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Scalability Analysis of NEMO Prefix

Delegation-based 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 delegation-based 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 delegation-based 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 large-scale 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 PD-based 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 PD-based schemes

for evaluation: Simple Prefix Delegation (SPD) [8], Mobile

IPv6-based Route Optimization (MIRON) [9], Optimal Path

Registration (OPR) [10] and Ad hoc protocol-based route

optimization (Ad hoc-based) [11]. We have used analytical

cost models for NEMO PD-based schemes [12] to perform

scalability analysis of the four schemes.

Our contributions are : (i) developing analytical models for

scalability analysis of PD-based 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 PD-based schemes are summarized

in Secs. II and III. Scalability analysis of four PD-based

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

978-1-4244-6971-0/10/$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-

of-Address (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. PD-BASED ROUTE OPTIMIZATION SCHEMES

PD-based 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 IPv6-based 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 hoc-based 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 hoc-based. 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 PD-based

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 two-level

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 req-reply 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 two-level 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 two-level 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 two-level 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 two-level 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 hoc-based

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 two-level hierarchy, the expression for

total cost (Eqn. (62) in [12]) at TLMR of Ad hoc-based 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 hoc-based 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 hoc-based 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 hoc-based 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 hoc-based 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 hoc-based 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 PD-BASED 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 hoc-based

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 PD-based 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 PD-based route opti-

mization schemes (SPD, MIRON, OPR, and Ad hoc-based)

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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