Scalability analysis of NEMO prefix delegationbased schemes.
ABSTRACT A number of prefix delegationbased schemes have been proposed to solve the route optimization problem in NEMO, where a group of hosts move together as a mobile network. The schemes trade off between inefficiency of routes and various overheads. With the rapid growth of mobile computing, this
overhead will give rise to the scalability issue of these schemes. However, there has been no quantitative study on the asymptotic scalability analysis of these schemes. In this paper, we have developed analytical models for scalability analysis of these schemes in terms of network size, mobility rate, distance between
mobility agents, and traffic rate. Our analysis shows that the prefix delegationbased schemes exhibit asymptotically identical overhead on the network, and they show better asymptotical scalability in terms of number of mobile routers. The analytical framework for scalability analysis presented in this paper will help in visualizing the effects of future network expansion on the performance of these route optimization schemes of NEMO.

Chapter: Prefix Delegation Based Route Optimisation in Cooperative Ad Hoc Interconnected Mobile Networks
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ABSTRACT: We consider a scenario where a number of mobile networks, e.g. vehicles equipped with Mobile Routers, travel together interconnected in a dynamic mesh structure, here called Ad Hoc Interconnected Mobile Network or AIMNET. The mesh topology interconnecting the mobile networks not only facilitates intermobilenetwork communications, but more importantly allows sharing of Internet access available to individual Mobile Routers. We first discuss the route optimisation problem in AIMNET and the prefix delegation based solutions. We then propose a twolevel addressing scheme that minimises the overhead and improves route optimisation. Then, we discuss routing in the AIMNET and provide experimental results to verify our proposals.Ad Hoc Networks, 01/2013: pages 302315; Springer Berlin Heidelberg.
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Scalability Analysis of NEMO Prefix
Delegationbased Schemes
Md. Shohrab Hossain
Abu Zafar M. Shahriar
Mohammed Atiquzzaman
University of Oklahoma, Norman, OK 73019
Email: {shohrab, shahriar, atiq}@ou.edu
William Ivancic
NASA Glenn Research Center
Cleveland, OH 44135
Email: wivancic@grc.nasa.gov
Abstract—A number of prefix delegationbased schemes have
been proposed to solve the route optimization problem in NEMO,
where a group of hosts move together as a mobile network. The
schemes trade off between inefficiency of routes and various
overheads. With the rapid growth of mobile computing, this
overhead will give rise to the scalability issue of these schemes.
However, there has been no quantitative study on the asymptotic
scalability analysis of these schemes. In this paper, we have
developed analytical models for scalability analysis of these
schemes in terms of network size, mobility rate, distance between
mobility agents, and traffic rate. Our analysis shows that the
prefix delegationbased schemes exhibit asymptotically identical
overhead on the network, and they show better asymptotical
scalability in terms of number of mobile routers. The analytical
framework for scalability analysis presented in this paper will
help in visualizing the effects of future network expansion on the
performance of these route optimization schemes of NEMO.
I. INTRODUCTION
Network Mobility (NEMO) [1] was proposed to efficiently
manage the mobility of multiple hosts moving together, such
as hosts in a vehicle. NEMO Basic Support Protocol (BSP)
[1] suffers from the problem of inefficient route. Route op
timization schemes, proposed to solve the problem, trade off
between inefficiency of route and overheads, such as signaling,
processing, and memory consumption. The schemes have been
classified and compared [2] based on the approaches used for
route optimization, and Prefix Delegation (PD)based schemes
have been found to perform better than other schemes in terms
of route efficiency and overheads [2].
In NEMO, network parameters (such as, network size,
mobility rate, traffic rate, distances from mobility agents)
influence signaling and routing overheads incurred by PD
based schemes. These overheads are termed as network mo
bility cost that include tunneling packets through partially
optimized routes, updating Home Agents and hosts about lo
cation change, and processing and lookup by mobility agents.
Expansion of the network size will increase the network mo
bility cost incurred at the mobility management entities (e.g.,
home agents, mobile routers, etc) resulting in performance
degradation of the network. Hence, the scalability of the route
optimization schemes has to be analyzed quantitatively to
choose a suitable scheme for efficient management of NEMO.
The work has been supported by NASA Grant NNX06AE44G.
The scalability of a protocol is defined as its ability to
support continuous increase of network parameters without de
grading performance [3]. Santivanez et al. [3] present a frame
work to study the scalability of ad hoc routing algorithms.
Philip et al. [4] use the same framework [3] for the scalability
analysis of location management protocols of MANETs. Gwon
et al. [5] present scalability and robustness analysis of MIPv6,
FMIPv6, HMIPv6 using largescale simulations. Some NEMO
route optimization schemes [6], [7] are claimed to be scalable
with no supportive quantitative evaluation.
Our objective is to quantitatively evaluate the scalability
of PDbased schemes using mathematical models to find
out the impact of network parameters on the network and
mobility management entities. The authors are not aware of
any such evaluation of route optimization schemes. In this
paper, we have selected four representative PDbased schemes
for evaluation: Simple Prefix Delegation (SPD) [8], Mobile
IPv6based Route Optimization (MIRON) [9], Optimal Path
Registration (OPR) [10] and Ad hoc protocolbased route
optimization (Ad hocbased) [11]. We have used analytical
cost models for NEMO PDbased schemes [12] to perform
scalability analysis of the four schemes.
Our contributions are : (i) developing analytical models for
scalability analysis of PDbased schemes for various mobility
entities and the network, and (ii) comparative analysis of the
schemes based on scalability. Results show that all the schemes
(except OPR) scale when compared to NEMO BSP. and they
exhibit better asymptotical scalability in terms of number of
mobile routers and hosts. This will provide useful framework
to analyze other route optimization schemes, and to select
suitable schemes in future network.
The rest of the paper is organized as follows. NEMO archi
tecture, NEMO BSP, and PDbased schemes are summarized
in Secs. II and III. Scalability analysis of four PDbased
schemes are presented in Sec. IV. Sec. V presents comparative
analysis of the schemes. Finally, Sec. VI has the concluding
remarks.
II. NEMO ARCHITECTURE AND NEMO BSP
Fig. 1 shows the architecture of a Mobile Network (MN)
[1] where Mobile Routers (MRs) act as the gateways for each
Mobile Network Node (MNN). Different types of MNNs are:
2010 International Conference on High Performance Switching and Routing
9781424469710/10/$26.00 ©2010 IEEE107
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Fig. 1.
Architecture of a MN used for Scalability analysis.
Local Fixed Nodes (LFN) that do not move with respect to
MN, Local Mobile Nodes (LMN) that usually reside in MN
and can move to other networks, and Visiting Mobile Nodes
(VMN) that get attached to the MN from another network. The
MR, directly attached to the wired network through an Access
Router (AR), is called Top Level MR (TLMR) while other
MRs are nested under TLMR. An MN is usually connected to
a home network to which an MR is registered with a router
called the Home Agent (HA). Nodes that communicate with
MNNs is called Correspondent Nodes (CNs).
In NEMO BSP [1], an MR gets a prefix in its home network
to advertise to MNNs that obtain addresses, called Home
Addresses (HoA), from the prefix. When the MN moves to
a foreign network, the MR obtains a new address called Care
ofAddress (CoA) from foreign network, and sends a Binding
Update (BU) to HA informing the CoA. The HA intercepts
packets sent to MNNs, and tunnels them to MR. Since an
MN, nested under another MN, obtains CoA from the prefix
of MN above, packets first go to the HA of nested MN and
then to the HA of the MN above, resulting in suboptimal route
and header overhead. Therefore, route optimization schemes,
based on various approaches, have been proposed.
III. PDBASED ROUTE OPTIMIZATION SCHEMES
PDbased schemes obtain CoAs for MNNs from the prefix
of foreign network, and let CN know the CoA. CN creates
a Binding Entry (BE) that maps the HoA of MNN to the
CoA. Therefore, CN can send packets directly to foreign
network (without going through HAs). Yet, CoA obtaining
process and route optimization for LFNs varies across the
schemes, and depending on the variations, we have selected
four representative schemes.
A. Simple Prefix Delegation (SPD)
In SPD [8], MRs are delegated a prefix, aggregated at
foreign network’s prefix, to advertise to MNNs for obtaining of
CoAs to perform MIPv6 like route optimization. Being MIPv6
incapable, LFNs cannot perform route optimization resulting
in packets to be tunneled through their HAs.
B. Mobile IPv6based Route Optimization (MIRON)
In MIRON [9], an MR, after obtaining a CoA, notifies
attached MNNs (except LFNs) to obtain a CoA. An MNN
sends a request which is relayed to the foreign network. A
reply with a CoA configured from foreign network prefix is
sent to the MNN. For LFNs’ route optimization, MRs’ CoAs
are used to communicate with CNs.
C. Optimal Path Registration (OPR)
In OPR [10], CoA obtaining procedure is similar to SPD,
except that only MRs obtain CoAs from the delegated prefix.
To optimize route for MNNs, MRs translate addresses inside
packets into new addresses using the delegated prefix, put the
original address in OPR header, and set a bit in OPR header
to register the translated address at CN by creating a BE.
D. Ad hocbased Scheme
Su et al. [11] proposes a scheme where an Ad hoc protocol
(e.g. AODV) is used by the MRs to find the AR to use it as
the gateway to the wired network. In this scheme, in addition
to MR’s own router advertisement for its network, the router
advertisement of the AR is broadcasted by the MRs to the
attached MRs. After handoff, CoAs are obtained by the MRs
from the router advertisement, and the route to the AR is
discovered using AODV to send BUs.
IV. SCALABILITY ANALYSIS
In this section, we analyze the scalability of NEMO BSP,
SPD, MIRON, OPR and Ad hocbased. We focus on six
network parameters: number of mobile nodes (Nm), number
of mobile routers (Nr), number of LFNs (Nf), speed of the
MNs (V ), number of hops (h) and average number of CNs
(Nc) with which an MNN is communicating. These parameters
mainly influence network mobility costs. To consider the effect
of mobility rate on scalability, we use subnet residence time,
Tr. The reciprocal of subnet residence time gives the handoff
frequency which is typically proportional to the speed (V ) of
MN; thus Tr∝ (1/V ).
A. Definition of Scalability
According to Santivanez et al. [3], scalability is the ability
of a network to support the increase of its limiting parameters
without degrading performance. Scalability of NEMO schemes
is defined as the ability to support continuous increase of
network parameters without degrading performance of various
network entities that are responsible for mobility management.
Let ΓX(λ1, λ2, ...) be the total overhead induced by PD
based scheme X, dependent on parameters λ1, λ2, λ3, and so
on. Therefore, scheme X’s network mobility scalability factor
with respect to λiis defined as
ρX
λi= lim
λi→∞
logΓX(λ1,λ2,...)
logλi
(1)
NEMO BSP is the base protocol on which the PDbased
schemes have been built. Let ρN
NEMO BSP with respect to parameter λi. Then scheme X is
said to be scalable with respect to parameter λi, if ρX
λibe the scalability factor of
λi≤ ρN
λi.
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B. Topology of MN
Since no standard architecture for NEMO exists, we use a
generalized topology. We assume the MN having a twolevel
hierarchy of MRs (Fig. 1). TLMR is at level 0, hence N(0)
(N(i)
r
is number of MRs at level i, and similar meaning for
Nmand Nf). No LFN, LMN or VMN is connected directly
to TLMR. The TLMR is connected to N(1)
1 routers, so N(1)
r
= Nr− 1 as there is no MR at level 2.
Hence, N(2)
r
= 0. There is no host at levels 0 and 1. So
N(0)
f
f
i.e., N(2)
f
= Nf.
r
= 1
r
number of level
m = N(0)
m = Nm, and N(2)
= N(1)
m = N(1)
= 0. All nodes are at level 2,
C. Notations
Notations [12] used in this paper are listed here.
ΛX
ΨX
ΦX
Nr= Number of MRs in MN
Nm= Number of LMNs and VMNs in MN
Nf = Number of LFNs in MN
Nc= Number of CNs communicating with each node,
l =Nesting Level (hops to TLMR),
hah= Average number of hops from AR to HA
hac= Average number of hops from AR to CN,
hhc= Average number of hops from HA to CN,
hhh= Average number of hops from HA to HA,
τl=Per hop transmission cost for location update
τs=Per hop transmission cost for session continuity,
τdt= Per hop transmission cost for sending data,
τd=Transmission cost of DHCPv6 messages,
τp= Avg. transmission cost of PANA messages,
τa=Avg. transmission cost of route reqreply messages,
τr=Transmission cost for the router advertisement,
σ =Proportionality constant of transmission cost over
wired and wireless network,
ψ =Linear coefficient for lookup costs,
πt=Tunnel processing costs at HA and MR,
λs= Average session arrival rate for a node,
S =number of sessions,
F =File size,
P =Maximum transmission unit,
Tr= Subnet residence time,
Tlf = Lifetime of BE,
Tra= Interval of sending periodic router advertisement.
Y= Cost of type Y incurred at network for scheme X,
Y= Cost of type Y incurred at TLMR for scheme X,
Y= Cost of type Y incurred at HA for scheme X,
D. NEMO BSP
Here, we derive the asymptotic expressions of costs [12] for
NEMO BSP on the TLMR, HA, and the complete network.
1) TLMR: For the twolevel hierarchy, the expression for
total costs (Eqn. (10) in [12]) at TLMR can be simplified as
the following using the Θ notation1:
1Standard asymptotic notation has been used. A function f(n) = Θ(g(n))
if there exists some positive constants c1, c2, and n0such that c1g(n) ≤ f(n)
≤ c2g(n) for all n ≥ no.
ΨN
T = ΨN
LU+ ΨN
1 + ?Tr
Tr
SC+ ΨN
PD
= 2στl
τip(Nr+ 2Nm− 1) + 2NcNm[(στs+ πt) + 2στip]?
×
Tr
+ σNmNcλs
S(τip+ τdt) = Θ(V (Nr+ NmNc) + NcNf)
The values of σ, τl, τs, πt, τip, Tr/Tlf, λs, F, P, and ψ are
invariant as far as scalability analysis is concerned. Therefore,
NEMO BSP’s scalability factors for TLMR w.r.t. Nm, Nr,
Nf, V , h and Ncare
log(V (Nr+ NmNc) + NcNf)
Tlf?
+ 2σ?(τl+ πt)(Nr+ Nm− 1)+
?Tr
Tlf?
+ NcλsF
P(Nf+ Nm)(τdt+ στip+ πt)
(2)
ρN(R)
Nm
= lim
Nm→∞
logNm
= 1
ρN(R)
Nr
= lim
Nr→∞
log(V (Nr+ NmNc) + NcNf)
logNr
= 1
ρN(R)
Nf
= lim
Nf→∞
log(V (Nr+ NmNc) + NcNf)
logNf
= 1
ρN(R)
V
= lim
V →∞
log(V (Nr+ NmNc) + NcNf)
logV
= 1
ρN(R)
h
= lim
h→∞
log(V (Nr+ NmNc) + NcNf)
logh
= 0
ρN(R)
Nc
= lim
Nc→∞
log(V (Nr+ NmNc) + NcNf)
logNc
= 1
2) HA: The total costs (Eqn. (11) in [12]) at HA of NEMO
BSP can be simplified as:
ΦN
T = ΦN
LU+ ΦN
SC+ ΦN
1 + ?Tr
PD
= φNr(2τl+ πh)
Tlf?
Tr
+ 2
?
(Nr+ Nm− 1)(τl
+ πt+1
2πh+ ψ(Nr+ Nm) + τip) + τipNm+ 2NcNm
×?τs+ 2τip+ πt+ ψ(Nr+ Nm)?
× (Nf + Nm)
+ Ncλs
SNm
= Θ((Nr+ Nm)(V (Nr+ NcNm) + NfNc))
So NEMO BSP’s scalability factors for HA w.r.t. Nm, Nr,
Nf, V , h and Ncare 2, 2, 1, 1, 0, and 1.
3) Complete Network: The location update cost (Eqn. (3)
in [12]) of NEMO BSP for the complete network is,
??Tr
Tlf?
Tr
+ NcλsF
P
?
(τdt+ 2τip) + (ψ (Nr+ Nm) + πt)
(τdt+ 2τip) + (ψ(Nr+ Nm) + πt)
?
?
?
(3)
ΛN
LU= (2(h + σ)τl+ πh)
1 + ?Tr
Tr
Tlf?
+ 2((Nr− 1)((σ + h)
× (5τl+ 4τip) + 6πt+ 3ψ(Nr+ Nm) + πh) + Nm(4πt
+ 3(τl+ τip)(σ + h) + 2ψ(Nr+ Nm) + πh/2))
?Tr
Tr
Tlf?
= Θ(V (Nr+ Nm)(h + Nr+ Nm))
We assume h = hah= hhc= hac= hhh. Similarly, session
continuity cost (Eqn. (6) in [12]) can be written as,
(4)
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ΛN
SC= 2NcNm
?Tr
Tr
Tlf?
?
?
3στs+ 3στip+ 4πt+ 3hτs+ 3hτip
+ 2ψ(Nr+ Nm)= Θ(V NcNm(h + Nr+ Nm))
(5)
And packet delivery cost (Eqn. (9) in [12]) can be written as,
ΛN
PD= NcλsF
P(Nf + Nm)
?
2ψ(Nr+ Nm) + 4πt
?
+ 3hτdt+ 3hτip+ 3σ(τip+ τdt)
?
= Θ(Nc(Nf + Nm)(h + Nr+ Nm))
+ Ncλs
SNm
×
h(2τdt+ 4τip) + ψ(Nr+ Nm) + πt+ 2στip
?
(6)
Thus total cost of NEMO BSP on complete network is,
ΛN
T = ΛN
= Θ((V (Nr+ NcNm) + NcNf)(h + Nr+ Nm))
LU+ ΛN
SC+ ΛN
PD
(7)
Hence, NEMO BSP’s scalability factors for complete net
work w.r.t. Nm, Nr, Nf, V , h and Ncare 2, 2, 1, 1, 1 and 1,
respectively.
E. SPD
In this section, we derive the asymptotic expressions of
network mobility cost [12] for SPD scheme on the TLMR,
the HA, and the complete network.
1) TLMR: The total cost (Eqn. (23) in [12]) at TLMR in
SPD scheme can be simplified as:
ΨS
T= ΨS
?
×
+2στd(Nr− 1)
LU+ ΨS
SC+ ΨS
PD+ ΨS
CO
=2στl(Nr+ Nm) + 2στsNmNc
?1 + ?Tr
+ στipNcNmλs
Tlf?
Tr
+ NcλsF
P
?
στipNf + στdt(Nf + Nm)
?
S
Tr
= Θ
?
V (Nr+ NmNc) + NcNf
?
(8)
So SPD’s scalability factors for TLMR w.r.t. Nm, Nr, Nf, V ,
h and Ncare 1, 1, 1, 1, 0, and 1, respectively.
2) HA: The total cost (Eqn. (24) in [12]) at HA is:
ΦS
T= ΦS
LU+ ΦS
PD
= (Nr+ Nm)(2τl+ πh)
1 + ?Tr
Tr
Tlf?
+
?
NmNcλs
S+
?
+ NfNcλsF
?
Therefore, SPD’s scalability factors for HA w.r.t. Nm, Nr,
Nf, V , h and Ncare 2, 1, 1, 1, 0, and 1.
P
??
ψ (Nr+ Nm) + τdt+ τip+ πt
= Θ(Nr+ Nm)(V + NfNc+ NmNc)
?
(9)
3) Complete Network: Finally, the total cost (Eqn. (25) in
[12]) on complete network is:
ΛS
T= ΛS
?
LU+ ΛS
SC+ ΛS
PD+ ΛS
CO
=(Nr+ Nm)(2τlh + πh) + 2στl(2Nr+ 3Nm− 1)
?1 + ?Tr
Tr
?
+ 3στdt(Nf + Nm)
+ 2τsNcNm(h + 3σ)
Tlf?
+ NcλsF
P
?
hNmτdt
+ Nf
ψ (Nr+ Nm) + 2πt+ 2hτdt+ (h + 2σ)τip
?
+ Ncλs
SNm
= Θ((Nr+ NcNm)(hV + Nm+ Nf))
?
+2στd(Nr+ Nm)
Tr
?
ψ(Nr+ Nm) + πt+ h(τdt+ τip) + 3στip
?
(10)
Hence, SPD’s scalability factors for complete network w.r.t.
Nm, Nr, Nf, V , h and Ncare 2, 1, 1, 1, 1, and 1.
F. MIRON
In this section, we derive the asymptotic expressions of
network mobility cost [12] of MIRON for the TLMR, the HA,
and the complete network.
1) TLMR: For the twolevel hierarchy, the expression for
total network mobility cost (Eqn. (36) in [12]) at TLMR in
MIRON can be simplified as follows:
ΨM
T = ΨM
?
+ στipNcλs
LU+ ΨM
SC+ ΨM
PD+ ΨM
CO
=2στl(Nr+ Nmh) + 2Nc(Nf + Nmh)στs
?1 + ?Tr
Tlf?
Tr
S(Nf+ Nm) + σNcλsF
+ 2σ(Nr− 1)τp+ (Nr+ Nm)τd
Pτdt(Nf+ Nm)
?
Tr
= Θ
V (Nr+ Nc(Nm+ Nf))
?
(11)
Hence, MIRON’s scalability factors for TLMR w.r.t. Nm,
Nr, Nf, V , h and Ncare 1, 1, 1, 1, 0, and 1.
2) HA: For the twolevel hierarchy, the expression for total
network mobility costs (Eqn. (37) in [12]) at HA in MIRON
can be simplified as follows:
ΦM
T = ΦM
LU+ ΦM
PD
= (Nr+ Nm)(2τl+ πh)
1 + ?Tr
Tr
Tlf?
+ (Nf + Nm)Ncλs
?
MIRON’s scalability factors for HA w.r.t. Nmh, Nr, Nf,
V , h and Ncare thus 2, 1, 1, 1, 0, and 1, respectively.
3) Complete Network: Finally, the expression for total
network mobility cost (Eqn. (38) in [12]) on the complete
network can be obtained as:
S
?
ψ(Nr+ Nm) + τdt+ τip+ πt
?
= ΘV (Nr+ Nm) + NC(Nf + Nm)(Nr+ Nm)
?
(12)
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ΛM
T = ΛM
?
LU+ ΛM
SC+ ΛM
PD+ ΛM
CO
=(Nr+ Nm)(2τlh + πh) + 2στl(2Nr+ 3Nm− 1)
+ 2τsNc(Nf + Nm)(h + 3σ)
?1 + ?Tr
Tlf?
Tr
+ Ncλs
S
×
+ πtNf+ στip(2Nf+ 3Nm)
?
(Nf + Nm)(ψ(Nr+ Nm) + πt+ 2hτdt+ hτip)
?
+ NcλsF
?
= Θ(Nc(Nf+ Nm+ hV )(Nr+ Nm))
Hence, MIRON’s scalability factors for the complete network
w.r.t. Nm, Nr, Nf, V , h and Nc are 2, 1, 1, 1, 1, and 1,
respectively.
G. OPR
In this section, we derive the cost [12] of OPR scheme at
TLMR, HA, and complete network.
1) TLMR: For the twolevel hierarchy, the total cost (Eqn.
(49) in [12]) at TLMR can be simplified as:
ΨO
1 + ?Tr
Tr
× (Nf + Nm)(τip
S
= Θ(V (Nr+ Nm) + Nc(Nf+ Nm))
OPR’s scalability factors for TLMR w.r.t. Nm, Nr, Nf, V , h
and Ncare, therefore, 1, 1, 1, 1, 0, and 1, respectively.
2) HA: The total cost (Eqn. (50) in [12]) at HA is:
ΦO
PD
?
(Nf + Nm)Ncλs
S(ψ (Nr+ Nm) + τdt+ τip+ πt)
= Θ(Nr+ Nm)(V + NC(Nf+ Nm))
P(τdth + 3στdt)(Nf + Nm)
8(Nr− 1 + Nm)τp+ 2τd(2Nr+ 3Nm− 1)+
?σ
Tr
(13)
T= ΨO
LU+ ΨO
SC+ ΨO
PD+ ΨO
CO
?Tr
= 2στlNr
Tlf?
+ 2στlNm
Tlf?
Tr
+ 0 + σNcλs
+F
Pτdt) +2στd(Nr− 1)
Tr
(14)
T= ΦO
LU+ ΦO
= (2τl+ πh)Nr
1 + ?Tr
Tr
Tlf?
+ Nm
?Tr
Tr
Tlf?
?
+
??
(15)
Now, OPR’s scalability factors for HA w.r.t. Nm, Nr, Nf,
V , h and Ncare 2, 1, 1, 1, 0, and 1, respectively.
3) Complete Network: Finally, the total cost (Eqn. (51) in
[12]) of OPR on complete network is:
ΛO
COT= ΛO
LU+ ΛO
SC+ ΛO
PD+ ΛO
= (2τl(Nrh + σ(2Nr− 1)) + Nrπh)
?
+ Ncλs
S
+ πtNf + στip(2Nf + 3Nm)
1 + ?Tr
Tr
Pψ(Nf+ Nm)2
Nr− 1
Tlf?
+
Nm
2τl(h + 3σ) + πh
?
??Tr
Tlf?
Tr
+ NcλsF
(Nf + Nm)(ψ(Nr+ Nm) + πt+ 2hτdt+ hτip)
?
P(τdth + 3στdt)(Nf + Nm) +2στdNr
= Θ((Nr+ Nm)(hV + NcNf(Nf+ Nm)))
+ NcλsF
Tr
(16)
Hence, OPR’s scalability factors for complete network w.r.t.
Nm, Nr, Nf, V , h and Ncare 2, 1, 2, 1, 1, and 1, respectively.
H. Ad hocbased
In this section, we derive the total costs [12] of Ad hoc
based scheme for the TLMR, HA, and complete network.
1) TLMR: For the twolevel hierarchy, the expression for
total cost (Eqn. (62) in [12]) at TLMR of Ad hocbased scheme
can be simplified as:
ΨA
T= ΨA
LU+ ΨA
1 + ?Tr
SC+ ΨA
PD
= 2Nrστl
Tlf?
Tr
+ 2σNm((τl+ τip) + Nc(τs+ τip))
?Tr
Tr
Tlf?
+ NcλsF
P(στip+ στdt)(Nf + Nm) + σNmNcλs
= Θ(V (Nr+ NmNc) + NcNf)
Sτip
(17)
So Ad hocbased scheme’s scalability factors for TLMR w.r.t.
Nm, Nr, Nf, V , h and Ncare 1, 1, 1, 1 , 0, and 1, respectively.
2) HA: The total cost (Eqn. (63) in [12]) at HA can be
simplified as:
ΦA
T= ΦA
LU+ ΦA
SC+ ΦA
1 + ?Tr
PD
= Nr(2τl+ πh)
Tlf?
Tr
+ Nm
?
2τl+ πh+ 2πt+
τip+ ψ(Nr+ Nm) + 2Nc(τs+ τip+ πt)
??Tr
Tlf?
Tr
+
(Nf+ Nm)NcλsF
P(ψ (Nr+ Nm) + πt+ τdt+ τip)
+ NmNcλs
S(ψ(Nr+ Nm) + τdt+ 2τip)
= Θ(Nc(Nr+ Nm)(V Nm+ Nf))
(18)
Therefore, Ad hocbased scheme’s scalability factors for HA
w.r.t. Nm, Nr, Nf, V , h and Nc are 2, 1, 1, 1, 0, and 1,
respectively.
3) Complete Network: Finally, the total cost (Eqn. (64) in
[12]) for Ad hocbased scheme on complete network is:
ΛA
T= ΛA
?
×
LU+ ΛA
SC+ ΛA
PD+ ΛA
CO
= 2(Nrh + σ(2Nr− 1))τl+ Nrπh
?1 + ?Tr
Tlf?
Tr
+ 2Nm
?
(2h + 3σ)τl+ πh+ (h + 2σ)τip+ ψ(Nr+ Nm) + 2πt
+ Nc
?
2hτs+ hτip+ 2πt+ σ(3τs+ 2τip)
???Tr
Tlf?
Tr
+ NcλsF
P(Nf + Nm)
?
ψ (Nr+ Nm) + 2πt+ 2hτdt
?
+ 3σNrτa1
Tr
+ hτip+ 2στip+ +3στdt
+ Ncλs
SNm
?
ψ (Nr+ Nmh) + πt
+ hτdt+ (2h + 3σ)τip
?
+ 2στrNr
1 + ?Tr
Tr
Tra?
= Θ((Nr+ NmNc)(hV + Nf + Nm))
(19)
Hence, Ad hocbased schemes’s scalability factors for the
complete network w.r.t. Nm, Nr, Nf, V , h and Ncare 2, 1,
1, 1, 1, and 1, respectively.
111
Page 6
V. COMPARATIVE ANALYSIS
Table I summarizes the asymptotic cost expressions of
NEMO BSP, SPD, MIRON, OPR and Ad hocbased schemes
for the TLMR, the HA, and the complete network. In Table
II, all the scalability factors are listed with respect to Nm,
Nr, Nf, V , h and Nc. Although the asymptotical scalability
factors of the four schemes are almost identical, there exist
some differences that are discussed below.
TABLE I
ASYMPTOTIC COST EXPRESSIONS
Scheme
NEMO
BSP
Network Mobility Cost
Θ(V (Nr+ NmNc) + NcNf)
Θ((Nr+ Nm)(V (Nr+ NcNm) + NfNc))
Θ((V (Nr+NcNm)+NcNf)(h+Nr+Nm))
ΘV (Nr+ NmNc) + NcNf
?
Θ((Nr+ NcNm)(hV + Nm+ Nf))
ΘV (Nr+ Nc(Nm+ Nf))
?
Θ(Nc(Nf+ Nm+ hV )(Nr+ Nm))
Θ(V (Nr+ Nm) + Nc(Nf+ Nm))
Θ(Nr+ Nm)(V + NC(Nf+ Nm))
Θ((Nr+ Nm)(hV + NcNf(Nf+ Nm)))
Θ(V (Nr+ NmNc) + NcNf)
Θ(Nc(Nr+ Nm)(V Nm+ Nf))
Θ((Nr+ NmNc)(hV + Nf+ Nm))
Entity
TLMR
HA
Com. Net.
TLMR
SPD
?
?
Θ(Nr+ Nm)(V + NfNc+ NmNc)
?
HA
Com. Net.
TLMR
MIRON
??
ΘV (Nr+Nm)+NC(Nf+Nm)(Nr+Nm)
?
HA
Com. Net.
TLMR
HA
Com. Net.
TLMR
HA
Com. Net.
OPR
??
Ad hoc
Based
TABLE II
SCALABILITY FACTORS OF NEMO AND FOUR PDBASED SCHEMES
Schemes
ρX
NmρX
Nr
ρX
Nf
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
ρX
V
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
ρX
h
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
ρX
Nc
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Entity
NEMO BSP
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
TLMR
HA
Com. Network
TLMR
HA
Com. Network
TLMR
HA
Com. Network
TLMR
HA
Com. Network
TLMR
HA
Com. Network
SPD
MIRON
OPR
Ad hocbased
It is found that all the schemes scale when compared to
NEMO BSP, except OPR in case of Nf. In OPR, MRs have to
lookup a database of size proportional to Nf. But for NEMO
BSP, lookup has to be performed for each LFN in a table
whose size is independent of Nf. OPR’s scalability could be
improved using techniques used in MIRON.
All the PDbased schemes scale better than NEMO BSP
with respect to Nr for HA and complete network since the
location update in NEMO BSP is tunneled through HAs,
resulting in lookup cost for each MR in a database (binding
cache) of size proportional to Nr. Therefore, lookup cost
becomes a quadratic function of Nrat HA of NEMO BSP.
VI. CONCLUSION
In this paper, we have developed mathematical models to
compute scalability factors for various mobility entities of
NEMO BSP and four representative PDbased route opti
mization schemes (SPD, MIRON, OPR, and Ad hocbased)
of NEMO in terms of network size, mobility rate, distance
between mobility agents, and traffic rate. Our results show that
all the schemes (except OPR) scale when compared to NEMO
BSP, and they exhibit better asymptotical scalability feature in
terms of Nr than NEMO BSP. Analytical models developed
in this paper will provide useful framework to analyze other
route optimization schemes, and to choose suitable scheme as
network expands.
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