Intelligent Mobility Support for IPv6

Intelligent Mobility Support for IPv6

Shengling Wang, Yong Cui

Department of Computer Science and Technology Tsinghua University

Beijing, China

[email protected] [email protected]

Sajal K.Das

Department of Computer Science and Engineering University Texas at Arlington

Arlington, TX , USA [email protected]

Abstract—Hierarchical MIPv6 (HMIPv6) is proposed to improve the system performance of Mobile IPv6 (MIPv6). However, HMIPv6 cannot outperform MIPv6 in all scenarios because of its double-registration when a user roams across regions and the longer packet delivery latency. Therefore, to select a proper mobility management scheme between MIPv6 and HMIPv6 becomes an interesting issue, for its potentials in enhancing the capacity and scalability of the system. In this paper, we develop an analytical model to analyze the applicability of MIPv6 and HMIPv6. Based on this model, we design an Intelligent Mobility Support (IMS) scheme that selects the better alternative between MIPv6 and HMIPv6 for a user according to its changing mobility and service characteristics. When HMIPv6 is adopted, IMS chooses the best mobility anchor point and regional size to optimize the system performance. Numerical results illustrate the impact of some key parameters on the applicability of MIPv6 and HMIPv6. Finally, it is demonstrated that IMS outperforms MIPv6 and HMIPv6.

Keywords - Mobile IPv6; Hierarchical Mobile IPv6; regional size

I. INTRODUCTION

The widespread growth of mobile services motivates providers to support seamless connectivity to Mobile Nodes (MNs). To realize this aim, the Internet Engineering Task Force (IETF) proposed Mobile IP (MIP) protocol. Both MIPv4 and MIPv6 enable MNs to move from one subnet to another while maintaining reachability and all on-going communications. Compared with MIPv4, MIPv6 has many advantages, making MIPv6 become the next generation mobile Internet solution.

To support IP mobility, MIPv6 [1] assigns one MN with two IP addresses: home address and Care of Address (CoA). The former is permanent, representing the MN’s identifier, while the latter is temporary, representing its current location. Their binding information is stored in the Home Agent (HA), a mobility management entity in the MN’s home network. If an MN leaves its home network and the Corresponding Nodes (CNs) do not know the MN’s location, the HA will receive all packets on behalf of the MN and forward them to the CoA through looking up the binding cache. To update the binding cache, the MN must launch the “home registration” process once it changes the point of attachment in a visited network. This will lead to the longer signaling delay when the MN roams far away from the HA or when it performs frequent handovers in a local region.

To tackle the issue, the most well-known solution is Hierarchical MIPv6 (HMIPv6). As shown in Figure 1, HMIPv6 [2] introduces a new entity called Mobility Anchor Point (MAP) to act as a local HA within a region. Each MAP administers a set of Access Routers (ARs) which form a region. The number of ARs beneath a MAP is defined as the regional size. Within a region, an MN is associated with two addresses: the Regional Care of Address (RCoA), indicating the MN’s MAP, and the on-Link CoA (LCoA), indicating the AR that the MN attaches to. When an MN enters into a new region and receives the RCoA and the LCoA, it will initiate a “regional registration” process to the MAP to bind these two addresses. Following a successful regional registration, the MN is requested to offer the binding between its home address and RCoA to the HA by a home registration. Due to serving as a local HA, the MAP intercepts all packets addressed to the MN’s RCoA and tunnels them to the LCoA. When the MN moves within the region, it only needs regional registration, thus reducing its interactions with the external networks, obtaining the lower signaling latency. HA CN Internet AR1 AR2 AR3 AR4 MAP1 region 1 regional size = 4 AR5 AR6 AR7 MAP2 region 2 regional size = 3

Figure 1. Framework of HMIPv6

The aim of HMIPv6 is to enhance the system performance by shielding the MNs’ micro-mobility (handovers within a region) from the CNs and HAs. But can it realize the aim in all scenarios? When the MNs roam within the region, the handover latency of HMIPv6 is smaller than that of MIPv6. However, this profit is obtained by paying two costs. The first cost is double-registration, which means an MN needs to launch not only a regional registration but also a home registration when it roams across regions. Double-registration undoubtedly increases the handover latency. The second cost is the longer packet delivery time. Because all packets destined to the MNs will be tunneled by the MAP, the packet processing delay of MAP prolongs the packet delivery delay. In addition, if the MAP is not the gateway, the packet delivery path will be

not optimal, further lengthening the packet delivery latency. If the costs are greater than the profit, the HMIPv6 cannot outperform MIPv6.

On the other hand, HMIPv6’s MAP and regional size are critical for the system performance. The smaller regional size will lead to more frequent macro-mobility (handover across regions), triggering more frequent double-registration. While the larger regional size will generate a higher traffic load on the MAP, increasing the packet processing delay of MAP, and leading to the longer packet delivery latency.

In summary, although HMIPv6 is an extension of MIPv6, it does not always perform better than MIPv6. Since the network can make a selection between MIPv6 and HMIPv6 for an MN, the selection that minimizes the overall registration and packet delivery time is an interesting problem to study, for its potentials in enhancing the capacity and scalability of the system. In addition, the MAP and regional size should be well chosen for optimizing the performance of HMIPv6 when it is a better alternative.

Aiming at the above problems, we propose a scheme called Intelligent Mobility Support (IMS), which addresses two issues. Firstly, it selects the better alternative between MIPv6 and HMIPv6 for a user according to its changing mobility and service characteristics. Secondly, when HMIPv6 is adopted, IMS chooses the best mobility anchor point and regional size to optimize the system performance.

To analyze the applicability of MIPv6 and HMIPv6, through which IMS can select the better one, we propose an analytical model referring to [3], which has two features. Firstly, it uses the Internet architecture to model the MIP network. While many existing literatures (e.g., [4, 5]) model the MIP network based on a cellular architecture used in a Personal Communication System (PCS). A major difference between PCS and the Internet is that the former is geographic-oriented while the latter is spatial-geographic-oriented [3]. In the geographic-oriented networks, the distance between two endpoints is measured by their physical space; while in the spatial-oriented networks, the distance is measured by the number of hops that packets travel. Therefore, the Internet architecture is suitable to abstract the MIP network.

Secondly, the proposed analytical model takes both registration and packet delivery performance into consideration. On the other hand, several existing literatures (e.g., [4-6]) prefer handover latency as a performance metric, which greatly depends on the registration performance of the mobility management schemes. However, the packet delivery performance is also an important metric as more and more delay-sensitive services appear in the mobile networks. Therefore, it is important to consider both registration and packet delivery performance in the analysis.

This paper is organized as follows. The performance comparison of MIPv6 and HMIPv6 is given in Section II. Then in Section III, we propose the IMS scheme. The numerical and simulation results are presented in Section IV. Finally, we conclude the paper in Section V.

II. PERFORMANCE COMPARISON OF MIPV6 AND HMIPV6

A.Registration Performance

To compare the registration performance, we give the following definition.

Definition 1: Average registration revenue, denoted as DR,

is defined as the average registration time saved through using HMIPv6 instead of MIPv6.

DR may be positive or negative. When it is positive, it

means the average registration delay of MIPv6 is shorter than that of HMIPv6, and otherwise longer. We do not take into consideration the periodic binding updates that an MN sends to its HA or CNs or MAP to refresh their binding records in the analysis, because they do not affect the handover latency. The main symbols in this subsection are shown in Table I.

TABLE I. MAIN SYMBOLS IN REGISTRATION PERFORMANCE ANALYSES

Symbols Definitions RM

D Average registration delay of MIPv6

AM

D Average delay of delivering registration signaling over wireless link between AR and MN

HA

D Average delay of delivering registration signaling between HA and AR

H

D Average registration signal processing latency of HA

intra

D Average delay of a registration process in HMIPv6 during an intra-MAP handover

inter

D Average delay of a registration process in HMIPv6

during an inter-MAP handover

MA

D Average delay of delivering registration signaling between MAP and AR

MA

l Average distance between MAP and its reachable ARs

HA

l Average distance between HA and AR

T Average dwell time that an MN stays in an AR μ Unit distance signaling transmission cost of wired link

To calculate DR, we assume that the signaling delivery

delays of uplinks and downlinks are the same for simplicity. According to RFC3775 [1] and RFC4140 [2], in MIPv6, the registration only includes a home registration. However, in HMIPv6, it includes a regional registration when the MN roams within a region as well as a home registration when the MN roams across regions. HenceD_RM, D_intra and D_intercan be calculated as formulas (1)-(3). 2 2 RM AM HA H D = D + D +D (1) intra 2 AM 2 MA M D = D + D +D (2) inter 4 AM 2 MA 2 HA H M D = D + D + D +D +D (3)

Let the number of handovers needed by an MN to move out of a region be m (m ≥ 1). That is, an MN will enter a new region at its mth _{handover. So the total average delay that an}

MN spends for m handovers in HMIPv6 and MIPv6 is given by (4) and (5). int int ( 1) IT ra er D = m− D +D (4) AT RM D =mD (5)

By Definition 1, DR can be calculated as:

int int ( ) (( 1) ) IT AT R ra er RM D D D mT m D D mD mT − = − + − = (6)

Assume that the average signaling delivery delay of wired link is proportional to the distance measured with the number of hops that the signal travels. Let the unit distance signaling transmission cost of wired link be μ, which includes the unit distance propagation delay and the queuing delay of each hop. Because the wireless bandwidth is usually smaller, we also assume the average signaling delivery delay of wireless link be θ μ⋅ , where θ>1. It is worthy of noting that the average signaling delivery latency is different in the core network and the access network. To simplify the analyses, μ reflects an average level of signaling transmission cost in the core network and the access network of one hop. Thus, DR can be

transformed as Formula (7). (2 2 MA 2HA( 1) ( M H) H) R ml l m m D D D D mT μ θ+ − − + − + = (7)

In light of Formula (7), we arrive at the following conclusions: the farther distance between the HA and the MN and the nearer distance between the MAP and the MN, the higher average registration revenue gained by HMIPv6. Based on Definition (1), only whenD_R<0, can HMIPv6 obtain the average registration revenue. According to Formulas (6) and (7), to makeD_R<0, m is required to satisfy:

int int int 2 ( ) 2 ( ) er ra HA H RM ra HA MA H M D D l D m D D l l D D μ θ μ − + + > = − − + − (8)

In fact, m is closely related to the regional size. Suppose each MN moves randomly among N different ARs and the regional size is K in HMIPv6. We can deduce the following theorems.

Theorem 1: When an MN always roams within a region,

HMIPv6 outperforms MIPv6 in terms of registration. Moreover, the average registration revenue is about 2μ⋅(l_MA−l_HA)T .

Proof: When an MN roams only within a region, K≥N. In this scenario, if HMIPv6 is adopted, the number of intra-MAP and inter-intra-MAP handovers will be m−1 and 0 respectively. However, if MIPv6 is adopted, the number of handovers will also be m−1. Thus, D_R is calculated as:

int ( 1) ( 1) ( 1) 2 ( ) ra RM R MA HA M H m D m D D m T l l D D T μ − − − = − − + − = (9)

In the actual scenario, l_MA−l_HA<0 is usually met, and there is no significant difference between the average registration signaling processing latency of HA and MAP. In this case, DR can be simplified as 2μ⋅(lMA−lHA) T . Due

to 2μ⋅(l_MA−l_HA) T<0, HMIPv6 outperforms MIPv6 in terms of registration. Moreover, the average registration revenue is about 2μ⋅(lMA−lHA) T . □

Theorem 1 is based on the fact that an MN will not be requested to register its HA when it roams within a region in HMIPv6, hence speeding up the registration process.

Theorem 2: When an MN roams across different regions,

DR lies on the regional size, K, and their relationship is

quantified by Formula (10). Moreover, only when Inequality (11) is satisfied, can HMIPv6 gain the average registration revenue. (2 ) (2 2 1) 2 (1 2 ) (2 2) 4 ( 1) 2( 1)( ) (2 2) H HA R MA M H D N K l K D N T N l N D D N T μ θ μ μ ⋅ + ⋅ − − + ⋅ ⋅ − = − ⋅ ⋅ − ⋅ + − − + − ⋅ (10) 2 ( ) 2 2 2 2 1 2 ( ) HA H HA MA H M l D N N K l l D D μ θ μ + + − _> − − − + − (11)

Proof: When an MN roams across different regions, K < N. In this case, the movements of an MN roaming across different ARs can be modeled as a Markov chain as shown in Figure 2, where the state i represents the MN entering the ARi

(i=1, 2,..., )N . As shown in Figure 2, it is assumed that the MN can move in two directions (except the boundary ARs), with an equal probability of 1/2 in each direction.

1 2 3 N-1 N 1 1/2 1/2 1/2 1/2 1/2 …… 1/2 1/2 1 1/2 Figure 2. State transition diagram

Defineπ_i(i=1, 2,..., )N as the steady state probability of state i. According to Figure 2, the balance equations for the Markov chain are given as:

1 2 2 1 3 1 1 1 2 1 2 + 1 2 ( + ) 1 2 3, 4,..., 2 1 2 i i i N N N i N π π π π π π π π π ₋ π− ₋ + π = × ⎧ ⎪ _{= ×} ⎪ ⎨ = × = − ⎪ ⎪ _{= × +} ⎩ (12)

Formula (12) can be recursively rewritten as:

1 2 1 1 0.5 3, 4,..., 2 0.5 i i N N i N π π π π π π + − = × ⎧ ⎪ = = − ⎨ ⎪ _{= ×} ⎩ (13)

Due to the fact that

1 1 i i π ∞ = =

∑

1 1 (2 ( 1)) 1 ( 1) 2,3,..., 1 N i N N i N π π π = = × − ⎧ ⎨ = − = − ⎩ (14)

Thus, the probability that the MN roams within the region is given by: int 1 2 1 2 2 K ra i i K P K N N π = − = = < −

∑

So the probability of the MN roaming out of the region isPinter = −1 Pintra. As a result, the probability that the MN

moves out of the region after m handovers ( m out P ) is derived as: 1 1 int int 2 1 2 1 ( ) (1 ) 2 2 2 2 m m m out ra er K K P P P N N − − − − = × = × − − − (16) Therefore, the expected handover times required by the MN to move out of the region are:

1 2 2 ( ) 2 2 1 m out m N E m mP N K ∞ = − = = − −

∑

With the help of Equation (17), Formulas (7) and (8) can be transformed as (10) and (11) respectively. Apparently, DR lies

on the regional size according to Equation (10). The larger K is, the higher is the average registration revenue. Moreover, we can conclude that only when Formula (11) is satisfied, can HMIPv6 gain the average registration revenue. □

B.Packet Delivery Performance

To compare the packet delivery performance, we give the following definition.

Definition 2: Average packet delivery cost, denoted as TP,

is defined as the average wasted time by using HMIPv6 instead of MIPv6 to forward packets from a CN to an MN.

The main symbols to analyze TP are shown in Table II. In

MIPv6 [1] and HMIPv6 [2], packets can be delivered by two modes. One mode is to deliver packets through HA. In this mode, the HA will receive all packets on behalf of the MN and forward them to the MN. The other mode is to forward packets directly to the MN. In the following analyses, we model the average packet delivery cost using the first mode, but the method is also applicable to the second mode.

TABLE II. MAIN SYMBOLS IN PACKET DELIVERY PERFORMANCE

ANALYSES

symbols definitions

PM

T Average packet delivery delay of MIPv6

α Average packet arrival rate

H

T Average packet processing latency of HA

CH

T Average delay of forwarding packets from CN to HA

HA

T Average delay of forwarding packets from HA to AR

AM

T Average delay of forwarding packets from AR to MN

PH

T Average packet delivery delay of HMIPv6

M

T Average packet processing delay of MAP

HM

T Average delay of forwarding packets from HA to MAP

HM

l Average distance between HA and MAP

According to RFC3775 [1] and RFC4140 [2], the average latency of forwarding packets from a CN to the MN in MIPv6 and in HMIPv6 can respectively be formulated as:

( ) PM H CH HA AM T = ⋅α T +T +T +T (18) ( ) PH H M CH HM MA AM T = ⋅α T +T +T +T +T +T (19) Now, according to Definition 2, the average packet delivery cost is given by:

( )

P PH PM M HM MA HA

T =T −T = ⋅α T +T +T −T (20) We formulate the average packet processing latency of MAP (T_M) using the method similar to that proposed in [3]. Assuming that an AR can servewMNs on average, thus the average number of MNs in a region iswK. So the complexity of looking up the binding cache in MAP is proportional towK. Moreover, since the IP routing table lookup is commonly based on the longest prefix matching which is usually implemented using Patricia trie [3], the complexity of IP routing table lookup is proportional to the logarithm of the length of the routing table, i.e., the regional size, K [7]. In addition, we assume that

the average delay of encapsulating a packet in MAP isδ , soT_Mcan be calculated using Formula (21), where A and B are positive coefficients.

lg

M

T =AwK B K+ + δ (21)

Assume that the average packet delivery delay of wired link is proportional to the number of hops that the packets travel with the proportionality constant η. Then Equation (20) can be transformed into Equation (22).

( lg ( ))

P HM MA HA

T = ⋅α AwK B K+ + +δ η l +l −l (22)

Sincel_HM +l_MA≥l_HA, Equation (22) leads to the conclusion that the average packet delivery cost, TP, is positive. According

to Definition 2, TP > 0 means the average packet delivery delay

of HMIPv6 is longer than that of MIPv6. This is based on the fact that the deployment of a MAP in a region results in the triangular routing problem. The packet forwarding path changes from the external network Æ MN in MIPv6 to the external network Æ MAP Æ MN in HMIPv6.

C. Total Cost Function

To compare the overall performance of HMIPv6 against MIPv6, we present the following definition.

Definition 3: Total Cost function, denoted as C_T ,

formulates the overall performance of HMIPv6 against MIPv6 in terms of both registration and packet delivery. It is defined by Formula (23), where n₁andn₂are the coefficients.

1 2

T R P

C = ⋅n D + ⋅ n T (23) According to Definition 3, C_T can reflect the applicability of HMIPv6 and MIPv6. WhenC_T <0, HMIPv6 will be more applicable than MIPv6, and otherwise MIPv6 is more suitable to be adopted.

III. THE IMSSCHEME

As described above, when K increases, HMIPv6 may gain more average registration revenue while paying more average packet delivery cost. However, K cannotincrease indefinitely due to the processing bottleneck of the MAP. The total average packet processing latency of the MAP is given byα⋅(AwK B K+ lg +δ), which depends on its load. Thus, a proper K that minimizes CT will optimize the overall

performance of HMIPv6 against MIPv6. We denote such K as

Kopt, which can be solved as follows:

min ( ) . . ( lg ) T C K s t AwK B K K Z α δ ψ + ⋅ + + < ∈ (24)

where ψ is a constant restricting the total packet processing latency of the MAP.

Definition 4: Cost function of HMIPv6,

calledC_HMIPv6formulates the absolute performance of HMIPv6 in terms of the average registration and packet delivery delay. It is given by int int 6 1 2 ( 1) _{ra er} HMIPv PH m D D C n n T mT − + = ⋅ + ⋅ (25)

where n₁ and n₂ are the same as in Definition 3.

Theorem 3: Under the constraint

of α⋅(AwK B K+ lg +δ)<ψ , the value of Kopt that

minimizesC_Talso minimizesC_HMIPv6, making HMIPv6 achieve the optimal relative performance as well as the absolute performance.

Proof: According to Definitions 3 and 4, we

have C_HMIPv6=C_T+ ⋅n D_{1 RM} + ⋅n T_{2 PM} . Because

1 RM 2 PM

n D⋅ + ⋅n T is independent of K, C_HMIPv6can be viewed as C_T moving upwards the Y-axis with a spacing of n D1⋅ RM + ⋅n T2 PM . As a result, under the constraint

of α⋅(AwK B K+ lg +δ)<ψ , the value of Kopt that

minimizesC_T also minimizesC_HMIPv6, thus making HMIPv6 achieve the optimal relative performance as well as the absolute performance. □

Formula (24) is too complicated to be computationally practical, so it is necessary to simplify it. Since K can not be arbitrarily large in practice, we assume its maximum value is N, the same as the maximum numbers of ARs that the MN can visit. As K increases, the following three cases will occur: case 1: C K_T( ) monotonically increases ifC_T'( ) 0N > , where C_T'is the first derivative of C_T. In this case, C_T(1) is the minimum; case 2: C K_T( ) monotonically decreases ifC_T'( ) 0K < . In this

case, C K_T( _max) is the minimum

( K_{max =}max{K_∈Z+:α_⋅(AwK B K₊ lg ₊δ)_<ψ}_{); case 3:} ( )

T

C K first increases and then decreases ifC_T'( )K changes from above zero to below zero. In this case, _{( )}'

T C K is the minimum, where ' max { : min( T( 1), T( ))} K = K C K= C K =K .

The above analyses simplify the solution for Koptas follows: ' max 1 ( ) 0 { : min( ( 1), ( ))} T opt T T C N K K C K C K K otherwise ⎧ > ⎪ = ⎨ = = ⎪⎩ (26)

Clearly, Kopt can optimize the performance of HMIPv6.

However, C K_T( _opt) 0> implies that the optimized performance of HMIPv6 is still worse than that of MIPv6. Therefore, if C K_T( _opt) 0> , MIPv6 is an optimal alternative. Otherwise, HMIPv6 is better, and then the questions are which

MAP is the best and how many ARs beneath it are suitable. Because CHMIPv6 formulates the absolute performance of

HMIPv6 and the Kopt that minimizes CT also minimizes

CHMIPv6, the MAP with minimum C KT( opt) should be chosen

as the optimal regional mobility management entity and theK_optshould be its optimal regional size.

Based on the above analyses, we propose a scheme named Intelligent Mobility Support (IMS). IMS addresses two issues. Firstly, it selects the better alternative between MIPv6 and HMIPv6 for a user according to its changing mobility and service characteristics. Secondly, when HMIPv6 is adopted, IMS chooses the best MAP and regional size to optimize the system performance. The operations of an MN in IMS are shown in Figure 3, where K_opt[ ]i and C i_T[ ]=C K_T( _opt[ ]i)are respectively the optimal regional size and the total cost function value of the ith _{MAP when}

opt

K [ ]i (i=1, 2,...,M)is the input parameter, andM is the number of MAPs in the domain. In addition, in Figure 3, OC is the minimum of C iT[ ] (i=1, 2,...,M) ; OKopt and OM record the value

ofK_optand the marker related to OC respectively.

(the MN gets the information on handover){

(( or changes) (the MN will leave the current MAP region) ){

MN computes the ( 1, 2,..., );

initialize ; // is a big posit

opt T if if T K i C i i M OC OC α = & [ ] and [ ] ive constant ( 1; ; ){ ( [ ] ){ ; [ ]; O ; } }

( 0) adpot MIPv6 as the mobility management solution;

else{ // < 0 adopt HMIPv6 as t T T opt opt for i i M i if C i OC OM i OC C i K K i if OC OC = ≤ + + < = = = ≥ [ ]

he mobility management solution; choose the MAP whose sequence number is as the regional mobility management entity;

the chosen MAP's regional size is O ;

} } } opt OM K

Figure 3. Operations of an MN in IMS

Let us illustrate the function of IMS with an example. As shown in Figure 4, we assume that the MN currently accesses AR1 and there are four MAPs in a domain, i.e., MAP1 to MAP4.

M AP1 AR1 M AP2 M AP3 M AP4 AR3 AR4 AR5 AR7 AR2 AR8 AR6 HA M N

Figure 4. Example of IMS

When the triggering conditions are satisfied, the MN computes each MAP’s total cost function value and optimal regional size. We assume the results of computation are:C_T[1]= −0.015, K_opt[ ]=1 4; [2]C_T = −0.045, K_opt[ ]=2 5;

[3] 0.01

T

C = , K_opt[ ]=3 5 ; [4]C_T = −0.015 , K_opt[ ]=4 3 . BecauseCT[2] is the minimum and negative, the MN adopts HMIPv6 and chooses MAP2 as the regional mobility

management entity. SinceK_opt[ ]=2 5, the MN considers that the optimal regional size of MAP2 is 5. As a result, AR1 ~ AR5

form a region for the MN as shown in the dot block diagram of Figure 4.

IMStakes into consideration both the network and the MN related factors. As far as the network factors are concerned, an important one is the load on MAP, which affects the values ofA,B and δ in Formula (22). To realize dynamic MAP discovery, RFC4140 [2] requires a MAP option in Router Advertisements to be propagated from the MAP to the MNs through certain (configured) router interfaces. The MAP option includes a field named preference ranging from 0 to 15, which may be used to reflect the load on MAP. IMS may take advantage of this field, mapping different preferences to different loads of MAP. Another important network factor is the average distance (lMA) between MAP and its reachable ARs.

Note l_MA can be manually configured in a MAP and contained in an extended MAP option to offer to MNs. In addition, the average distance (l_HA) between HA and AR, and the average distance (l_HM) between HA and MAP are also needed in IMS. An MN or a MAP may use the Time-To-Live(TTL) field in the IP packet headers to obtain the number of hops that the packets or signals travel [3]. Then the average value may be used to calculate CT .

As far as the MN related factors are concerned, the most important ones are the average dwell time (T) that an MN stays in an AR, and the average packet arrival rate, α.Now T can be calculated by the method introduced in [8], while the algorithms for estimatingα can be found in [9, 10]. Such parameters can be periodically collected by each MN using statistical analysis. The period of collecting these parameters lies on the experiential data, and how to obtain it is beyond the scope of this paper.

IV. NUMERICAL RESULTS

In this section, we employ numerical analyses to show the impact of some key parameters on the selection between HMIPv6 and MIPv6. Then we compare IMS with pure MIPv6 and HMIPv6. The values of parameters used in this section are listed in Table III.

In MIPv6 or HMIPv6, the registration delay directly results in the handoff delay which is an important metric for evaluating the quality of service in the network. Due to the importance of the handoff delay, we set n₁>n₂

.

TABLE III. PARAMETERS USED IN NUMERICAL AND SIMULATION ANALYSES

μ η θ w N n1 n2 DH DM A B δ l_HM T_H ψ

0.008 0.008 2 15 30 10 1 0.008 0.008 0.00003 0.00007 0.00005 18 0.008 0.015

According to RFC 3344 [1], it is assumed that the MNs will generally not change their point of attachment to the Internet more frequently than once per second, so in this section, T≥1. Since the TTL field in IP header is usually initialized by the sender to 32 or 64 [11], i.e., the upper limit on the number of hops through which a packet can pass is 32 or 64, we let that

25

HM

l = andl_MA=10.

Figure 5 illustrates the impact of T on CT. In this

scenario,α=0.05

and

.

CT is greater than 0 and increases with the decreasing of T.

However, for K>9, CT is below 0 and decreases with the

decreasing of T. This is because T reflects an MN’s mobility rate. The larger T is, the more slowly the MN moves, and vice versa. When the regional size is smaller, say K≤9, the faster an MN moves, the higher is the rate with which the MN moves out of a region. This will lead to the longer registration delay owing to double-registration in HMIPv6. In this case, HMIPv6 cannot gain the average registration revenue; and the faster the MN moves, the worse is the registration performance of HMIPv6. On the other hand, when K is larger enough, sayK>9, the probability of an MN moving out of a region is lower even though the MN runs fast. In other words, most mobility belongs to micro-mobility. In this case, HMIPv6 gains the average registration revenue.

0 5 10 15 20 25 30 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 regional size CT T=100 T=500 T=1500 Figure 5. Impact of T on CT

Figure 6 illustrates the impact of α on CT. In this scenario, T

= 100 and l_MA=6

.

increases. This is due to the fact that the average packet delivery cost will increase as α increases, hence leading to the increase in CT.

Figure 7 illustrates the impact of the distance (l_MA) between MAP and AR on CT. In this scenario, α= 0.05 and T = 100.

From these two figures, we observe that CT increases with the

increase of l_MA. This is because whenl_MAincreases, both the

average registration delay and the average packet delivery delay in HMIPv6 increase, resulting in the increase in CT.

0 5 10 15 20 25 30 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 regional size CT α=0.05 α=0.8 α=1.5 Figure 6. Impact ofαon CT 0 5 10 15 20 25 30 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 regional size CT l_ma=6 l_ma=10 l_ma=14 Figure 7. Impact of lMA on CT

In the above figures, no matter how CT changes, when CT <

0, HMIPv6 is a better alternative. Otherwise, it is suitable for the MN to use MIPv6 as the solution.\

Figures 8 and 9 compare the performance of IMS, HMIPv6 (the regional size is 5 or 10) and MIPv6, using cost as the metric. The cost is the combination of the registration delay and the packet transmission delay. In detail, the cost of IMS is the cost value in Formula (25) when K=Kopt, while the cost of

HMIPv6 is the cost value in the Formula (25) when K= 5 and 10. At last, the cost of MIPv6 can be calculated as

1 RM 2 PM

n D⋅ + ⋅n T .

Figs. 8 and 9 respectively show how cost changes with T

and α. In both scenarios, l_CH =8 and the load of the MAP is light. Moreover, in Figure 8, α=0.05 while in Figure 9, T = 50. From these figures, we observe that the cost of IMS is

minimum, demonstrating that Kopt indeed enhances the performance of system. 0 20 40 60 80 100 120 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

the average dwell time

Co st IMS HMIPv6,K=10 HMIPv6,K=5 MIPv6 Figure 8. Cost vs.T 0 0.5 1 1.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

the average packet arrival rate

Co st IMS HMIPv6,K=10 HMIPv6,K=5 MIPv6 Figure 9. Cost vs. α V. CONCLUSION

MIPv6 and HMIPv6 are both mobility management solutions for IPv6 network. Although HMIPv6 is an extension of MIPv6, it does not outperform MIPv6 in all scenarios. In this paper, we propose an analytical model to formulate the performance of HMIPv6 against MIPv6. Based on the analytical model, a scheme called IMS is proposed for an MN to choose the better alternative between MIPv6 and HMIPv6. When HMIPv6 is adopted, IMS decides which MAP is the best and how many ARs under it are optimal. Numerical results illustrate the impact of some key parameters on the application scopes of MIPv6 and HMIPv6. Finally, it is shown that IMS outperforms MIPv6 and HMIPv6.

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