ERS and make comparison

on their performances using our two models. In the general product model

C(E,T )=C(n)Tα(n), we consider α=0.5,1 and 2, respectively. We plot the

energy-time cost against Hrin the same diagram for both BERS and ERS and

try to answer the following questions: (i) Under what conditions is BERS supe-

rior than ERS in terms of energy-time saving? (ii) When time is critical, how

would the answer to question (i) change? (iii) Similarly, when time is not so

critical, how would the answer to question (i) diﬀer?

7Results

The energy-time eﬃciency of BERS and ERS are demonstrated in this section

based on the simulation results under various node distributions using product

and trade models.

7.1 Product Model

We discuss the results for the uniform and pseudo-normal node distributions

separately.

Uniform Distribution. This distribution is the simplest case. It is interesting

because it corresponds to an ideal situation.

Figure 2 shows the cost measured from the product model when α=0.5, 1

and 2. When α= 2, two curves have no signiﬁcant diﬀerence, demonstrating

that the performances of two systems are nearly the same under the weight

α=2.Whenα≤1, the performance of BERS is signiﬁcantly better than that

of ERS when Hr>7. It is demonstrated that low weighting should be used for

the assessment of energy-time eﬃciency.

Pseudo-Normal Distribution. Figure 3 (left) shows the performance of

BERS and ERS in the uniform distribution and (right) in the pseudo-normal

distribution, both under the product model when α=1.

The two results are diﬀerent. For the pseudo-normal distribution because there

aremorenodesinthecentrethanoutside of the centre, there is more energy

saving. The good performance for BERS in the pseudo-normal distribution starts

at Hr≥6, while in the uniform distribution which starts at Hr≥7.

484 I. Pu, Y. Shen, and J. Kim

Fig. 2. Energy-time cost from product model when α=0.5, 1 and 2 (from left to right)

under uniform distribution

Fig. 3. Energy-time cost from product models when α= 1, (left) under uniform dis-

tribution and (right) under pseudo-normal distribution

7.2 Trade Model

Figure 4 shows the behaviours of BERS in terms of the energy saving traded oﬀ

by the unit time delay in comparison to that of ERS under two node distribu-

tions, namely, uniform distribution and pseudo-normal distribution.

We plo t ∆E/∆T against Hr. As we can see in Figure 4 (left), for example,

when Hr<= 5, BERS actually consumes more energy instead of saving any for

uniform distribution. In Figure 4 (right), the threshold of Hris approximately

4 for the case of pseudo-normal distribution.

Similarly, ∆T/∆E,where∆E = 0 can be used to measure the time delay

caused by unit energy saving.

This measure, although convenient, appears to have at least two disadvantages.

The ﬁrst disadvantage is that the measure will be invalid unless the time delay of

the two systems under assessment is suﬃciently diﬀerent in value. The denomina-

tor ∆T (or ∆E) will approach zero in the equation otherwise. Secondly, it is not

ﬂexible enough to be used to describe the tradeoﬀ of the energy-time eﬃciency.

Fig. 4. ∆E/∆T vs Hr: (left) uniform distribution; (right) pseudo-normal distribution

Measuring Energy-Time Eﬃciency of Protocol Performance 485

The results are consistent to the previous ones. For example, in case of uniform

distribution, while the product model shows when (Hr= 7) BERS starts to gain

from the energy-time trade, the trade model tells us when (Hr=5)thetrade

process actually begins. Together, the two models tell us: when 5 <H

r<7,

although BERS starts to save energy, the saving amount is not suﬃcient to

cover the lost of time in comparison to ERS.

8 Conclusions

We have introduced two new metrics for assessment of energy-time tradeoﬀs in

MANETs, namely, cost models and trade model (or product models and energy

saving per unit-time latency model). The product models measure the cost of

combined eﬀect of energy consumption and time delay. The trade model mea-

sures the energy saving gained from unit time delay and it tells how much an

energy-time tradeoﬀ is worth and when precisely the trade begins. The cost

models have been extended and generalised for more complex systems.

We have analysed the behaviours of the BERS and ERS, two TTL-based

expending ring search protocols, under diﬀerent MANET node distributions ap-

plying our new measures. The energy-time tradeoﬀs of the two protocols are

compared and evaluated using the proposed models. We found that the new

measures are eﬃcient for assessment of the energy-time tradeoﬀs of diﬀerent

systems.

With these new measures, heuristics of protocols can be further explored

and more interesting quantitative questions can be answered about energy-time

tradeoﬀs. For example, given a distribution of nodes for a geometric area, which

protocol is more eﬃcient in terms of energy-time eﬃciency? In contrast, these

questions would not have been so easy to answer with conventional separate

measures.

Our work is not restricted to measuring energy-time tradeoﬀs in MANETs.

The approaches can be adopted to investigate other energy eﬃciency problems

for wireless networks. In fact, the deﬁned models can be applied for any systems

that involve tradeoﬀs.

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A Framework for Joint Cross-Layer and Node Location

Optimization in Mobile Sensor Networks

Vladimir Marbukh and Kamran Sayrafian-Pour

Information Technology Laboratory

National Institute of Standards and Technology

{marbukh,ksayrafian}@nist.gov

Abstract. This paper proposes an extension to Network Utility Maximization

(NUM) framework, referred to as L-NUM (Location-aware NUM). This

framework is intended to characterize both the amount of the received sensor

information and the network ability to deliver the information to the intended

recipient(s). The sensor location is controlled by maximization of the system

utility production, which accounts for both rate of the network utility increase

and the negative effects of the energy consumption as a result of sensor motion.

Definition of sensor utility in L-NUM incorporates the value of sensor

information which is affected by sensor locations. Once model-specific network

utility and system utility production are defined, L-NUM provides intuitively

appealing and tractable framework for mobile sensor network optimization.

1 Introduction

Mobile sensor networks are envisioned for detecting and tracking potential targets and

events for civilian as well as military purposes. Locations of sensors in a mobile

sensor networks affect both the network ability to detect and track the identified

targets and events as well as the ability to communicate the relevant information to

the intended recipients. The communication ability can be improved if sensors are

capable of optimally self-organizing into a multihop mobile network where sensors

cooperate in relaying each other information in addition to transmitting their own

information. Since the detecting and tracking needs could potentially compete with

the communication needs, optimal realization of mobile sensor networks requires

node ability to balance these competing requirements using local, and typically

incomplete, information. Energy conservation requirements could also be a major

factor in controlling sensor position due to their possible impact on the sensor lifespan

and in turn on the rest of the network performance. Developing self-organized mobile

sensor networks capable of adjusting to target movement and/or other environmental

changes requires developing sophisticated algorithms capable of balancing numerous

inherent trade-offs. This paper proposes a tractable extension to Network Utility

Maximization (NUM) framework aimed at addressing some of these algorithmic

challenges.

NUM framework for fair bandwidth allocation in a wire-line network has been

proposed in [1]. This framework assumes elastic users, sources or applications whose

488 V. Marbukh and K. Sayrafian-Pour

satisfaction can be quantified by a utility function of the corresponding end-to-end

bandwidth. Framework [1] assumed that elastic users/sources are capable of adjusting

their bandwidth requirements in response to the network congestion. This framework

has been extended to include cross-layer optimization of wire-line as well as wireless

networks [2]-[4]. The extended NUM jointly optimizes flow control, routing,

scheduling and power control. The optimization is achieved by a decentralized,

adaptive closed-loop algorithm with feedback signals which can be interpreted as

resource congestion prices.

In [5], a combination of utility-based flow model with potential field based

approach to control the sensor positions has been proposed. This hybrid framework

accounts for the effect of sensor locations on their ability to transmit sensor

information to the intended recipient(s). This is achieved through link capacity

constraints in the mobile ad-hoc network formed by the sensors. The corresponding

optimal, location-dependent network utility, viewed as a potential field, defines

potential forces guiding the sensors motion. However, the network utility only

quantifies communication abilities of the sensor network and does not take into

account the effect of sensors locations on the sensor ability to get valuable

information on the target(s). Instead, the value of sensor information is incorporated

through phenomenologically defined forces, e.g., “attractive forces towards goals”.

Also, sensor motion in [5] is guided by a mass-damper model driven by the sum of

the potential and phenomenological forces with damping coefficients that represent

the energy expended on the sensor motion.

Here, we propose another utility-based framework for mobile sensor network

optimization, referred to as Location-aware Network Utility Maximization (L-NUM).

L-NUM assumes that the aggregate sensor utility quantifies the value of the sensor

information, which is a function of both sensor information rates and sensor physical

locations. Given sensor locations, aggregate sensor utility maximization subject to the

communication constraints yields the optimal cross-layer network design. The

corresponding optimal sensor network utility quantifies both value of sensor

information and ability of the network to deliver this information to the intended

recipient(s). The maximum of this aggregate network utility yields the optimal sensor

locations. In practice, reaching these optimal locations by mobile sensors may be

infeasible due to the un-accessible terrain and/or limitations on the node energy

supply. L-NUM proposes to account for these factors through utility production,

which is a function of both, sensors locations and speeds. The sensor speeds are

selected to maximize the utility production, given the sensor locations.

Once the model-specific network utility and system utility production are defined,

L-NUM provides intuitively appealing, self-contained and tractable framework for

mobile sensor network optimization. This paper describes L-NUM framework with a

very brief discussion of some of the numerous methodological, computational and

implementation issues. The main methodological issues include quantifying the

location-dependent value of sensor information, i.e., sensor utility, as well as utility

production. Computational and implementation issues include decentralized

optimization based on local and typically incomplete information.

The rest of this paper is organized as follows. Section II summarizes the

conventional NUM framework. Section III describes L-NUM as a natural extension

of the conventional NUM by incorporating spatial effects into cross-layer

A Framework for Joint Cross-Layer and Node Location Optimization 489

optimization and energy conservation considerations into position control. Section IV

briefly illustrates L-NUM on an example of single mobile sensor transmitting

information to a single receiver. Finally, Conclusion summarizes the proposed

approach and outlines direction for future research.

2 Network Utility Maximization

Consider a network comprised of a set of sources S and a set of resources (i.e. links)

Ll∈ with capacities l

c. Each source Ss ∈ identifies a unique source-destination

pair and a set of feasible routes s

R. Each route s

Rr ∈ is a collection of resources

rl∈. Source s satisfaction of having end-to-end bandwidth

is characterized by

the utility function Ssus∈),(

which is assumed to be monotonically increasing

and concave in 0≥

. For example, widely used weighted ),( w

- fair rate allocation

[6] is based on utilities

⎪

⎩

⎪

⎨

⎧

≠

−

1ln

)(

αλ

ifw

u, (1)

where 0, >

are parameters. When 1=

w, the cases 0→

, 1→

and ∞→

correspond respectively to an allocation which achieves maximum throughput, and is

proportionally fair or max-min fair.

In a link-centric formulation each source Ss ∈ with end-to-end rate s

is split

into rates r

over feasible routes s

Rr ∈:

∑

∈

λλ

(2)

This results in the aggregate load l

on link Ll∈ where

∑

⊆∈

sRrlr

λµ

(3)

The link-centric utility maximization framework selects vector of flow rates

),..,1,,( SsRr sr =∈=Λ

which maximizes the aggregate user utility

∑

Σsss

uU )()(

λλ

. (4)

where ),..,1,( Ss

s==

λλ

. This maximization is subject to the link capacity

constraints ll c≤

, (2) and (3).

One can also account for capacity constraints ll c≤

through congestion penalty

∑

Σllls cfcF ),(),(

µµ

, (5)

490 V. Marbukh and K. Sayrafian-Pour

where ),( Ll

l∈=

µµ

, ),( Llcc l∈= . Penalty function ),( lll cf

quantifies losses

in terms of delays or packet loss due to buffer overflows as the link l utilization l

approaches link capacity l

c. Functions ),( lll cf

are assumed to be monotonically

increasing and convex in 0>

. A steep function ),( lll cf

increase as l

approaches l

c prevents violation of the capacity constraints. NUM with capacity

constraints incorporated through the congestion penalty can be expressed as follows

)},()({max

*cFUU

µλ

ΣΣ

≥Λ −= (6)

where maximization is subject to constraints (2) and (3). Such formulization and its

distributed price-based solution have been proposed in [1].

While in a wire-line network link capacities l

c are typically assumed fixed, in a

wireless, interference-limited network link capacities are functions of the transmission

powers on neighboring links and channel conditions affecting transmission on link l

as well as interference from transmissions on other links. A large number of cross-

layer optimization frameworks accounting for these interactions have been proposed,

e.g., see [2]-[4]. These frameworks often assume that “elastic” link capacities are

given functions of the vector of average transmission powers on all links

()( ,Llpp l∈= ) i.e.:

)( pcc ll = (7)

For example, [4] assumes

)](1log[)( 21 pSIRkkpc ll += , (8)

where 1

k,2

k are constant coefficients, and the Signal-to-Interference Ratio on link

),( jil = is

∑≠≠

jinjikn njnkj

ijij

ij p

SIR

,),,(),(

ξη

(9)

In (9) ij

is the path loss on link ),( ji , and j

is the noise power at the receiver of

node

Elasticity of the link capacities in a wireless network naturally lead to the

following NUM formulation:

)},()({max

*cFUU

µλ

ΣΣ

≥Λ −= (10)

with maximization to be subject to capacity constraints (2)-(3), wireless channel

model (7), and possibly power constraints

Pp ∈ (11)

A Framework for Joint Cross-Layer and Node Location Optimization 491

where P is the feasible power region. Much more sophisticated versions of NUM

could also include optimization over packet scheduling on different links [2]-[4].

3 Location-Aware NUM

Joint Cross-Layer and Node Location Framework Model

Here, we propose a location-aware extension of NUM for mobile sensor networks by

assuming that the aggregate value of the information gathered by S sensors can be

quantified by the utility function ),( xU

Σ, where vectors ),..,(1S

λλλ

),..,(1S

xxx = describe information collection rates s

and physical locations

(coordinates) s

x of all sensors Ss ,..,1=.

We assume that the aggregate utility ),( xU

Σ is additive:

∑

ss xUxU ),(),(

λλ

(12)

where utility (i.e. information value) of each sensor Ss ,..,1= information is the

following product

)()(),( xvuxU sssss

λλ

=. (13)

The first multiplier )( ss

is an increasing and concave function of the information

collection rate s

, e.g., of form (1). The second multiplier )(xvs quantifies the

effects of the physical locations of all S sensors ),..,(1S

xxx = on the value of

information captured by the sensor s. The dependence of )( xvs on the physical

locations of all S sensors ),..,(1S

xxx = can be explained as follows. While the

value of the information collected by a single sensor s from the intended target(s)

depends on the sensor physical location s

x relative to the target(s), this value can be

reduced if other sensors are located close to sensor s due to redundancy of the

obtained information. In a situation when all S sensors Ss ,..,1= gather

information from a single target, it is natural to assume that utilities )( xvs depend on

the target location T

x: )()( Tss xxvxv =

Physical location of mobile sensors ),..,(1S

xxx = also affects the quality of

wireless channels between different sensors and between sensors and the intended

recipient(s) of the sensor information. This is modeled by considering that capacity

c of the wireless link ),( jil= depends on the locations of sensors

i, (i.e. ji xx ,):

),,( jiijijij xxpcc = (14)

In particular, the path loss component in (9) is a function of the locations of the two

communicating sensors i.e.

492 V. Marbukh and K. Sayrafian-Pour

),( jiijij xx

ξξ

= (15)

For example, in case of free-space propagation [7]:

ρχξ

−

=ijijij (16)

where ij

and

are positive constants, and ),( jiij xx

ρρ

= is the physical distance

between sensors i and j with physical coordinates i

x and j

x respectively.

As a result of these spatial effects, the optimal network utility (10) is a function of

the vector of sensor locations ),..,(1S

xxx =

)]},(,[),({max)( 0,

*xpcFxUxU

µλ

ΣΣ

≥Λ −= (17)

where the maximization is subject to capacity constraints (2)-(3) and power

constraints (11). For the case of a single target and destination, optimal utility (17)

depends on the target and destination locations T

x and D

x respectively, i.e.

),()( **

DT xxxUxU =.

Location Optimization

For given sensor locations ),..,(1S

xxx =, the cross-layer optimized utility can be

obtained by solving equation 17. The optimal sensor locations ),..,(1

opt

optopt xxx =

maximize this cross-layer optimal utility by:

)(maxarg *xUx

ss Ax

opt

∈

= (18)

where s

A is the allowable (or feasible) area for sensor s. Terrain information

including unreachable or undesirable locations can be incorporated here.

Sensor motion (i.e. trajectory) should also take into account the corresponding

energy consumption. To account for the “cost” of sensor smotion, we introduce a

dissipative function ),( sss xx &

which quantifies negative effect of energy supply

depletion as a result of sensor s motion with speed s

& at location s

x. Functions

),( sss xx &

are assumed to be monotonically increasing and convex in s

&. Also,

0),( >

ss xx &

if 0≠

and 0),( =

sss xx &

if 0=

We assume that the total “cost” of sensor motion is additive:

∑

=Φ

sss xxxx ),(),( &&

(19)

where ),..,(1S

xxx &&& = is the vector of sensors velocities. Now consider the effect of

sensor s motion on the system performance. The rate of network utility change due

to the sensor motion is

⎟

⎠

⎞

⎜

⎝

⎛∑∇−

∑∇=∇=

llx

ssxx fxUxxUxU *** )()( &&

& (20)

A Framework for Joint Cross-Layer and Node Location Optimization 493

where T

nx xx )/,..,/( 1∂∂∂∂=∇ . Functions ]),([)( ** xxUxU ss

= and

]),([)( ** xxfxf sl

= in (2) are calculated at the optimum (17). Expression (20)

implies that cross-layer optimization (17) is performed at much faster time scale than

sensors change their locations.

Now, define system utility production ),( xxW &as

),()(),( xxxUxxW &

&Φ−= (21)

where network utility production U

& is given by (20) and dissipative function

),( xx &

Φ is given by (19). We propose to control sensor position by selecting sensor

velocity vector x

&, which maximizes the utility production (21):

),(maxarg xxWx x

= (22)

Interpreting (22) as a dynamic system, one can realize that since 0),( 0≡Φ =x

xx &

&, the

optimal sensor location opt

x is an equilibrium point of this dynamic system. It is

clear from (21)-(22) that the optimal sensor motion depends on both, potential )(xU

and the nature of the friction affecting the dissipative function ),( xx &

Φ. For brevity,

we only consider two particular cases of static and viscous friction. We assume that

)( smsxx = are Cartesian coordinates of sensor swith components sm

In the case of static friction, sensor s dissipative function is

∑

smsmss xxaxx && )(),(

(23)

and in the case of viscous friction, sensor s dissipative function is

))(()21(),( smssmsmsm xxaxx && =

(24)

where positive functions 0)( >xasm characterizes the “difficulty” of moving sensor

s at the direction of the dimension m at the point )( smsxx =. It is easy to see that

for static friction (23), sensor s either holds its position s

x if the static friction is

sufficiently strong or moves at the highest allowable speed otherwise.

In the case of viscous friction (24), the dynamic system (22) takes the following

form:

∑

−

∑

∇= ll

ssx

ssm

sm xfxU

xsm ))()((

)(

1**

& (25)

Sensor motion (25) balances change in the value of sensor information, represented

by the term ∑

∇ssx xU

sm )(

*, with the change in the sensor ability to deliver this

information to the intended recipient, represented by ∑

∇llx xf

sm )(

*. Increase in the

494 V. Marbukh and K. Sayrafian-Pour

friction force represented by friction coefficient )(xasm causes sensor to slow down.

In practical situations one may expect a combination of static and viscous friction

effects.

4 Example: A Single Mobile Sensor

Consider a single mobile sensor collecting information from a single target and

transmitting this information to a single destination. In this case the network utility

takes the following form:

)],(,[)()(),,( xpcfxvuxpU

−= (26)

We assume that power constraints (18) impose upper bound on the average

transmission power p. It is easy to see that under natural assumptions utility is

maximized for the maximum allowable power p. Therefore, power p can be

assumed to be fixed in (26). Formal differentiation of the joint utility function (26)

with respect to

yields the following first-order cross-layer optimality conditions:

),()()( cfuxv

λλ

′

′ (27)

We consider weighted ),( w

fair rate allocation utility (1) for which

λλ

−

′wu )( ; (28)

We also consider the following penalty function associated with the communication

capacity constraints:

−

)( (29)

Parameter

represents the maximum tolerable communication delay. Equation (29)

naturally arises from expression )(1

−c for the average delay in 1// MM queuing

system [8]. Combining equations (27)-(29), we obtain the following first-order cross-

layer optimality conditions:

)(]),([ 2xvwpxc

θλλ

=− (30)

Equation (30) has a single solution

),(

*px

λλ

= (31)

which is a function of both, sensor location

and transmission power p. Since

sensor utility ),( xU

is an increasing function of

, the optimal sensor location

),(maxarg)( *pxpx

opt

∈

= (32)

A Framework for Joint Cross-Layer and Node Location Optimization 495

which maximizes sensor information rate also maximizes the utility. In (32), A is the

feasible region for the mobile sensors. The optimal sensor motion is characterized by

the equation (22).

In some cases, function (32) can be explicitly identified. For example, in the case

of 0=

)]([),( −

−= xvwpxc

θλ

(33)

and, in the case of 2=

),(

)(1

)( pxc

xvw

= (34)

Now, consider the situation of low power transmissions: 0→p, when

0)()(),( 0→+= paspopxcpxc (35)

where 0)(

0>xc . For example, with the channel capacity expressions in (8)-(9):

ηξ

),()(

xxkxc =, (36)

where k is a constant coefficient, ),( D

is the path loss from the sensor location

to the destination location D

x, and

is the noise power at the destination location

x. We also assume that the sensor tracks a single target with location T

x, and the

spatial component of sensor information value depends on both, sensor and target

locations: ),()( T

xxvxv =. Under these assumptions equations (33) and (34) take the

following forms respectively:

)],([),()( −

−= TD xxwvxxpk

θξηλ

(37)

),(1

),(

),()(

Dxxwv

xxwv

xxpk

ξηλ

= (38)

It is reasonable to assume that the spatial component of the sensor utility ),( T

xxv is

qualitatively similar to the path loss from the target to the sensor ),( xxT

. Also, for

simplicity, we assume

),(),( xxxxv TT

βξ

= (39)

where 0>

is some coefficient, then equations (37) and (38) take the following

forms respectively:

)],([),()( −

−= xxwxxpk TD

ξβθξηλ

(40)

),(1

),(

),()(

xxw

xxpk

ξβθ

ξηλ

= (41)

496 V. Marbukh and K. Sayrafian-Pour

Considering equations (40) and (41), the following qualitative conclusions can be

driven. The optimal sensor location opt

xx =, which maximizes (40) or (41), is

determined by the trade-off between path loss from the target to the sensor ),( xxT

and from the sensor to the destination ),( D

. The optimal sensor location opt

xx =

depends on the terrain through the path loss. Increase in the transmission power p

moves the optimal sensor location opt

xx = “closer” to the target and “farther” from

the destination since power increase enhances communication and allows sensor to

concentrate on obtaining information from the target.

5 Conclusion and Future Research

This paper has proposed a framework for self-organization of mobile sensor

networks, which includes cross-layer network optimization as well as controlling

sensors position. Given sensor locations, cross-layer network optimization allocates

resources and configures protocols to ensure delivering the highest utility of the

sensor information to the intended recipient(s). Controlling sensor location further

enhances this utility.

Future efforts should address numerous research and implementation challenges,

including quantification of sensor utility and utility production. Also, a simulation

platform is currently under construction to further evaluate the performance of such

networks in case of large number of nodes.

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Author Index

Abu-Ghazaleh, Nael B. 58, 251

Acampora, Anthony S. 230

A¨

ıache, Herv´e 391

Al Hamra, Anwar 189

Altan, Nicola 15

Altman, Eitan 122

Aron, Felix 357

Barakat, Chadi 189

Benenson, Zinaida 279

Bermond, Jean-Claude 204

Bernhard, Pierre 122

Bestehorn, Markus 279

Blondia, Chris 94

Braem, Bart 94

Braun, Torsten 72

Bryce, Ciar´an 439

Buchmann, Erik 279

Cavalli, Ana 345

Chan, H. Anthony 321

Chelius, Guillaume 29

Chen, Yung-chih 463

Choi, Jaeyoung 189

Conan, Vania 391

Darties, Benoˆıt 451

De Cleyn, Peter 94

De Soete, Marijke 94

Derhab, Abdelouahid 401

Durand, Sylvain 451

Dziong, Zbigniew 293

Elkin, Michael 425

Endler, Markus 29

Freiling, Felix C. 279

Gagnon, Fran¸cois 293

Gansterer, Wilfried N. 369

Gol

ebiewski, Zbigniew 241

Gomes, Antˆonio Tadeu A. 29

Hamam, Yskandar 357

Han, SeonYeong 251

Haring, G¨

unter 369

Heurtefeux, Karel 218

Hurni, Philipp 72

Ip, Louisa Pui Sum 230

Jawurek, Marek 279

Kareem, Tope R. 321

Kastrinogiannis, Timotheos 307

Khan, Majid I. 369

Kik, Marcin 333

Kim, Jinguk 475

Kosek, Katarzyna 380

Kouraogo, Pegdwind´e Justin 293

Kranakis, Evangelos 1, 108

Kunz, Thomas 43

Lando, Yuval 425

Latr´e, Benoˆıt 94

Lebrun, Laure 391

Leone, Pierre 148

Leung, Ian 463

Lima, Luciana S. 29

Li`o, Pietro 463

L´opez Villafuerte, Freddy 162

Lu, Xiaofeng 463

Majcher, Krzysztof 241

Mallouli, Wissam 345

Marbukh, Vladimir 487

Matthee, Karel 321

Mbarushimana, C. 265

Moerman, Ingrid 94

Moraru, Luminita 148

Natkaniec, Marek 176, 380

Nikoletseas, Sotiris 148

Ntlatlapa, Ntsibane 321, 357

Nutov, Zeev 86, 425

Odhiambo, Marcel 357

Olwal, Thomas 357

Pach, Andrzej R. 176, 380

Palaysi, J´erˆome 451

498 Author Index

Papavassiliou, Symeon 307

Paquette, Michel 108

Peeters, Michael 94

Pelc, Andrzej 108

Peleg, David 135

Preneel, Bart 94

Pu, Ida 475

Qin, Liang 43

Rathgeb, Erwin P. 15

Razak, Saquib 58

Roditty, Liam 135

Rolim, Jose 148

Rousseau, St´ephane 391

Sayraﬁan-Pour, Kamran 487

Sbai, Mohamed Karim 189

Schiller, Jochen 162

Segal, Michael 425

Shahrabi, A. 265

Shen, Yuji 475

Shpungin, Hanan 425

Silva, Alonso 122

Singel´ee, Dave 94

Sun, Jun-Zhao 413

Szott, Szymon 176

Tsiropoulou, Eirini-Eleni 307

Turletti, Thierry 189

Valois, Fabrice 218

van Wyk, Barend J. 357

Wehbi, Bachar 345

Wiese, Andreas 1

Xiong, Zhang 463

Yu, Min-Li 204

Zag´orski, Filip 241

Ziviani, Artur 29

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Utility-Based Uplink Power Control in CDMA Wireless Networks with Real-Time Services

Conference Paper

September 2008

Timotheos Kastrinogiannis · Eirini Eleni Tsiropoulou · Symeon Papavassiliou

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ADHOC NOW 2008 Utility-Based Uplink Power Control in CDMA Wireless Networks with Real-Time Services

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