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Performance analysis of distributed mapping system in ID/locator
separation architectures
$,$$
Younghyun Kim
a
, Haneul Ko
a
, Sangheon Pack
a,
n
, Jong-Hyouk Lee
b
, Seok-Joo Koh
c
,
Heeyoung Jung
d
a
School of Electrical Engineering, Korea University, Seoul, South Korea
b
Department of Computer Software Engineering, Sangmyung University, Cheonan, South Korea
c
College of IT Engineering, Kyungbuk National University, South Korea
d
Internet Future Technology Department, ETRI, South Korea
article info
Article history:
Received 5 February 2013
Received in revised form
3 June 2013
Accepted 16 July 2013
Available online 29 July 2013
Keywords:
Centralized mapping system
Distributed mapping system
ID/locator separation
Distributed hash table
abstract
An ID/locator separation architecture is one of the most recognized technologies that enable the Future
Internet. In ID/locator separation architecture, an ID/locator mapping system is indispensable to provide
location management in mobile environments. This paper conducts a comparative study on two different
ID/locator mapping approaches: centralized and distributed ID/locator mapping systems. We develop
analytical models on the signaling cost incurred in location update and location query procedures of the
centralized and distributed ID/locator mapping systems. Numerical results demonstrate that the
distributed ID/locator mapping system with enhanced distributed hash table (DHT) has comparable
signaling cost to the centralized ID/locator mapping system while providing higher scalability and
robustness.
&2013 Elsevier Ltd. All rights reserved.
1. Introduction
With the increase of smart devices and demand for new
networking applications (i.e., online games, social networking
services, and high definition multimedia), Internet has been
explosively grown in terms of data traffic and the number of
connected devices in recent years (Saleh and Simmons, 2011).
However, current Internet routing and addressing systems are
facing various challenges such as routing scalability, mobility
support, multihoming support, etc., due to the use of an IP address
as a single namespace simultaneously expressing an identifier and
a location of a mobile node (MN) (Meyer et al., 2007). In order to
address the single namespace issue in the Internet, several ID/
locator separation architectures have been proposed and widely
recognized as a promising technology for the Future Internet
(Kafle and Inoue, 2012).
ID/locator separation architectures can be categorized into two
approaches: host-based approach and network-based approach.
Host-based approaches, such as host identify protocol (HIP)
(Moskowitz et al., 2008), Shim6 (Nordmark and Bagnulo, 2009),
and identifier-locator network protocol (ILNP) (Atkinson et al.,
2010), decouple IDs from locators in the host's protocol stack. On
the other hand, network-based approaches separate core networks
and edge networks by means of routers. Locator/identifier separa-
tion protocol (LISP) (Farinacci et al., 2012) is a representative
example of network-based ID/locator separation architectures.
Mobile-oriented Future Internet (MOFI) is another proposal for
network-based ID/locator separation protocol in mobile environ-
ments (http://www.mofi.re.kr/). As reported in Kim et al. (2008),
since network-based approaches have some advantages (e.g., low
implementation cost and easy deployment) over host-based
approaches, a network-based approach similar to LISP is assumed
throughout this paper.
Figure 1 shows a LISP architecture where ingress tunnel routers
(ITRs) and egress tunnel routers (ETRs) are gateways between
core and edge networks. When an MN moves to ITR/ETR2 from
ITR/ETR1, ITR/ETR2 registers the ID/locator binding of the MN to a
mapping system. If a packet destined to the MN arrives at
ITR/ETR0, ITR/ETR0 requests the MN's location information from
the ID/locator mapping system. After obtaining the location
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/jnca
Journal of Network and Computer Applications
1084-8045/$ - see front matter &2013 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.jnca.2013.07.005
☆
A preliminary version of this paper was presented at the 4th IEEE GLOBECOM
International Workshop on Mobility Management in the Networks of the Future
World (MobiWorld), December 2012 (Kim et al., 2012).
☆☆
This research was supported in part by the KCC, Korea, under the R&D program
supervised by the KCA (KCA-10913-05004) and in part by National Research
Foundation of Korea Grant (2012K2A1A2032693 and 2012R1A1B4000894).
n
Corresponding author. Tel.: +82 2 3290 4825; fax: +82 2 921 0544.
E-mail addresses: younghyun_kim@korea.ac.kr (Y. Kim),
st_basket@korea.ac.kr H. Ko), shpack@korea.ac.kr (S. Pack),
jonghyouk@ieee.org (J.-H. Lee), sjkoh@knu.ac.kr (S.-J. Koh),
hyjung@etri.re.kr (H. Jung).
Journal of Network and Computer Applications 39 (2014) 223–232
information, ITR/ETR0 can transmit the packet to the MN through
ITR/ETR2.
As shown in Fig. 1, an ID/locator mapping system consisting of
one or multiple mobility agents (MAs) is indispensable to register
and retrieve the location information of MNs.
1
The ID/locator
mapping system can be organized in centralized and distributed
manners. A centralized mapping system (CMS) employs only one
MA and thus the MA can be a single point of failure and bottle-
neck. On the contrary, several MAs are employed in a distributed
mapping system (DMS) and thus an additional mechanism is
needed to find out the serving MA for a specific MN. In the
literature, DMS with multicast and DMS with distributed hash
table (DHT) have been suggested (Fischer et al., 2008; Zhai et al.,
2011; Gohar and Koh, 2012). However, to the best of our knowl-
edge, no works on comparative study among these mapping
systems have been reported.
In Kim et al. (2012), we developed analytical models for
evaluating CMS, DMS with multicast, and DMS with DHT in ID/
locator separation architectures. The analytical models evaluate
the signaling and processing overheads for location update and
location query procedures. Two well-known topologies (i.e., mesh
and tree) are considered to represent the both ends of network
deployments. By extending out previous work (Kim et al., 2012),
we propose an enhanced DHT to reduce the signaling overhead
incurred in DMS with DHT and develop its analytical model. We
also present a new analytical model on the processing latency at
the mobility agent to assess the scalability of the mobility agent.
Numerical results demonstrate that DMS with enhanced DHT
provides higher scalability with comparable or low signaling
overhead compared with other mapping systems (i.e., CMS, DMS
with multicast, and DMS with DHT).
The remainder of this paper is organized as follows. Related
works and the detailed descriptions of CMS and DMS are described
in Sections 2 and 3, respectively. Section 4 describes the analytical
models for CMS, DMS with multicast, DMS with DHT, and DMS
with enhanced DHT. Numerical results and concluding remarks are
given in Sections 5 and 6, respectively.
2. Related work
As mentioned before, the ID/locator separation architecture
requires a mapping system to resolve the MN's ID to the corre-
sponding locator. A number of ID/locator mapping systems have
been proposed in the literature that can be classified into (1) cen-
tralized mapping system (CMS) and (2) distributed mapping
system (DMS).
LISP-NERD is one of the examples for CMS (Lear, 2012). In LISP-
NERD, a mapping server located at ITRs/ETRs is refreshed at the
regular time interval. To this end, the mapping server pushes the
updated mapping information to all ITRs/ETRs. That is, LISP-NERD
can provide the strong consistency on the ITR/ETR mapping at the
expense of high traffic overhead.
Gohar and Koh (2012) introduce a multicast-based DMS in
localized mobile LISP networks. When an ITR/ETR receives a
packet destined to an MN, the ITR/ETR sends a request message
on the ID/locator mapping to all other ITRs/ETRs. In spite of the use
of multicast, the signaling overhead is not quite high since only a
local LISP domain is considered.
LISP-TREE (Jakab et al., 2010) is a partially distributed mapping
system. In LISP-TREE, IDs are assigned in a hierarchical manner,
and a discovery domain is defined to provide the ID/locator
mapping information. Since the discovery domain is organized in
a hierarchical manner, the request on the ID/locator mapping can
be resolved iteratively. For example, when an ITR/ETR receives a
packet destined to an MN, the ITR/ETR asks the ID/locator mapping
information to the low-level discovery domain in LISP-TREE. Only
when the low-level discovery domain cannot resolve the request,
the request is forwarded to the upper-level discovery domain.
Although LISP-TREE can improve the scalability, it does not pay
attention to the mobility.
Qiu et al. (2009) propose a hierarchical DMS to avoid the
bottleneck of a centralized mapping server. At the top level,
multiple mapping servers are connected by means of DHT. On
the other hand, mapping servers at the intermediate levels
maintain the ID/locator mapping information of MNs currently
located in their domains. The proposed hierarchical mapping
system can reduce the signaling overhead and guarantee higher
scalability than the centralized mapping system.
Luo et al. (2011) propose a scalable and robust proxy mobile
IPv6 (SARP) where mobile access gateway (MAG) and local
mobility anchor (LMA) are co-located. In conventional PMIPv6,
only LMA provides the ID/locator mapping function in the PMIPv6
domain. On the other hand, the ID/locator mapping function is
distributed to every MAGs for better scalability and robustness in
SARP. Also, a DHT based ID/locator mapping system is introduced.
Similarly, LISP-DHT (Mathy and Iannone, 2008)defines a fully
distributed mapping system based on DHT. Due to the properties
of DHT, LISP-DHT can provide salient features such as self-
organization, robustness, and load balancing. However, a longer
path is expected to deliver signaling messages.
3. CMS and DMS
In this section, we describe the procedures for location man-
agement in CMS, DMS with multicast, DMS with DHT, and DMS
with enhanced DHT. In terms of network topology, we consider
both the mesh topology and the tree topology. In the mesh
topology, all access routers (ARs) are directly connected to each
other. A centralized MA is located at the root node in the tree
topology if CMS is applied. On the other hand, in DMS, MAs are
located at leaf nodes in a balanced binary tree.
3.1. CMS
Figure 2 shows the location update and location query proce-
dures of CMS on the mesh and tree topologies. As shown in Fig. 2,
there is only one MA and the MN informs the MA of the changed
Fig. 1. ID/locator separation architecture.
1
The MA is a general term for representing an ID/locator mapping data storage
server throughout this paper.
Y. Kim et al. / Journal of Network and Computer Applications 39 (2014) 223–232224
location information when the MN moves from one AR to
another AR.
In Fig. 2(a), when a correspondent node (CN) sends a packet to
the MN, the packet first arrives at AR5. Then, AR5 requests the
location information of the MN from the centralized MA. After
receiving the location response message for the MN, it can be
found that the MN is connected to AR2, and thus the packet is
transmitted to AR2. Finally, AR2 delivers the packet to the MN.
As shown in Fig. 2(a), signaling messages (i.e., location regis-
tration, request, and response messages) can reach the MA
through only one-hop link in the mesh topology. On the contrary,
several hop links are needed for signaling messages to get to the
MA in the tree topology as illustrated in Fig. 2(b). In other words,
the location update/query messages are delivered from the AR
(e.g., AR4 and AR7 if Fig. 2(b)) at the leaf level to the MA at the
root level.
3.2. DMS with multicast
In CMS, the MA can be a single point of failure and can lead to
the increased processing overhead and delay. Furthermore, multi-
ple MAs are needed for fault-tolerant and scalable mapping
systems. As shown in Fig. 3, in DMS with multicast, MAs are co-
located with ARs for distributed mobility management and a
location query message is multicasted to all MAs (Bertin et al.,
2009). Note that although DMS with multicast can provide higher
availability than CMS, it does not include any specific handling
functions for MAs'join/leave and failure events.
Figure 3 shows the location update and location query proce-
dures in DMS with multicast. In DMS with multicast, each AR/MA
maintains the location information of its serving MNs. Hence, the
MN registers its location to the nearest MA (e.g., MA2 in Fig. 3
(a) and MA4 in Fig. 3(b) after movement). As shown in Fig. 3(a),
when MA5 receives a packet destined to the MN, MA5 multicasts a
location query message to all MAs to find out the current serving
MA. Then, the current serving MA, i.e., MA2, responds to the
request and then MA5 can forward the packet to MA2. Although
DMS with multicast is simple and easy to implement, it leads to
significant signaling overhead due to multicast location query
messages to all MAs. This signaling overhead becomes more
apparent in the tree topology because signaling messages are
routed over multi-hop links as shown in Fig. 3(b).
3.3. DMS with DHT
To mitigate the signaling overhead in DMS with multicast, MAs
can be organized based on DHT. Specifically, we assume the use of
Chord (Stoica et al., 2001), which is one of the most representative
DHT schemes and provides high availability even for dynamic
events (e.g., join/leave of MAs and failed MAs). In Chord, unique
m-bit identification numbers are determined by a hashing func-
tion and the hashed values can be used as identification numbers
of MNs and MAs. In addition, if an MN's identification number is k,
an MA with the minimum identification number among MAs
whose identification numbers are larger than kis assigned as the
serving MA for the MN.
To efficiently manage the distributed data (i.e., location infor-
mation), an MA maintains a shortcut routing table called finger
table. The finger table at each MA stores at most mentries and one
entry is composed of three fields, i.e., start,interval, and successor.
Fig. 2. Centralized mapping system. (a) Mesh topology and (b) tree topology.
Fig. 3. Distributed mapping system with multicast. (a) Mesh topology and (b) tree topology.
Y. Kim et al. / Journal of Network and Computer Applications 39 (2014) 223–232 225
start and interval fields represent the identification number range
covered by an entry. If the identification number of an MA is k,
start and interval fields of the ith entry are set to ðkþ2
i1
Þmod 2
m
and [start of the ith entry, start of the ðiþ1Þth entry
2
), respectively.
On the other hand, successor of the ith entry indicates that the
shortcut to reach the serving MA of MNs belonging to the range of
the ith entry. For example, assume that MA5 receives a location
request with N53 in Fig. 4(a). Then, from the third entry of its
finger table, MA5 can infer that the shortcut to the serving MA for
N53 is MA6 since N53 belongs to [N50, N54).
When a location update or query message is received, the MA
first determines the unique identification number of the MN by
using the hashing function. Then, the MA checks the entry of the
finger table to determine the shortcut MA in finding the serving
MA. As shown in Fig. 4(a), since the identification numbers of the
MN and MA8 are N61 and N63, respectively, MA8 becomes the
serving MA for the MN. When the MN moves from MA4 to MA2,
the location update message should be sent to the serving MA,
MA8. Since the identification number of MA8 is N63 and the finger
table in MA2 indicates the next shortcut should be MA6, the
location update message is delivered to MA6, which repeats the
same delivery procedure by checking its own finger table. Finally,
the location information of the MN can be notified to MA8.
In the same manner, location update and query procedures can
be performed in the tree topology as shown in Fig. 4(b). Due to the
properties of Chord, each MA serves a comparable number of MNs
and thus load balancing can be achieved. However, as illustrated in
the above example, location update and location query messages
should be routed over a longer path compared with DMS with
multicast.
3.4. DMS with enhanced DHT
DHT can achieve load balancing and fault-tolerance at the
expense of longer routing path. Therefore, we extend the finger
table in DHT to accommodate more shortcuts to MAs. Specifically,
the enhanced DHT defines a new finger table that includes routing
information on all MAs. Note that the original DHT maintains the
shortcut information of only mMAs, which is a reasonable number
when we consider very large distributed systems (e.g., peer-to-
peer (P2P) systems). On the contrary, our extension of the finger
table is valid because even large wireless/mobile networks will
deploy at most a few tens or hundreds MAs.
In the enhanced finger table, the first entry indicates the
identification number range covered by the MA itself. On the
other hand, the ith entry (i≥2) includes the identification number
range handled by the ði1Þth MA in a clock-wise direction from
the current MA. Consequently, location update and query mes-
sages can be directly delivered by means of the enhanced finger
table through one-hop link. Unlike the conventional DHT, the
enhanced finger table of each MA maintains the same entries
(with different orders) because the enhanced finger table includes
routing information on all MAs.
In Fig. 5(a), it is assumed that the MN whose ID is N61 moves
from MA4 to MA2. Then, the location update message can be
directly sent to the serving MA, i.e., MA8. This direct transmission
is possible since the finger table of MA2 includes the routing
information for the MN (N61) as shown in Fig. 5(a). Also, in terms
of packet delivery, MA5 directly sends the location query message
to MA8 by means of its enhanced finger table. In short, since each
MA maintains the extended finger table on all MAs, the location
update and location query messages can be sent to the serving MA
through only one-hop overlay link. Also in the tree topology, it is
possible to reduce the transmission cost by introducing the
extended finger table as shown in Fig. 5(b).
4. Performance analysis
In this section, we derive analytical expressions for the signal-
ing costs incurred in location update and location query proce-
dures. Also, we develop a two-dimensional continuous time
Markov chain (CTMC) in order to evaluate the processing latency
at the MA. It is assumed that the MA's database (DB) is maintained
by a binary tree structure; thus the search and update costs at the
MA are proportional to the logarithm of the amount of location
information. Transmission cost over the wireless link is neglected
since it is a common term in all four mapping systems. Important
notations for the analytical model are summarized in Table 1.
4.1. CMS
When an MN moves to an AR, it informs the central MA of its
location. After that, the MA updates its DB and responds to the AR.
If all ARs are inter-connected by the mesh topology, the distance
between two ARs is only one-hop link. Since the MA manages all
MNs'mobility in the domain, the location update cost LU
mesh
CMS
and
the location query cost LQ
mesh
CMS
in the mesh topology can be
expressed, respectively, as
LU
mesh
CMS
¼2T
RR
þαlog
2
ðN
AR
N
Host=AR
Þð1Þ
Fig. 4. Distributed mapping system with DHT (m¼6). (a) Mesh topology and (b) tree topology.
2
For the last entry, start of the first entry is used.
Y. Kim et al. / Journal of Network and Computer Applications 39 (2014) 223–232226
and
LQ
mesh
CMS
¼2T
RR
þβlog
2
ðN
AR
N
Host=AR
Þ;ð2Þ
where N
AR
N
Host=AR
represents the total number of MNs in the
domain.
On the other hand, a signaling message arrives at the MA
through d1 routers in the tree topology as shown in Fig. 2(b).
Hence, the total transmission cost of a packet becomes 2 dT
RR
,
and thus the location update cost LU
CMStree
and the location query
cost LQ
CMStree
in the tree topology are, respectively, given by
LU
tree
CMS
¼2dT
RR
þαlog
2
ðN
AR
N
Host=AR
Þð3Þ
and
LQ
tree
CMS
¼2dT
RR
þβlog
2
ðN
AR
N
Host=AR
Þ:ð4Þ
4.2. DMS with multicast
In DMS with multicast, the location information of an MN is
registered to the nearest AR from the MN. Since all MAs are
located only at the leaf levels in the tree topology and the number
of MNs managed by each MA is N
Host=AR
, the location update costs
of DMS with multicast in mesh and tree topologies are the same
and they can be expressed as
LU
mesh
multi
¼LU
tree
multi
¼αlog
2
N
Host=AR
:ð5Þ
On the other hand, the location information of MNs is dis-
tributed to multiple MAs in DMS with multicast. Specifically, the
MN registers its location information to the nearest MA. Let p
h
be
the probability that the CN and MN locate in the same subnet.
Then the MN's location can be found without further routing of
location query messages with the probability p
h
. Since we assume
that all MNs are uniformly distributed among ARs, p
h
is given by
p
h
¼1
N
AR
:ð6Þ
When an AR receives a packet destined to an MN, the AR first
checks whether the MN's location information exists in its DB. If
then, the AR transmits the packet without any query routing, and
thus only the DB search cost, βlog
2
N
Host=AR
, is involved. Other-
wise, the AR should ask for the location information from MAs by
multicasting location query messages. A location query message is
delivered to all MAs except the originating one, and those MAs
should check their DBs. Hence, the corresponding cost is given by
ðN
AR
1ÞðT
RR
þβlog
2
N
Host=AR
Þin the mesh topology. After that,
the serving MA with the requested location information replies to
the AR, and the cost is T
RR
. Consequently, the location query cost
of DMS with multicast in the mesh topology, LQ
mesh
multi
, can be
expressed as
LQ
mesh
multi
¼ð1p
h
ÞððN
AR
1ÞðT
RR
þβlog
2
N
Host=AR
Þ
þT
RR
Þþβlog
2
N
Host=AR
:ð7Þ
In case of the tree topology, a location query message should be
delivered to all leaf nodes except the originating one. The sum of
distances (numbers of hop links) to all leaf nodes except the
originating MA is ∑
d
k¼1
2
k
and thus the transmission cost is given
by ∑
d
k¼1
2
k
T
RR
. In addition, since the number of leaf nodes
except the originating MA is 2
d
1, the DB lookup cost is given by
ð2
d
1Þβlog
2
N
Host=AR
. After multicasting the location query mes-
sage, the location information can be obtained only from the
serving MA. In the tree topology, the average number of hops
between two arbitrary MAs, ξ, can be derived as (see Appendix A)
ξ¼ðd1Þ2
dþ1
þ2
2
d
1:ð8Þ
To sum up, the location query cost of DMS with multicast in the
tree topology, LQ
multitree
, is given by
LQ
tree
multi
¼ð1p
h
Þ∑
d
k¼1
2
k
T
RR
þξT
RR
þð2
d
1Þβlog
2
N
Host=AR
!
þβlog
2
N
Host=AR
:ð9Þ
4.3. DMS with DHT
In Chord, it has been proved that each MA maintains the
location information of Oðlog
2
N
AR
ÞARs, and a lookup message is
delivered to a serving MA through Oðlog
2
N
AR
ÞMAs (Stoica et al.,
2001). Hence, it is assumed that there are (in average) log
2
N
AR
intermediate MAs including the originating MA when it sends a
location update or a location query message to the serving MA.
Also, let p
′
h
be the probability that a CN resides in the serving MA
of the MN. Since MNs are uniformly served by MAs due to the
property of DHT, p
′
h
is equal to p
h
as defined in the previous
subsection.
The average lookup cost to determine the next hop is
βlog
2
ðlog
2
N
AR
Þsince the MA's DB is maintained by a binary tree
structure. Then, the total transmission and lookup costs for
Fig. 5. Distributed mapping system with enhanced DHT. (a) Mesh topology and (b) tree topology.
Table 1
Notations for performance analysis.
Parameter Description
T
RR
Transmission cost of a packet between two adjacent routers
N
AR
Number of ARs in the domain
N
Host=AR
Number of nodes in each AR
dDepth of tree topology
αCoefficient of DB update
βCoefficient of DB lookup
λ
u
Location update arrival rate
λ
q
Location query arrival rate
1=μ
u
Location update service time
1=μ
q
Location query service time
Y. Kim et al. / Journal of Network and Computer Applications 39 (2014) 223–232 227
message routing are, respectively, given by log
2
N
AR
T
RR
and
ðlog
2
N
AR
þ1Þβlog
2
ðlog
2
N
AR
Þwhen the originating MA is dif-
ferent from the serving MA (with the probability of 1p
′
h
). Finally,
the serving MA updates the location information of the MN with
the cost of αlog
2
N
Host=AR
, and sends an acknowledgement to the
AR with the cost of T
RR
. On the contrary, if the originating MA is
the same as the serving MA after checking the routing table (with
the probability of p
′
h
), the serving MA simply updates its location
information. Therefore, the location update cost LU
mesh
DHT
in the
mesh topology is given by
LU
mesh
DHT
¼ð1p
′
h
ÞðT
RR
ðlog
2
N
AR
þ1Þ
þð log
2
N
AR
þ1Þβlog
2
ðlog
2
N
AR
ÞÞ
þp
′
h
βlog
2
ðlog
2
N
AR
Þþαlog
2
N
Host=AR
:ð10Þ
The total transmission cost and lookup cost to determine the
next hop for the location query message are the same as ones for
location update. The only difference between location query and
location update procedures is that the DB update process should
be substituted with the DB search process. That is, αlog
2
N
Host=AR
should be changed into βlog
2
N
Host=AR
. Consequently, the location
query cost LQ
mesh
DHT
in the mesh topology is given by
LQ
mesh
DHT
¼ð1p
′
h
ÞðT
RR
ðlog
2
N
AR
þ1Þ
þð log
2
N
AR
þ1Þβlog
2
ðlog
2
N
AR
ÞÞ
þp
′
h
βlog
2
ðlog
2
N
AR
Þþβlog
2
N
Host=AR
:ð11Þ
Under the tree topology, since the average number of hops
between two arbitrary MAs is given by ξ,LU
DHTtree
and LQ
DHTtree
are, respectively, obtained from
LU
tree
DHT
¼ð1p
′
h
ÞðT
RR
ξðlog
2
N
AR
þ1Þ
þð log
2
N
AR
þ1Þβlog
2
ðlog
2
N
AR
ÞÞ
þp
′
h
βlog
2
ðlog
2
N
AR
Þþαlog
2
N
Host=AR
and
LQ
tree
DHT
¼ð1p
′
h
ÞðT
RR
ξðlog
2
N
AR
þ1Þ
þð log
2
N
AR
þ1Þβlog
2
ðlog
2
N
AR
ÞÞ
þp
′
h
βlog
2
ðlog
2
N
AR
Þþβlog
2
N
Host=AR
:ð12Þ
4.4. DMS with enhanced DHT
As mentioned before, by using the enhanced DHT, each MA has
a rich finger table on all MAs. Hence, the location update and
query messages can be transmitted through the optimal path (e.g.,
one-hop link in the mesh topology). If the finger table is main-
tained by a binary tree structure, the average lookup cost to
determine the serving MA is βlog
2
N
AR
. If the originating MA is
different from the serving MA (with the probability of 1p
′
h
), the
sum of the transmission and lookup costs for location update/
query message routing can be expressed by T
RR
þ2βlog
2
N
AR
since both the originating MA and the serving MA check their
finger tables. When the location update message arrives at the
serving MA, it updates the location information of the MN with
the cost of αlog
2
ðN
Host=AR
Þ, and sends an acknowledgement to the
originating MA with the cost of T
RR
. On the other hand, when the
originating MA is the same as the serving MA after checking the
finger table (with the probability of p
′
h
), the originating MA does not
need to send any location update message, and simply searches the
finger table and updates the location information of the MN with the
cost of βlog
2
N
AR
þαlog
2
ðN
Host=AR
Þ. Therefore, the location update
cost LU
mesh
ENDHT
in the mesh topology can be computed as
LU
mesh
ENDHT
¼ð1p
′
h
Þð2T
RR
þ2βlog
2
N
AR
þαlog
2
ðN
Host=AR
ÞÞ
þp
′
h
ðβlog
2
N
AR
þαlog
2
ðN
Host=AR
ÞÞ
¼ð1p
′
h
Þð2T
RR
þ2βlog
2
N
AR
Þþp
′
h
βlog
2
N
AR
þαlog
2
ðN
Host=AR
Þ:
ð13Þ
The location query cost of DMS with enhanced DHT, LQ
mesh
DHT
, can
be obtained by replacing αwith β, due to the same reason
described in the previous subsection. Hence, LQ
mesh
DHT
is given by
LQ
mesh
ENDHT
¼ð1p
′
h
Þð2T
RR
þ2βlog
2
N
AR
Þþp
′
h
βlog
2
N
AR
þβlog
2
ðN
Host=AR
Þ:ð14Þ
Under the tree topology, since the average number of hops
between two arbitrary MAs is given by ξ,LU
DHTtree
and LQ
DHTtree
can be, respectively, obtained from
LU
tree
ENDHT
¼ð1p
′
h
Þð2ξT
RR
þ2βlog
2
N
AR
Þþp
′
h
βlog
2
N
AR
þαlog
2
ðN
Host=AR
Þð15Þ
and
LQ
tree
ENDHT
¼ð1p
′
h
Þð2ξT
RR
þ2βlog
2
N
AR
Þþp
′
h
βlog
2
N
AR
þβlog
2
ðN
Host=AR
Þ:ð16Þ
4.5. Processing latency
In this subsection, we compare the scalability of CMS and DMS
in terms of the processing latency at the MA. Specifically, we
consider a queueing system where the process of the location
update message has higher priority than that of the location query
message to satisfy the consistency in the location information. In
other words, only when the location update message queue is
empty, the location query message can be served. The queueing
system can be analyzed by a two-dimensional CTMC in Fig. 6
where the arrival rates of location update and query messages are
denoted by λ
u
and λ
q
, respectively, and the service rates of location
update and query messages are represented by μ
u
and μ
q
, respec-
tively. In state (i,j) where 0≤i;j≤Kand iþj≤K,iand jrepresent the
numbers of messages in the location query and location update
queues, respectively. Note that since the location update message
has higher priority than the location query message, the transition
rate from state (i,j) to state ði1;jÞis 0 when 0 oi≤K,1≤j≤K, and
iþj≤K. Then, the steady state probability π
i;j
can be obtained by
the balance equations for the CTMC (see Appendix B) and an
iterative algorithm (Lin et al., 2004).
Table 2 shows the location update/query arrival rates into each
MA under different mapping systems. In CMS, the central MA
receives all location update/query messages and thus the location
update and query request arrival rates are simply given by λ
u
and
λ
q
, respectively. On the other hand, location update requests are
distributed to all MAs in DMS schemes, and therefore the location
Fig. 6. Two-dimensional continuous time Markov chain.
Y. Kim et al. / Journal of Network and Computer Applications 39 (2014) 223–232228
update arrival rate is λ
u
=N
AR
. In terms of location query message,
all MAs in DMS with multicast receive all generated query
messages and thus the corresponding rate is λ
q
. On the contrary,
the location query arrival rate is given by λ
q
=N
AR
in DMS with DHT/
enhanced DHT since only one MA processes the location query
message. Note that the routing process for delivering signaling
messages is neglected in DMS with DHT/enhanced DHT since it is
not directly related to the location update and location response
processes.
The location update/query requests are blocked when the
queue is fully occupied (i.e., iþj¼K). Thus the location update/
query request blocking probability P
B
can be obtained as
P
B
¼∑
iþj¼K
π
i;j
:ð17Þ
Let λ
e
be the effective location update and query arrival rate into
the MA. Then, since the location update and query requests are
blocked when the queue is fully occupied, λ
e
can be given by
λ
e
¼ðλ
u
þλ
q
Þð1P
B
Þ:ð18Þ
Also, the average number of requests in the queue N
Q
can be
obtained by
N
Q
¼∑
K
i¼0
∑
Ki
j¼0
ðiþjÞπ
i;j
:ð19Þ
Finally, by Eqs. (18) and (19), the average processing latency in the
system, L, is given by
L¼N
Q
λ
e
:ð20Þ
5. Numerical results
In this section, we evaluate CMS, DMS with multicast, DMS
with DHT, and DMS with enhanced DHT in terms of the location
update/query costs and the processing latency at the MA.
The location update/query costs quantify the traffic overhead
(i.e., traffic volume) for forwarding signaling packets and the
processing overhead (i.e., computing power) for updating/search-
ing the MA's DB. On the other hand, the processing latency
represents the elapsed latency until a location query or update
message is completely processed by the MA.
For numerical results, T
RR
,α, and βare set to 1, 3, and 2,
respectively (Gohar and Koh, 2012). In addition, the number of
hosts per AR and the number of ARs are set to 1000 and 8,
respectively. For the MA queuing model, the default location query
arrival rate λ
q
and the location update rate λ
u
are set to 32 and 12,
respectively (Munasinghe and Jamalipour, 2009). In addition, the
service rates for location query and location update are fixed at 30
and 20, respectively. Also, the maximum queue size is set to 50.
5.1. Effect of N
AR
Figure 7 shows the location update cost under different
numbers of ARs, N
AR
. From Fig. 7, it can be found that the location
update cost of DMS with multicast is constant and the lowest
among four mapping systems regardless of N
AR
, because the MN
registers its location to the nearest AR in DMS with multicast. On
the other hand, the location update costs of CMS, DMS with DHT,
and DMS with enhanced DHT increase logarithmically to N
AR
due
to the growth of the transmission and DB update costs. Specifi-
cally, in Fig. 7(a), the location update cost of DMS with DHT is the
highest since it needs more than one-hop link to deliver the
location update message to the serving MA whereas CMS and DMS
with enhanced DHT need only one-hop link in the mesh topology.
On the other hand, CMS maintains the location information for all
MNs and thus CMS has higher location update cost than DMS with
enhanced DHT due to the processing cost at the MA. As shown in
Fig. 7(b), the tree topology results in higher location update costs
than the mesh topology in all schemes except DMS with multicast.
This is because more hop links are needed to deliver signaling
messages in the tree topology. In particular, in the tree topology,
d-hop links are needed in CMS in order to transmit the location
update message to the serving MA whereas DMS with enhanced
DHT requires ξhop links where ξ≥d. On the contrary, the
processing cost of CMS is much higher than that of DMS with
enhanced DHT. Hence, from Fig. 7(b), it can be observed that CMS
and DMS with enhanced DHT have comparable location update
costs although more hop links to deliver location update messages
are needed in DMS with enhanced DHT.
Figure 8 shows the location query cost as a function of N
AR
. The
location query cost of DMS with multicast linearly increases both
Table 2
Location update/query arrival rates into each MA.
Scheme Location update arrival
rate
location query arrival
rate
CMS λ
u
λ
q
DMS with multicast λ
u
=N
AR
λ
q
DMS with DHT/enhanced
DHT
λ
u
=N
AR
λ
q
=N
AR
20
30
40
50
60
70
80
5 10 15 20 25 30
Location update cost
Number of ARs
CMS in MS
DMS with multicast in MS
DMS with DHT in MS
DMS with Enhanced DHT in MS
20
30
40
50
60
70
80
90
100
110
5 10 15 20 25 30
Location update cost
Number of ARs
CMS in TS
DMS with multicast in TS
DMS with DHT in TS
DMS with Enhanced DHT in TS
Fig. 7. Location update cost vs. number of ARs. MS: mesh topology (a) and TS: tree topology (b).
Y. Kim et al. / Journal of Network and Computer Applications 39 (2014) 223–232 229
in the mesh and tree topologies since its number of location query
messages is proportional to the number of ARs. On the other hand,
other schemes have relatively low location query costs regardless
of N
AR
. This is because that the location query costs of CMS, DMS
with DHT, and DMS with enhanced DHT logarithmically increase
with the increase of N
AR
.
From Figs. 7 and 8, it can be shown that the total cost, which is
defined as the sum of location update and query costs, of DMS
with multicast is proportional to N
AR
while the total costs of other
schemes increase logarithmically with the increase of N
AR
.In
terms of the total cost, CMS exhibits similar performance to DMS
with enhanced DHT. However, CMS leads to the increased proces-
sing latency at the MA, which is a single point of failure/bottleneck
(see Section 5.4). To sum up, DMS with enhanced DHT is prefer-
able for reducing the total cost as well as the processing latency.
5.2. Effect of N
Host=AR
Figures 9 and 10 show the effects of the number of hosts per
AR, N
Host=AR
. From Figs. 9 and 10, it can be found that the location
update cost and the location query cost slightly increase as the
number of hosts per AR increases. This is because N
Host=AR
only
affects on the DB update/query processes not the transmission
cost. Also, it can be observed that DMS with multicast has the
lowest location update cost whereas it exhibits the highest
location query cost due to the same reason mentioned in the
previous subsection. In terms of the total cost, DMS with multicast
has the highest total cost, and it is followed by DMS with DHT,
CMS, and DMS with enhanced DHT. To conclude, DMS with
enhanced DHT outperforms other schemes under different values
of N
Host=AR
.
5.3. Effect of p
h
Figure 11 shows the location query cost as a function of p
h
,
which is the probability that the CN and the MN co-locate in the
same subnet. In such a situation, the AR does not need to query
about the location information of the MN in DMS schemes. Hence,
as p
h
increases, the location query cost decreases except CMS. Note
that the location query messages in CMS should be always
delivered to the centralized MA even when the CN and the MN
reside in the same AR. On the other hand, the location query cost
of DMS with multicast decreases drastically with the increase of
p
h
, since the AR does not send any location query messages to all
MAs if the CN and the MN are in the same AR. As shown in Fig. 11,
the location query costs DMS with DHT and DMS with enhanced
DHT can be reduced when a higher value of p
h
is evaluated. To
have a higher value of p
h
, a caching scheme can be exploited in
DMS schemes. In other words, a cache deployed at the distributed
0
100
200
300
400
500
600
700
5 10 15 20 25 30
Location query cost
Number of ARs
CMS in MS
DMS with multicast in MS
DMS with DHT in MS
DMS with Enhanced DHT in MS
0
100
200
300
400
500
600
700
5 10 15 20 25 30
Location query cost
Number of ARs
CMS in TS
DMS with multicast in TS
DMS with DHT in TS
DMS with Enhanced DHT in TS
Fig. 8. Location query cost vs. number of ARs. (a) Mesh topology and (b) tree topology.
25
30
35
40
45
50
55
60
65
70
1 2 3 4 5 6 7 8 9 10
Location update cost
Number of host per AR(Unit:1000)
CMS in MS
DMS with multicast in MS
DMS with DHT in MS
DMS with Enhanced DHT in MS
30
40
50
60
70
80
1 2 3 4 5 6 7 8 9 10
Location update cost
Number of host per AR(Unit:1000)
CMS in TS
DMS with multicast in TS
DMS with DHT in TS
DMS with Enhanced DHT in TS
Fig. 9. Location update cost under different N
Host=AR
. (a) Mesh topology and (b) tree topology.
Y. Kim et al. / Journal of Network and Computer Applications 39 (2014) 223–232230
MA can increase the value of p
h
and thus reduce the location query
cost accordingly.
5.4. Effect of λ
q
Figure 12 shows the processing latency Las a function of the
location query arrival rate λ
q
. Since all location update and location
query messages are concentrated to the central MA, CMS shows
the highest processing latency. Although DMS with multicast
exhibits low processing latency due to its distributed nature, its
processing latency drastically increases when the location query
arrival rate exceeds a certain point (e.g., λ
q
of 11 in Fig. 12). On the
other hand, it can be seen that DMS with DHT/enhanced DHT
maintains low processing latency in spite of the increase in λ
q
because the processing of location update and location query
messages is distributed to all MAs. Hence, from Fig. 12, it can be
concluded that DMS with DHT/enhanced DHT is more scalable and
fault-tolerant than other schemes.
6. Conclusion
In this work, we have conducted a comparative study of
centralized mapping system (CMS) and distributed mapping
system (DMS) in ID/locator separation architecture. Specifically,
analytical models on location update cost, location query cost, and
processing latency are developed. Numerical results demonstrate
that CMS and DMS with enhanced DHT are tolerant to the scale of
networks in terms of signaling overhead compared with DMS with
multicast. On the other hand, CMS has several weak points such as
higher processing overhead. DMS with DHT can mitigate the
overhead incurred in CMS at the expense of the increased signal-
ing cost. In particular, DMS with enhanced DHT can reduce the
signaling cost by extending the finger table. Consequently, DMS
with enhanced DHT is a more attractive solution for scalable and
fault-tolerant mapping systems in ID/locator separation architecture.
20
40
60
80
100
120
140
160
180
1/256 1/128 1/64 1/32 1/16 1/8 1/4 1/2
Location query cost
Ph
CMS in MS
DMS with multicast in MS
DMS with DHT in MS
DMS with Enhanced-DHT in MS
20
40
60
80
100
120
140
160
180
1/256 1/128 1/64 1/32 1/16 1/8 1/4 1/2
Location query cost
Ph
CMS in TS
DMS with multicast in TS
DMS with DHT in TS
DMS with Enhanced-DHT in TS
Fig. 11. Location query cost under different P
h
. (a) Mesh topology and (b) tree topology.
Fig. 12. Processing latency as a function of λ
q
.
20
40
60
80
100
120
140
160
180
200
1 2 3 4 5 6 7 8 9 10
Location query cost
Number of host per AR(Unit:1000)
CMS in MS
DMS with multicast in MS
DMS with DHT in MS
DMS with Enhanced DHT in MS
20
40
60
80
100
120
140
160
180
200
1 2 3 4 5 6 7 8 9 10
Location query cost
Number of host per AR(Unit:1000)
CMS in TS
DMS with multicast in TS
DMS with DHT in TS
DMS with Enhanced DHT in TS
Fig. 10. Location query cost under different N
Host=AR
. (a) Mesh topology and (b) tree topology.
Y. Kim et al. / Journal of Network and Computer Applications 39 (2014) 223–232 231
Currently, we are building a testbed for DMS with (enhanced) DHT
under the MOFI project (http://www.mofi.re.kr/), and thus an
experimental study over the testbed will be conducted in the
future. We will also investigate how to use efficient caching
strategies in DMS schemes for better performance.
Appendix A. Derivation of (8)
In a balanced binary tree having ddepth, the total number of
hop links from a leaf node to the others can be obtained as
∑
d
k¼1
2k2
k1
¼∑
d
k¼1
k2
k
¼2∑
d
k¼1
k2
k
∑
d
k¼1
k2
k
¼d2
dþ1
∑
d
k¼1
2
k
¼ðd1Þ2
dþ1
þ2:ðA:1Þ
Then, since the number of leaf nodes is 2
d
, the average number
of hop links between two leaf nodes can be derived as
ξ¼ðd1Þ2
dþ1
þ2
2
d
1:ðA:2Þ
Appendix B. Balance equations for Fig. 6
1. i¼0 and j¼0,
π
i;j
ðλ
q
þλ
u
Þ¼π
iþ1;j
μ
q
þπ
i;jþ1
μ
u
2. 0oioKand j¼0,
π
i;j
ðλ
q
þλ
u
þμ
q
Þ¼π
iþ1;j
μ
q
þπ
i;jþ1
μ
u
þπ
i1;j
λ
q
3. i¼Kand j¼0,
π
i;j
μ
q
¼π
i1;j
λ
q
4. i¼0 and 0ojoK,
π
i;j
ðλ
q
þλ
u
þμ
u
Þ¼π
i;jþ1
μ
u
þπ
i;j1
λ
u
5. i¼0 and j¼K,
π
i;j
μ
u
¼π
i;j1
λ
u
6. 0oioK,0ojoKand iþjoK,
π
i;j
ðλ
q
þλ
u
þμ
u
Þ¼π
i;jþ1
μ
u
þπ
i1;j
λ
q
þπ
i;j1
λ
u
7. 0 oioK,0ojoKand iþj¼K,
π
i;j
μ
u
¼π
i1;j
λ
q
þπ
i;j1
λ
u
:ðB:1Þ
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