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Self-Adaptive Ad-Hoc/Sensor Network Routing
with Attractor-Selection
Kenji Leibnitz∗, Naoki Wakamiya∗, Masayuki Murata∗
∗Osaka University, Graduate School of Information Science and Technology
1-5 Yamadaoka, Suita, Osaka, 565-0871 Japan
Email: {leibnitz|wakamiya|murata}@ist.osaka-u.ac.jp
Abstract— In this paper we propose MARAS, a biologically-
inspired method for routing in a mobile ad-hoc/sensor network
environment. We assume that all nodes have no explicit knowl-
edge of the network topology, except for their coordinates and
the neighboring nodes within an RF transmission range. MARAS
then selects the next hop for forwarding a packet towards
a destination node which is best suited depending on some
measured metric values. The benefit of our proposed method
is its ability to operate entirely in a self-adaptive manner and
that it can easily compensate for sudden changes in the topology
of the network.
I. INTRODUCTION
Routing in mobile ad-hoc networks has recently attracted
many researchers due to the flexibility in controlling the topol-
ogy. Unlike conventional Internet routing which is constrained
by the underlying OSPF routing functionality, ad-hoc networks
and sensor networks use wireless links and can be configured
in a highly dynamic way. While we consider in this paper
ad-hoc and sensor networks in the same fundamental way,
their actual requirements differ significantly. Ad-hoc nodes
may be mobile computers or PDAs that are simply connected
in an ad-hoc manner, whereas, sensor networks usually have
limited computational capabilities and a limited lifetime due
to exhausted battery power. Our focus in this paper lies on
generic ad-hoc network architectures.
In general, there are two major reactive routing concepts
for ad-hoc networks: source routing, e.g. in Dynamic Source
Routing (DSR) [1], and distance vector-based, e.g. Ad-Hoc
On-Demand Distance Vector (AODV) [2]. When a new route
to a destination node is requested, the source routing approach
uses probe packets to determine the path from source to
destination node and stores this information in each packet.
On the other hand, in AODV each node uses routing tables
to maintain the information of forwarding nodes. The routing
tables are also set up by flooding the network with probe pack-
ets. Several variants of DSR and AODV have been proposed
to consider multiple paths between source and destination to
increase transmission reliability, cf. [3].
In this paper we consider a geographical routing scheme
for ad-hoc networks. This means that we assume that each
node is capable of determining its own location as well as an
estimate of the destination node location. Although our method
is also capable to operate without this restriction, it clearly
helps to reduce the number of packets flooded in the network
by having a rough idea in which direction the packet should
travel. The selection of the next hop is performed with the
biologically inspired adaptive response by attractor selection
(ARAS) concept [4].
The remainder of this paper is organized as follows. In
Section II we briefly introduce related work on routing in ad-
hoc networks, especially with focus on randomized methods.
This is followed in Section III by a description of the proposed
biologically-inspired approach and we elaborate on how to
apply it for self-adaptively determining the next hop in routing.
The proposal is evaluated in Section IV by simulation results
and future extensions are discussed in Section V.
II. RELATED WORK
While many proposals for ad-hoc routing have been pub-
lished, we are mainly interested in a robust and flexible
concept that can self-adaptively react to sudden changes in the
network topology. A possible approach to enforce resilience
is to deviate from deterministic routing algorithms and to
perform the selection of the next hop in a probabilistic manner.
Since the selection is done independently by each node, these
ad-hoc routing schemes scale well with the number of nodes.
In order to simplify the task we assume that the hop
forwarding mechanism uses geographical information, i.e., the
nodes are aware of their own locations. The advantage of
using location information in routing is that the number of
packets required for searching the paths to the destination
node can be limited in the direction of the destination node,
cf. LAR (Location-Aided Routing) [5]. However, location
based routing may have problems if the selection of the
next hop is performed in an entirely greedy way. Packets
must be routed around void areas where no forwarding node
exists in the direction to the destination. For instance, GPSR
(Greedy Perimeter Stateless Routing) [6] switches from greedy
forwarding to routing around the perimeter of the void region
when one is encountered. Finding the destinations can also be
performed using specific location servers which are queried
by nodes to find the destination [7].
Another class of random forwarding protocols is represented
by GeRaF (Geographic Random Forwarding) [8] and ExOR
[9]. Here, each node also assumes some limited geographic
information of itself and the sink node. When a node wishes
to forward a packet toward the destination, it broadcasts it to
its neighboring nodes, which then cooperate among each other
to determine the best choice as next hop.
©
1-4244-0357-X/06/$20.00 2006 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE GLOBECOM 2006 proceedings.
Fig. 1. General concept of ARAS
III. THE PROPOSED MARAS MECHANISM
We propose MARAS (mobile ad-hoc routing with attractor
selection), an entirely distributed multi-path routing mech-
anism, where each node operates autonomously and only
gathers information about the network topology by exchanging
messages with its neighbors. MARAS uses the concept of
adaptive response by attractor selection (ARAS) for each node
to select its next hop. In contrast to this paper, previous work
in the field of overlay networks [10], [11] uses ARAS to self-
adaptively select the primary path among a set of multiple
predetermined paths at the source node. Those paths are
obtained by using an underlying routing protocol on network
layer and ARAS is used there to reduce the selfishness of flows
in order to improve the overall performance of the network.s
A. Adaptive Response by Attractor-Selection
Adaptive response by attractor selection is a biologically
inspired method for adaptively selecting one of several can-
didates which best reflects the current situation in a dynamic
environment. ARAS is originally a model for its host E. coli
cells to adapt to changes in the availability of a nutrient
for which no molecular machinery is available for signal
transduction from the environment to the DNA [4].
Basically, we can outline the attractor selection method as
follows. Using a set of differential equations, we describe
the dynamics of an M-dimensional system. Each differential
equation has a stochastic influence from an inherent Gaussian
noise term. Additionally, we introduce an activity α∈[0,1]
which changes the influences from the noise terms. For ex-
ample, if αis large, the system behaves rather deterministic
and converges to attractor states defined by the structure of
the differential equations. However, for small αthe noise term
dominates the behavior of the system and essentially a random
walk is performed. When the input values (nutrients) require
the system to react to the modified environment conditions,
activity αchanges accordingly causing the system to search
for a more suitable state, see Fig. 1. This may involve that α
causes a previously stable attractor to become unstable.
Consider a set of Annodes of which we wish to select
one to forward the packet as next hop of a node n.Letthe
cardinality of set Anbe M. For each node i∈Anwe define
the proportion of selecting node ias miwith mmax being
the maximum over all mi. The dynamic behavior of miis
Fig. 2. Influence of αon output probabilities
characterized by the stochastic differential equation system
given in Eqn. (1) for i=1,...,M.
dmi
dt =syn(α)
1+m2
max −m2
i−deg(α)mi+ηi(1)
The functions syn(α)and deg(α)are the rate coefficients of
mRNA synthesis and degradation in the original biological
model, respectively. They are both functions of α, which
represents cell activity or vigor. The terms ηiare independent
white Gaussian noise inherent in gene expression.
syn(α)=α[βα
γ+ϕ∗]deg(α)=α(2)
The parameters βand γin (2) are factors which influence
the mapping of activity to the output probabilities and we use
β=50and γ=3throughout this study. The variable ϕ∗is a
special offset point which we will discuss below. For the sake
of simplicity we also define ϕ(α)=syn(α)
deg(α).
When we define the functions syn(α)and deg(α)as given
in (2), we obtain Mequilibrium solutions x(k)of Eqn. (1) in
the form of
x(k)=x(k)
1,...,x
(k)
MT
k=1,...,M
with components x(k)
i,see(3).
x(k)
i=ϕ(α)i=k(Hvalue)
1
24+ϕ(α)2−ϕ(α)i=k(Lvalues) (3)
The behavior can be summarized as follows. The system
in Eqn. (1) converges to solutions which have a single “high”
value (H) and all other values are “low” (L). The dynamics of
activity αinfluences the selected values. When αis high, the
high value Halso approaches 1.0, i.e., the selection becomes
more deterministic. On the other hand, for small α,Hand L
become equal and the probabilities for selecting the next hop
is controlled by the noise term, see Fig. 2.
Note that at ϕ∗=1/√2we have a special point, as the
solutions x(k)are only defined when ϕ(α)≥ϕ∗(i.e., H≥L).
For ϕ(α)=ϕ∗we obtain a single solution xwith the same
entries. Finally, the resulting state vector is normalized to yield
the probabilities for selecting a neighboring node as the next
hop.
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE GLOBECOM 2006 proceedings.
Fig. 3. Comparison of activity evaluation for two paths
B. Mapping of Activity
The activity value αreflects the “goodness” of the current
solution of ARAS. It is evaluated at the destination node
and fed back to all nodes along the taken path. Its desired
behavior is summarized as follows. If we have no information
about which hop to choose (e.g. when selecting the hops
for an initially unknown destination) the selection should be
performed uniformly among all neighbors. Therefore, each
node should initialize α=0as this corresponds to the “no
preference” case. The same applies to the case when the
maximum number of hops (maxhops) is exceeded. A low α
means that the current solution is not suitable and a new one
should be searched. If a path to the destination exists, we
wish to keep it with an activity of 0.0<α<1.0. The larger
αis, the greater is the difference between Hand L, which
corresponds to the case where we have a clearly identified
optimal choice as path as shown in Fig. 2. Therefore, we use
in the following experiments an αas defined in (5).
α∗=1−1−dist(s, d)
len 1−hmin
h(4)
dα
dt =δ(α∗−α)(5)
The first term in (4) is the ratio of the direct distance
dist between source sand destination dover the path length
len found by ARAS. Thus, α∗is small when the difference
between both paths is large (i.e. the current path deviates much
from the shortest, direct connection). In the second term, hmin
h
is the fraction of the previously found minimal number of hops
over the current hops. Thus, by using this activity mapping,
we achieve that short paths with a small number of hops are
preferred over long paths. For example, in Fig. 3, path 1 is
preferred over path 2, which leads to a higher activity feedback
for path 1. Finally, δis the rate of adaptation of αwhich we
keep constant at δ=0.1. Finally, in order to avoid outdated
information, activity decays over time.
C. Selection of the Candidate Nodes
Consider a scenario as shown in Fig. 4 where a source
node transmits packets to the destination node of which it
only knows its coordinate location. Each intermediate node
decides autonomously with its own ARAS mechanism to
which of its neighbors it forwards the packet. Once a packet
has been delivered successfully (or not), the quality of the
path is evaluated and used to update the decision of the node
to maintain the current path or to dismiss it.
Fig. 4. Decision of next hop with ARAS
Let us assume the set of all nodes as Nand an arbitrary
node n∈Nwhich receives a packet for the destination
node d∈N. On reception of the packet, the node identifies
its current environment, by sending a distance request to
its neighboring nodes. In order to reduce traffic load, this
request can be done at a certain time interval. However, the
more frequently this query is performed, the more accurate
is the information about the current network topology. All
neighboring nodes ireply to this request by reporting their
respective distances dist(i, d)to the destination. Based on
this information, the node nmaintains its neighbors in two
logical sets: the neighbor set Nnand the candidate set Cn.
The neighbor set contains all nodes within the transmission
radius rnof node n, i.e.,
Nn={i∈N|dist(i, n)<r
n}.(6)
On the other hand, the candidate set is a subset of the neighbor
set of all nodes which are nearer to the destination than n, i.e.,
Cn={i∈Nn|dist(i, d)<dist(n, d)}.(7)
All nodes in Cnare potential candidates for forwarding, since
the packet would get closer towards the destination with each
hop. Which one is chosen is up to ARAS itself and will be
described in the following section. For simplicity. we also
define the complementary candidate set w.r.t. its neighbor set
as Cn=Nn\Cn.
D. Extension of the Basic Algorithm
We can now summarize the basic algorithm for packet
forwarding with MARAS when a node nreceives a packet
for destination node d:
1) If n=d, calculate α∗from (5), update all nodes along
the path, and process packet at destination d.
2) Determine neighbor set Nnand candidate set Cn.
3) If Cn=∅, then there is no suitable candidate in the
direction of the destination. In order to avoid getting
stuck in dead ends, we then set the ARAS set An=Cn.
Otherwise, i.e., if Cn=∅,setAn=Cn.
4) Perform ARAS on set Anand forward packet to next
hop according to resulting probabilities.
The dynamic behavior of the algorithm is illustrated in
Fig. 5. There are |N| = 100 nodes randomly distributed in
a unit area size of [0,1] ×[0,1]. Each node has a transmission
radius of r=0.3. A snapshot of the system is given in
Fig. 5(a). The source node (24) continuously sends packets to
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE GLOBECOM 2006 proceedings.
(a) Network layout (b) Next hop probabilities of node 24
Fig. 5. Example of simulation scenario
the destination node using the previously described mechanism
to determine its next hop. In Fig. 5(b) the next hop selection
probabilities of the source node over the first 1000 time
steps are given. Until about time step 500, node 11 is first
chosen as relay hop. Then, this node leaves the system and
the next hop is immediately switched to node 0 as shown
in Fig. 5(a). The lower number of nodes in the candidate
set leads to a higher selection probability of the primary hop
candidate. Furthermore, although the probability for selection
is about 0.95, the next hop is still chosen randomly, leading to
slight variations in the path for each packet being transmitted.
This also assists in resolving sometimes not optimal paths as
highlighted in Fig. 5(a).
In order to actively remove such zigzag-shaped paths, we
propose the following step when the activity of each node
along the path is updated (step 1). Since this update is
performed by a packet sent from the destination back to the
source in the reverse direction of the original path, it is possible
to check in the stored path in the packet if the i-th node along
the original path has the j-th node (i+2 ≤j) within its
transmission range. All nodes of the path lying between these
two nodes are eliminated simply by removing them from the
respective sets An. The result of this operation would be the
dashed line shown in Fig. 5(a).
IV. NUMERICAL EVA L U AT I O N
In the following we will evaluate the influence of the pa-
rameter settings on the performance of our method. The nodes
are randomly distributed according to a spatial homogeneous
Poisson process with density λin a unit square, see [12].
We construct the process with increasing xcoordinate and
choose as source the node with the smallest xcoordinate and
as destination the one with the largest. Since the randomness
of the node locations has a great influence, a large number of
simulation replications is required. Thus, the following results
are averaged over all connections of 500 simulation runs with
3000 time steps each. Error bars in the curves indicate the
95% confidence levels of the sampled mean values.
We compare the results of our method to those obtained
from a simple greedy selection of the next hop. In the greedy
method, each node forwards the packet deterministically to its
neighboring node which lies nearest to the destination. It is
expected that when the node density is large enough, greedy
Fig. 6. Delivery rate over node density
will always outperform our proposal since the latter will use
a random decision for the next hop. Our focus therefore lies
on the more interesting cases when the node density is low or
the radius of the nodes is small.
A. Rate of Successful Delivery
Figure 6 shows the average packet delivery rate as a function
of the node density λ. When the node density is very small,
there is often no connectivity to the destination which leads to
a high failure rate regardless of the routing method. We can
see in Fig. 6 that MARAS achieves better performance than
the greedy approach especially when the radius is small.
B. Resilience to Topology Changes
In order to cope with sudden changes in the network
topology, we now also take the state of the nodes into account.
Since we are interested how well the system performs in the
presence of suddenly changing topologies, we let all nodes in
the transit area with an xcoordinate between 0.25 and 0.75
become inactive with a probability q. When qis large, many
transit nodes will be unavailable for routing so the mechanism
must adapt to find a new route to the destination.
It can be recognized in Fig. 7 that the delivery rate with
MARAS is higher than that of the greedy approach due to the
greater flexibility in the selection of the next hop. This effect
is even greater for smaller node radius r.
Fig. 7. Delivery rate over state-change probability
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE GLOBECOM 2006 proceedings.
Fig. 8. Probability of finding an empty candidate set
C. Analytical Discussion on Density vs. Radius
The radius and density greatly influence the probability of
finding a next hop within the coverage range. Due to the
assumption that all nodes are distributed as a homogeneous
Poisson process with density λ, we can analytically elaborate
further on this. Assume that a node nis randomly located
in the plane at distance dfrom the destination node. Our
algorithm tries to find a next hop node in its coverage range
rthat lies closer to the destination than itself. Using simple
geometry, the intersection area of the circle around nwith
radius rand the circle around the destination node with radius
dcan be given as V(r, d)
V(r, d) = arccos ˜
X
rr2+ arccos d−˜
X
dd2−d˜
Y
with ˜
X=r2
2dand ˜
Y=r2−˜
X2. The number of nodes in
area V(r, d)follows a Poisson distribution with rate λ,sothe
probability to find an empty candidate set of nodes is given
as in Eqn. (8) and illustrated in Fig. 8 for d=1.0.
P(K=0)=e−λπ V (r,d)(8)
In Fig. 8 we can recognize that for densities of λ<50 and
small radius r, there is a high probability of finding no node in
the candidate set. In these cases the complementary candidate
set Cxis used for MARAS, which may result in long detours
of paths or dead ends.
V. C ONCLUSION AND OUTLOOK
In this paper we presented a new approach for self-adaptive
routing in an ad-hoc network. The concept is inspired from
biology and is capable of rapidly reacting to changes in the
environment. Basically, the proposed mechanism determines
the probabilities for choosing the next hop of a packet on
its path to the destination. Suitable paths with small number
of hops or high path length-to-distance ratio are rewarded,
whereas long paths or those which do not lead to the destina-
tion are penalized. The whole mechanism is controlled by an
activity term which evaluates the current path and is fed back
from the destination to all nodes along the path. Although we
focused here on finding short paths, our method can easily take
into account further metrics, e.g. radio link quality (signal-to-
interference ratio), load of each node, etc. Numerical results
indicate that the proposed method operates well when the node
density and transmission radius are sufficiently large. Removal
of nodes as well as node additions can be easily compensated.
The implementation itself can be performed in a straight-
forward manner with numerical methods which makes it also
applicable for networks with nodes that have only limited
computational capabilities like sensor networks. We can easily
consider the total energy consumption per path and the residual
energy of each node for selecting the path with the least energy
dissipation. More detailed studies on appropriate input metrics
for evaluating the paths as well as performance comparisons
to other existing randomized mechanisms are the subject of
future studies. Especially, when we consider a high churn rate
of the nodes or high mobility, we expect that our method
operates well compared to other approaches. Additionally,
due to the randomization of the hop selection, a better load
distribution will be achieved,
ACKNOWLEDGMENTS
This research was supported by “The 21st Century COE
Program: New Information Technologies for Building a Net-
worked Symbiosis Environment”, “Special Coordination Funds
for Promoting Science and Technology: Yuragi Project”, and
a Grant-in-Aid for Scientific Research (A)(2) 16200003 of the
Ministry of Education, Culture, Sports, Science and Technol-
ogy in Japan.
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE GLOBECOM 2006 proceedings.
