Mobility Management Approaches

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					1312                                                                    IEEE TRANSACTIONS ON MOBILE COMPUTING,                    VOL. 8,   NO. 10,   OCTOBER 2009




        Mobility Management Approaches for Mobile
          IP Networks: Performance Comparison
                 and Use Recommendations
                                                          Nadjia Kara, Member, IEEE

         Abstract—In wireless networks, efficient management of mobility is a crucial issue to support mobile users. The Mobile Internet
         Protocol (MIP) has been proposed to support global mobility in IP networks. Several mobility management strategies have been
         proposed which aim reducing the signaling traffic related to the Mobile Terminals (MTs) registration with the Home Agents (HAs)
         whenever their Care-of-Addresses (CoAs) change. They use different Foreign Agents (FAs) and Gateway FAs (GFAs) hierarchies to
         concentrate the registration processes. For high-mobility MTs, the Hierarchical MIP (HMIP) and Dynamic HMIP (DHMIP) strategies
         localize the registration in FAs and GFAs, yielding to high-mobility signaling. The Multicast HMIP strategy limits the registration
         processes in the GFAs. For high-mobility MTs, it provides lowest mobility signaling delay compared to the HMIP and DHMIP
         approaches. However, it is resource consuming strategy unless for frequent MT mobility. Hence, we propose an analytic model to
         evaluate the mean signaling delay and the mean bandwidth per call according to the type of MT mobility. In our analysis, the MHMIP
         outperforms the DHMIP and MIP strategies in almost all the studied cases. The main contribution of this paper is the analytic model
         that allows the mobility management approaches performance evaluation.

         Index Terms—Mobile IP, mobility approach, performance evaluation.

                                                                                  Ç

1       INTRODUCTION

I   Pmultimedia applications are becoming popular in the
   packet-based wireless networks. The integration of these
applications in wireless networks requires the support of
                                                                                      micromobility is the MT movements through different
                                                                                      subnets belonging to a single network domain. For
                                                                                      micromobility where the MT movement is frequent, the
seamless terminal mobility. Mobile IP (MIP) has been                                  MIP concept is not suitable and needs to be improved [3].
proposed by the Internet Engineering Task Force (IETF) to                             Indeed, the processing overhead related to location update
provide global mobility in IP networks [1]. It allows                                 could be high specifically under high number of MTs and
maintaining mobile terminals ongoing communications                                   when MTs are distant from the HAs yielding to high-
while moving through IP network [1], [2].                                             mobility signaling delay [4].
    In the MIP protocol, Mobile Terminal (MT) registers with                             Hierarchical Mobile IP (HMIP) has been proposed to
its home network from which it gets a permanent address                               reduce the number of location updates to HA and the
(home address). This address is stored in the Home Agent                              signaling latency when an MT moves from one subnet to
(HA). It is used for identification and routing purpose. If                           another [5], [6]. In this mobility scheme, FAs and Gateway
MT moves outside the home network visiting a foreign                                  FAs (GFAs) are organized into a hierarchy. When an MT
network, it maintains its home address and obtains a new                              changes FA within the same regional network, it updates its
one from the Foreign Agent (FA). This Foreign address is                              CoA by performing a regional registration to the GFA.
called Care-of-Address (CoA). To allow continuity of                                  When an MT moves to another regional network, it
ongoing communications between the MT and a remote                                    performs a home registration with its HA using a publicly
end point, the MT shall inform the HA of its current                                  routable address of GFA. The packets intercepted by the
location when it moves outside the home network. The HA                               HA are tunneled to a new GFA to which the MT is
delivers to MT the intercepted packets by tunneling them to                           belonging (e.g., GF A2 following MT handoff from F A3 to
the MT’s current point of attachment.                                                 F A5 in Fig. 1). The GFA checks its visitor list and forwards
    IP mobility in wireless networks can be classified into                           the packets to the FA of the MT (F A5 in Fig. 1). This
macro- and micromobility. The macromobility is the MT                                 regional registration is sensitive to the GFAs failure because
mobility through different administration domains. The                                of the centralized system architecture [7], [8]. Moreover, a
                                                                                      high traffic load on GFAs and frequent mobility between
                                                                                      regional networks degrade the mobility scheme perfor-
. The author is with INRS Energy, Materials et Telecommunications (INRS-
                                                `re
  EMT), Place Bonaventure, 800, de La Gauchetie West, Gate North-West,                mance [4]. In order to reduce the signaling load for
  Suite 6900, Montreal, Quebec, Canada, H5A 1K6.                                      interregional networks, mobility dynamic location manage-
  E-mail: kara@emt.inrs.ca.                                                           ment approaches for MIP have been proposed: A Hier-
Manuscript received 21 Sept. 2007; revised 4 Jan. 2009; accepted 21 Jan. 2009;        archical Distributed Dynamic Mobile IP (HDDMIP) and
published online 6 Feb. 2009.                                                         Dynamic Hierarchical Mobile IP (DHMIP).
For information on obtaining reprints of this article, please send e-mail to:
tmc@computer.org, and reference IEEECS Log Number TMC-2007-09-0290.                      In the HDDMIP approach, each FA can act either as an
Digital Object Identifier no. 10.1109/TMC.2009.36.                                    FA or GFA according to the user mobility. The traffic load
                                                1536-1233/09/$25.00 ß 2009 IEEE       Published by the IEEE CS, CASS, ComSoc, IES, & SPS
KARA: MOBILITY MANAGEMENT APPROACHES FOR MOBILE IP NETWORKS: PERFORMANCE COMPARISON AND USE...                             1313




                                                                  Fig. 2. DHMIP mobility approaches.
Fig. 1. MIP and DHMIP mobility approaches.

in a regional network is distributed among the FAs. The           location update and packet route processing in FAs
number of FAs attached to a GFA is adjusted for each MT.          belonging to the hierarchy increasing the mobility signaling
Thus, the regional network boundary varies for each MT.           and packet delivery delay. Moreover, the path extension
                                                                  through the FAs hierarchy increases the network resources
This number is computed according to the MT mobility
                                                                  used for packet delivery and location update signaling for
characteristics and the incoming packet arrival rate. This
                                                                  an ongoing communication.
number is adjustable from time to time according to the
                                                                     In [12], another inter-FAs tunneling approach has been
variation of the mobility and the packet arrival rate for each
                                                                  proposed to optimize the route between the remote end
MT. In [9] and [10], analytic models are proposed to
                                                                  point and the MT. This approach enables remote end point
compute this number such as the total signaling traffic for
                                                                  to get the CoA associated to the MT and to use it to reach
location update and packet delivery is transferred with
                                                                  the MT through the foreigner network without passing
minimal network resource and low delay, respectively.
                                                                  through the home network. When the MT moves from one
Nevertheless, this approach requires that each FA is able to
                                                                  foreigner network to another, it communicates its new CoA
act as an FA and a GFA. Moreover, it adds processing load
                                                                  to its previous FA through its new FA. The previous FA
on the MT to estimate the average packet arrival rate and
                                                                  tunnels the received traffic from the remote end point to the
the subnet residence time. Hence, the main advantage of           MT’s new location. At the same time, it sends a message to
this approach is the system robustness enhancement since          the HA requesting that the remote end point be notified of
the GFA failure affects only the packets routing to MTs           the MT’s new CoA. Upon receiving this new CoA, the
belonging to this GFA. The disadvantages are the system           remote end point uses it to reach the MT through the new
infrastructure and MTs costs which could be high.                 foreigner network without passing through its previous
   The DHMIP approach has been proposed to reduce the             foreigner network. This approach requires to restore an
location update messages to the HA by registering the new         optimized route after each CoA change. It aims to transfer
CoA to the previous FA and building a hierarchy of FAs .          packets through the resulting route with smaller delay than
Hence, the user’s packets are intercepted and tunneled            that experienced when these packets transit through the
along the FAs hierarchy to the MT. The hierarchy level            home network. However, this may not be always the case,
numbers are dynamically adjusted based on mobile user’s           and such performance will depend on the route optimiza-
mobility and traffic load information. Fig. 2 illustrates an      tion mechanism used and a set of influencing factors such
example of DHMIP approach with a maximum of hierarchy             as remote end point to FAs distance, the loads of the
level number equal to 3. When MT is attached to F A2 , F A3 ,     networks the optimized route should pass through, and the
F A5 , or F A6 , the CoA update is sent to the previous FAs. If   MT inter-FAs mobility frequency. Such analysis is needed
the MT becomes attached to F A4 the level number reach the        to compare this approach with the existing ones, but it is out
threshold and the MT will set up a new hierarchy. The MT          of the scope of this paper.
registers its new CoA directly to the HA. In this approach,          Another alternative that reduce the signaling load in
the location update to the new FA, which is close to the          Mobile IP network is to use a multicast-based mobility
previous FAs, could be less expensive than that to the HA.        approaches. These approaches have been proposed to
In [11], authors propose an analytic performance model to         reduce the mobility signaling delay by setting a multicast
evaluate the signaling transmission, the packet delivery, and     group (see Section 2). The MTs address update processes
the total costs of HMIP, HDDMIP, and DHMIP mobility               are concentrated into the multicast network nodes (e.g.,
approaches using a one-dimensional random walk model.             routers). They are reachable under these multicast group
The performance analysis shows that the DHMIP scheme              addresses. However, these approaches could be resource
outperforms compared to the HMIP and HDDMIP ones.                 consuming except for next-generation IP-based radio access
Despite that, the DHMIP approach still requires the new           technologies such as 3rd Generation Partnership Program
1314                                                      IEEE TRANSACTIONS ON MOBILE COMPUTING,     VOL. 8,   NO. 10,   OCTOBER 2009


(3GPP) and 3GPP2 future cellular communication system                 Different Mobile IP multicast protocols have been
called Long Term Evolution (LTE) [13], [14]. In LTE                proposed. In [20], Mobility Supporting Agents (MSA)-based
systems, where small cells deployment is expected, MT              architecture has been proposed using IGMPv2 and PIM SM
with high mobility will be able to access different wireless       IP multicast protocols. In [21], an Core Based Trees (CBT)-
networks frequently yielding to increase traffic overhead          based multicast mobile IP approach has been proposed for
due to MIP signaling and tunneling. This signaling includes        micromobility. In [22], authors propose a set of multicast
not only location update signaling but also security               mobility protocols called Candidate Access Router set (CAR-
                                                                   set). The performance of multicast mobility approaches has
association signaling required for MIP support [14], [15].
                                                                   been evaluated through simulation or through analytic
HAs could be signaling traffic bottleneck for such future
                                                                   models [22], [23]. In [22], a set of performance metrics (such
mobile networks with high-mobility MTs. Hence, MHMIP
                                                                   as handoff delay, packet loss, and bandwidth overhead due
mobility approach is proposed to reduce the signaling delay        to handoff) have been identified and evaluated for multicast
using multicast groups. The MT with high mobility could            mobility approaches that have been simulated using NS2
reuse the multicast resources for signaling and packet             network simulator. In [23], a software platform, set up
delivery for several handoff events that occur during its call     testbeds, has been used to analyze multicast mobility
holding time. From that we expect that the resource usage is       protocols in terms of handoff delay, packets losses and
no greater than that of the DHMIP mobility approach.               duplications, and relative TCP throughput. There is a large
Hence, we propose to compute the mean bandwidth per                number of multicast approaches that could be used to
call and the mean handoff delay per call used for signaling        implement mobility into MIP networks. The analysis of these
and packet delivery according to the MT mobility and call          approaches and their design is not the focus of this paper. We
holding time duration, and to compare the performance of a         refer the reader to [23], where four case studies for multicast-
Multicast Hierarchical Mobile IP approach (MHMIP) with             based mobility are presented based on different multicast
those of the DHMIP and MIP mobility strategies. We derive          service models and protocols. In this paper, we focus on
a set of recommendations for the usage of these mobility           usage of the multicast hierarchical architecture for IP
management approaches according to the MTs mobility.               mobility support and its performance in terms of bandwidth
The main contribution of this paper is the analytic model          usage and handoff delay. The example used in this paper of
                                                                   such architecture is given in Section 2.2.
that allows performance evaluation of three mobility
management approaches.                                             2.2 Multicast Hierarchical Mobile IP
   This paper is organized as follows: Section 2 discusses         In this approach, we propose to build hierarchical multicast
the multicast-based mobility approaches. Sections 3 and 4          groups. In each group, FAs are connected to each other
present the analytic model and the numerical results,              through a GFA. A set of GFAs are connected to an HA.
respectively. Section 5 gives the conclusions.                     When an MT moves through FAs belonging to the same
                                                                   group, the GFA of this group multicasts the received packet
2      MULTICAST-BASED MOBILITY APPROACHES                         (coming from the HA) to the MT. When the MT moves
                                                                   outside a group, the new CoA is registered to the GFA of
2.1 Overview
                                                                   the new group to which the MT is currently belonging. This
The multicast has been proposed to be used for mobility            GFA sends this CoA to the HA. This latest tunnels the
support and specifically in wireless networks with small           packet to the new GFA which will multicast the received
radio cells and high mobility of MTs. Several multicast-           packets within the new FAs group. This approach reduces
based mobility approaches have been proposed. They can             the frequency of the location update to the HA. This update
be classified into multicast-based mobility in connection-         is performed every inter-GFAs mobility rather than every
oriented and connection-less networks. For connection-             inter-FAs mobility limiting the location update processing
oriented networks, Acampora and Naghshineh propose a               only at the GFA. In this example, the group creation is static
virtual tree concept, where a multicast connection tree is         in the sense that the numbers of groups and FAs do not
preestablished. This tree is a collection of radio base stations   change and remain fix.
and ATM network switches connected to the tree’s root. The            In Fig. 3, when the MT moves from F A2 to F A5 , the
signaling delay is limited to the activation and deactivation      location registration is performed between HA and GF A2 .
of preestablished branch in the tree [16].                         GF A2 multicasts packets to F A4 , F A5 , and F A6 . Thus,
    For Connection-less network, Seshan, in [17], proposes to      when MT moves to F A6 or F A4 there is no need for the MT
apply a multicast to Mobile IP to reduce the handoff delay.        location registration. Hence, this approach allows reducing
The HA encapsulates the intercepted packets into multicast         the mobility signaling delay compared to the HMIP and
packets and sends them to the targeted MT over multiple            DHMIP mobility approaches specifically for high-mobility
FAs. In [18], Ghai and Singh propose to divide the wireless        MTs. However, it is network resources consuming ap-
network into regions controlled by a supervisor host. Each         proach due to multicast protocol use. Consequently, it is
region includes groups of cells such as each cell may be part      required for comparison purpose to evaluate the perfor-
of several of these groups. A unique IP multicast ID is            mance not only in term of handoff signaling delay but also
assigned to each of these groups. In [19], authors extend this     in term of bandwidth use. This latest is the bandwidth used
work by considering multiple wireless networks and cases           for signaling transfer and packet delivery.
where mobile device is not able to use channel character-             If we take the same MIP network architecture for the
istics to trigger handoffs due to the frequent network             three mobility management approaches, the bandwidth
interface change.                                                  used by MHMIP signaling is smaller than that of MIP or
KARA: MOBILITY MANAGEMENT APPROACHES FOR MOBILE IP NETWORKS: PERFORMANCE COMPARISON AND USE...                                       1315


                                                                 The DHMIP uses also path extension which requires
                                                                 additional signaling messages to establish the path part
                                                                 that extends the mobile connection from the previous FA to
                                                                 the new one when the mobile move and becomes attached
                                                                 to this latest.
                                                                    Each connection is subjected to a certain number of
                                                                 handoffs through its life duration (call holding time). This
                                                                 latest is divided into n time intervals enough small to allow
                                                                 the occurrence and the end of only one handoff during this
                                                                 interval. In each time interval, we define

                                                                    .     qa as the probability that an FAs handoff (handoff
                                                                          between two FAs) occurs and ends in this interval and
                                                                    . qf as the probability that the call ends in this interval.
                                                                 The number of handoffs that could occur during a call
Fig. 3. Hierarchical handoff scheme.                             holding time depends on the MT dwelling time in a radio
                                                                 cell and the traffic type: voice or data. Several voice traffic
DHMIP approaches because the path reestablishment is             researches have supposed that the dwelling time in a radio
performed only between HA and GFAs. However, the                 cell is an exponential distribution [24], [25]. In fact, this
bandwidth used by an MT for packet delivery is high              assumption depends on the shape of the radio cell and the
because several connections are used for packets’ transfer to    specific distributions of the mobile’s speed and direction
the MT. It is clear that the total bandwidth used for            which are difficult to characterize. In [26], [27], [28], [29],
signaling and packet delivery in MHMIP approach is higher        [30], authors have demonstrated that the exponential
than that used by the other approaches. Nevertheless, in         distribution for the dwelling time in radio cell is not
case of MTs with high mobility (high handoff requests), the      appropriated. They propose to replace it with complex
multicast resource in the GFA groups are reused by the MT        distributions such as Phase-Type, Lognormal, Hyperexpo-
every handoff event that occurs during its call holding time.    nential, and HyperErlang requiring the identification of
Consequently, we expect that the MHMIP mean bandwidth
                                                                 several parameters related to the selected traffic model. In
per call for MTs with high mobility is no greater than that of
                                                                 order to simplify the computation of the mean bandwidth
the DHMIP and MIP mobility approaches. We also expect
                                                                 and mean delay per call, we consider that the time between
that the MHMIP mean handoff delay (including signaling
                                                                 the handoff events and the call duration is a geometric
and packet delivery delays) is smaller than that of the
                                                                 distribution of mean 1=qa 1 and 1=qf , respectively.
DHMIP and MIP mobility approaches.
   Hence, we propose to derive an analytic model that               For data traffic, researches have addressed the problem
allows computation of mean bandwidth and mean handoff            of the persistent congestion periods with non-negligible
delay per call for MIP, DHMIP, and MHMIP mobility                packet losses [31], [32], [33], [34]. They show that these losses
approaches. These performance measurements are com-              do not allow the usage of Poisson model to model the TCP
puted according to the MTs mobility type (high or low) and       traffic. In [33], [34], authors have demonstrated that the Self-
the call holding time duration. The model description and        Similar processes are better models for TCP traffic mod-
the performance comparison of the three mobility ap-             elization than the exponential ones. However, in this study,
proaches are discussed in the following sections.                we are interested by the data session arrivals rather than the
                                                                 data packet generation in the sessions. Hence, we propose
                                                                 that the assumption made for the voice traffic remains valid
3       ANALYTIC MODEL                                           for the data traffic.
This section describes the analytic model and the set of            The proposed discrete time model is a generalization of
established assumptions.                                         the one proposed in [35]. The novelty of this model consists
                                                                 in the definition of generic analytical model that applies to
3.1 Assumptions                                                  more than one handoff approach and that allows to
Generally, during each handoff, a path reestablishment is        compute not only mean bandwidth due to handoff but also
required to maintain or to improve call quality. This            mean handoff delay of the analyzed handoff approaches.
reestablishment uses signaling messages and involves a           The temporal diagram given in Fig. 4 is used to compute
change in the number of links of the mobile connection.          these means. First, we compute the bandwidth and the
   Note that the three mobility approaches described here        delay within each interval and their means over the handoff
are based on a mobile connection path reestablishment            events. Then, we compute the bandwidth and the delay
which leads to perform the following operations:                 sums over the total call holding time. Finally, we evaluate
    .    CoA update with the HA,                                 their means over all the call durations. In order to
    .    new path establishment from HA to FA for DHMIP          understand the modelization mechanism, we illustrate by
         and MIP, and from HA to GFA for MHMIP,                  taking as an example the mean bandwidth computation. In
    .    user data traffic transfer from the previous path to    this figure, the holding time of ongoing call is divided into
         the new one,
                                                                    1. The respective temporal means are obtained while multiplying by the
    .    previous path discard.                                  interval duration.
1316                                                           IEEE TRANSACTIONS ON MOBILE COMPUTING,                   VOL. 8,       NO. 10,   OCTOBER 2009


                                                                       represents the mean number of intervals during a call.
                                                                       Then, we obtain

                                                                                            l            s      XÂ
                                                                                                                1                    Ã
                                                                                   B¼B þB ¼                           Bl ðnÞ þ Bs ðnÞ P ðnÞ
                                                                                                                n¼1
                                                                                                                                                         ð5Þ
                                                                                        X
                                                                                        1                              X
                                                                                                                       1
                                                                                    ¼               Bl ðnÞP ðnÞ þ             Bs ðnÞP ðnÞ:
                                                                                        n¼1                             n¼1

Fig. 4. Discrete diagram of a call holding time.                       Let E½Bx Š; x 2 fs; lg, a variable that designates the E½Bl Š or
                                                                                i                                                  i
                                                                       E½Bs Š entity. In the bandwidth computations given later,
                                                                           i
time intervals small enough that we may assume that in                 E½Bx Š could be variable or not during a call. If variable, then
                                                                           i
each time interval Ši; i þ 1Š, at most one handoff may occur.          we obtain
In each interval, let
                                                                                        X
                                                                                        1                               XX Â Ã
                                                                                                                        1 nÀ1

   .   n be the number of intervals for a call,                                  Bx ¼               Bx ðnÞP ðnÞ ¼             E Bx P ðnÞ
                                                                                                                                 i
                                                                                        n¼1                             n¼1 i¼0
   .   Bl be the bandwidth used by a call during the time
         i                                                                                                                                               ð6Þ
       interval Ši; i þ 1Š,                                                                     X
                                                                                                1
                                                                                                                  ðnÀ1Þ
                                                                                                                          X Â Ã
                                                                                                                          nÀ1
                                                                                    ¼ qf              ð1 À qf Þ               E Bx ;
    . Bs be the signaling bandwidth used by a call during
         i                                                                                      n¼1                       i¼1
                                                                                                                                 i

       handoff that occurred in the time interval Ši; i þ 1Š, and
    . Bi be the total bandwidth used by a call during the              otherwise, we have
       time interval Ši; i þ 1Š;
                                                                                      X
                                                                                      1                                XX Â Ã
                                                                                                                       1 nÀ1
Bl and Bs are random variables with values that depend on
  i       i                                                                    Bx ¼         Bx ðnÞP ðnÞ ¼                    E Bx P ðnÞ
                                                                                                                                i
the occurrence or not of a handoff during the interval Ši; i þ 1Š                     n¼1                              n¼1 i¼0

and on the possible path reestablishment once the handoff                            X Â ÃX
                                                                                     1      nÀ1          Â ÃX1
                                                                                   ¼   E Bx     P ðnÞ ¼ E Bx   nP ðnÞ                                    ð7Þ
occurs. The variable Bl can take two values. When a handoff
                          i                                                           n¼1
                                                                                          i                i
                                                                                                           i¼0                          n¼1
occurs for a call in the interval Ši; i þ 1Š, Bl represents the sum                                                                       Ã
                                                i                                               Â        ÃX
                                                                                                          1
                                                                                                                              ðnÀ1Þ     E Bxi
of the allocated bandwidth over the original path and the                          ¼ qf E           Bx
                                                                                                     i          nð1 À qf Þ            ¼       :
                                                                                                          n¼1
                                                                                                                                         qf
one allocated over the links of the new established path.
Otherwise, it represents the bandwidth used on the link of                The same procedure applies for the mean handoff delay
the ongoing connection. Bi represents the sum of the                   computation by substituting to variable B the variable D
bandwidth used by the ongoing call (Bl ) and the bandwidth
                                              i
                                                                       which represents the delay. Note that B and D are random
used for signaling (Bs ). Otherwise, it represents the allocated       variables due to handoff.
                        i
bandwidth to the ongoing call (Bl ). Then, we obtain                      In the following sections, the mean bandwidth per call is
                                        i
                                                                       the network bandwidth needed to support a mobile
            & l        s
               Bi þ Bi ; if a handoff occurs in Ši; i þ 1Š;            connection over its total duration, and it is given by the
      Bi ¼                                                       ð1Þ   sum of the bandwidth used on the paths’ links of the
               Bl ;
                 i          otherwise:
                                                                       ongoing connection and the signaling bandwidth due to
The mean of Bi over the handoff events is given by                     handoffs. Likewise, the mean handoff delay per call is the
                 Â Ã      Â Ã     Â Ã                                  network handoffs’ durations to support a mobile connec-
                E Bi ¼ E Bl þ E Bs :                             ð2Þ
                            i        i                                 tion which is given by the sum of the duration of the
  For fixed value of n, the total mean bandwidth BðnÞ used             resource establishment on the paths’ links and the signaling
by an ongoing call during the n time intervals is                      duration due to handoff. The paths’ links are the total
                                                                       network links of all paths used by the ongoing connection
                                      X Â Ã X Â Ã
                                      nÀ1        nÀ1                   during its holding time. Let
       BðnÞ ¼ Bl ðnÞ þ Bs ðnÞ ¼           E Bl þ
                                             i       E Bs :
                                                        i        ð3Þ
                                      i¼0              i¼0                .  BP D be the allocated bandwidth on each link for
   As the call duration n is a random variable, the mean                     packet delivery of a call,
bandwidth B is computed over all the call durations                      . BP E be the signaling bandwidth used per call for
                                                                             each path extension,
n ¼ 1; . . . ; 1. With our assumptions, the probability that a
                                                                         . BP R be the signaling bandwidth used per call for
call runs n periods is defined as P ðnÞ:
                                                                             each path reestablishment,
               P ðnÞ ¼ qf ð1 À qf ÞnÀ1       n ¼ 1; 2; . . .     ð4Þ     . DP D be the duration per call to allocate bandwidth
                                                                             BP D on a link of a new extended path and/or a
such as                                                                      reestablished path,
                                                                         . DP E be the signaling duration per call for a path
                    X
                    1                X
                                     1
               n¼         nP ðnÞ ¼         nqf ð1 À qf ÞnÀ1                  extension, and
                    n¼1              n¼1                                 . DP R be the signaling duration per call for a path
                        X
                        1                                                    reestablishment.
                 ¼ qf         nð1 À qf ÞnÀ1 ¼ 1=qf                     Note that BP D and DP D are, respectively, the bandwidth
                        n¼1
                                                                       and the duration for packet delivery on each link of a path
KARA: MOBILITY MANAGEMENT APPROACHES FOR MOBILE IP NETWORKS: PERFORMANCE COMPARISON AND USE...                                     1317


for an ongoing call. The BP D can take different fixed values     reestablishment. The second term (q  a          q ð1ÀpÞð1Àq ÞH
                                                                                                                  f
                                                                                                                          BP D )
according to the traffic type carried through the path links:                                         ½1Àð1Àpqa Þð1Àqf ފ
                                                                                                              f
                                                                  represents the additional bandwidth due to the path
voice or data (e.g., 64 kbps). A link is the network                                         qa
connection between two network entities such as an FA             extensions. The last term (qf ðBP E þ pBP R Þ) represents the
and a router (e.g., in Fig. 3, there is three links between the   signaling bandwidth due to the extensions and path
F A1 and HA). The signaling duration is the time taken for        reestablishments.
the transmission and the execution of the different handoff           In (9), the term qa =qf represents the mean number of
signaling messages. The parameters BP E and DP E are,             handoffs of a call. The second term ½DP D ½ð1 À pÞH þ pLp Š þ
respectively, the bandwidth and the duration necessary to         DP E þ pDP R Š represents the handoff delay which is the sum
set up the path extension between two FAs involved in a           of the resource reservation delay on the links of the extended
handoff. The parameters BP R and DP R include the                 and the reestablished paths (DP D ½ð1 À pÞH þ pLp Š), and the
bandwidth and the duration, respectively, for 1) CoA              signaling delay due to the path extensions and the path
registration, 2) setting up the new portion of connection         reestablishments (DP E þ pDP R ).
between HA and FA in case of DHMIP and MIP, and                       The reader is referred to Appendix A.1 and B.1 for a
between HA and GFA in case of MHMIP (e.g., path between           detailed demonstration of these formulas.
HA and F A4 in Fig. 2), and 3) terminating the old portion of
a connection (e.g., path between HA and F A3 in Fig. 2).          3.3 MIP Analytic Model
                                                                  The MIP mobility approach is based only on the path
3.2 DHMIP Analytic Model                                          reestablishment protocol. This latest allows maintaining
The DHMIP mobility approach combines the path rees-               the call connectivity when the MT moves between FAs. In
tablishment and the connection extension protocols. The           this case, events that may occur at each time i ¼ 1; 2; . . .
path reestablishment protocol is invoked to set up a new          are 1) path reestablishment and 2) call termination. Let
FAs hierarchy. This protocol allows a path establishment
between the HA and a new FA in the new hierarchy. In                 .  qa be the probability that there is an inter-FAs
this latest, the path extension is used to maintain the                 handoff and thus a partial reestablishment,
mobile connection when mobile moves through the FAs                 . L be the number of links between the FA to which
belonging to this hierarchy. The path reestablishment may               the MT is attached and the remote end point with
occur after each new FAs hierarchy setup. Events that may               which the MT is communicating, and
                                                                    . Lr be the number of links between the HA and the
occur at each time i ¼ 1; 2; . . . are 1) path reestablishment,
                                                                        new FA to which the MT moved (e.g., the number of
2) path extension, and 3) call termination. Let
                                                                        links between the HA and the F A3 following the
   .   p be the probability that a new FA hierarchy is set and          handoff from F A1 to F A3 in Fig. 1).
       consequently a path reestablishment is performed,            L and Lr are random variables with general distributions
   . L be the number of links between the FA to which             and with mean L and Lr , respectively.
       the MT is attached and the remote end point with             The mean bandwidth per call is
       which the MT communicates,                                                                        
   . Lp be the number of links between the HA and the                                  1           qa
                                                                                  Br ¼      LBP D þ BP R :              ð10Þ
       initial FA through which a new hierarchy is set (e.g.,                          qf          qf
       F A1 and F A4 in Fig. 2), and
   . H be the number of links of the path extension                  In (10), the first term q1f LBP D is the bandwidth of the
       (e.g., in Fig. 2, this number is equal to 1 when MT        original connection and the reestablished paths. The second
                                                                        qa
       moves from F A1 to F A2 and becomes connected              term qf BP R is the signaling bandwidth due to the path
       to F A2 ).                                                 reestablishments.
     p
L, L , and H are random variables with general distribu-             The mean handoff duration per call is
tions and with mean L, Lp , and H, respectively.                                            qa r P D
   The mean bandwidth per call is                                                    Dr ¼      ðL D þ DP R Þ:                      ð11Þ
                                                                                            qf
               L PD       qa ð1 À pÞð1 À qf ÞH                                         qa
                                                                     In (11), the term qf represents the mean number of handoffs
        Bp ¼      B þ                              BP D
               qf     qf ½1 À ð1 À pqa Þð1 À qf ފ                for a call. The term Lr DP D þ DP R represents the handoff
                                                           ð8Þ
                  qa                                              delay which is the sum of the delay for resource allocation on
               þ ðBP E þ pBP R Þ;
                  qf                                              the reestablished path (Lr DP D ) and the signaling delay (DP R ).
while the mean handoff delay per call is                             Details on these computations are given in Appendix A.2
                                                                  and B.2.
                       qa P D
                Dp ¼      D ½ð1 À pÞH þ pLp Š                     3.4 MHMIP Analytic Model
                       qf
                          qa                               ð9Þ    The MHMIP mobility approach is based on the path
                       þ ½DP E þ pDP R Š:
                          qf                                      reestablishment and the multicast protocols. When the MT
                                                                  moves within a GFA group, the mobile connection is
                        L
In (8), the first term (qf BP D ) represents the bandwidth        maintained using the multicast protocol. When the MT
used on the original path and the paths resulting from the        moves outside this hierarchy, a combination of the path
1318                                                      IEEE TRANSACTIONS ON MOBILE COMPUTING,         VOL. 8,   NO. 10,   OCTOBER 2009


reestablishment and the multicast protocols allows main-
taining the call’s connection. Events that may occur at
each time i ¼ 1; 2; . . . are 1) path reestablishment and
2) call termination.
                0
   We define qa as the probability that there is an inter-
GFAs handoffs and thus path reestablishments such as
 0
qa ¼ qa with 0  1.  is the fraction of inter-GFAs
MHMIP handoffs on the whole possible handoffs qa (intra-
and inter-GFAs).
   The inter-GFAs handoff arrivals are modeled using a
Bernoulli process. For each mobile connection, we define

    .   Lh as the number of links between the GFA to which
        the mobile is currently attached and the remote end
        point with which the MT is communicating,
   . Lhp as the number of links between the HA and the
        GFA to which the mobile is currently belonging, and
   . Lhr as the total number of links in the GFA hierarchies.
   Lh , Lhp , and Lhs are random variables with general            Fig. 5. Symmetric hierarchical IP network architecture.
distributions and with means Lh , Lhp , and Lhs , respectively.
   The mean bandwidth per call is                                  Fig. 5 shows an architecture with Lp ¼ Lr ¼ 7, Lhp ¼ 3, and
                    1 h PD             q
                                             0
                                                                   Lhr ¼ 240.
             Bh ¼      L B þ Lhr BP D þ a BP R :           ð12Þ       For comparison purpose, we take the number of links
                    qf                 qf
                                                                   between the HA and the end point the same for the three
   In (12), the first term q1f Lh BP D is the bandwidth used on    mobility management approaches. For a fixed remote end
the original path and the reestablished paths. The second          point, the number of links between the HA and this end
term Lhr BP D is associated to the multicast resources used by
                                                     0
                                                                   point do not change for an ongoing call of an MT. Then, we
                                                    qa
the call in the GFA hierarchies. The last term qf BP R is the      consider that the end point is directly connected to HA
signaling bandwidth due to the path reestablishment                (e.g., Lh ¼ Lhp ¼ 3 and L ¼ Lp ¼ Lr ¼ 7 for the example
following the GFA handoffs.                                        given in Fig. 5).
   The mean call duration per call is                                 Two types of configurations are considered for the
                                                                   network given in Fig. 5:
                             0
                             qa hp P D
                    Dh ¼        ½L D þ DP R Š:             ð13Þ       .     Configuration 1: the average number of links are
                             qf
                         0                                                  Lh ¼ Lhp ¼ 3 and Lr ¼ Lp ¼ L ¼ 7. These values
                     q
   In (13), the term qf is the mean number of handoffs of a
                      a
                                                                            result in the number of link where the resources
call. The second term ½Lhp DP D þ DP R Š is the handoff delay               were allocated Lhr ¼ 240.
which is the sum of the delay of resource allocated on the             . Configuration 2: the average number of links are
reestablished path (Lhp DP D ) and the signaling delay (DP R ).
                                                                            Lh ¼ Lhp ¼ 1 and Lp ¼ Lr ¼ L ¼ 7. From these
   The details on these computations are given in
Appendix A.3 and B.3.                                                       values, we obtain Lhr ¼ 252.
                                                                   For each configuration, two cases are analyzed: realistic and
                                                                   critical. In the realistic case, the inter-GFAs handoffs may
4       RESULTS ANALYSIS                                           occur less frequently than the intra-GFAs handoffs
In this section, we compare the performance in terms of              0
                                                                   (qa ¼ 0:1 Â qa ). In the critical case, the intra- and the inter-
mean bandwidth and mean handoff delay per call of the              GFAs handoffs may occur with the same probability
three mobility management approaches MHMIP, DHMIP,                   0                        0
                                                                   (qa ¼ qa , where qa and qa are variables).
and MIP.                                                               For both cases, the path extension for the DHMIP
4.1 Numerical Data                                                 mobility management approach should occur after each
                                                                   handoff and the path reestablishment should occur after
The mean call holding time is a random value chosen
                                                                   each two consecutive handoffs (p ¼ qa =2). For p > qa =2, the
between 60 and 120 seconds for voice traffic and between           mean bandwidth and mean delay is higher than that get
900 and 1,200 seconds for data traffic. For simplification         with p ¼ qa =2 (see Section 4.2).
purpose of the mean number of links computation (Lr , Lp ,             We suppose that the MT handoff to a new FA involves a
L, H, Lh , Lhp , and Lhr ), a symmetric hierarchical IP network    path extension of mean length H ¼ 1. For length greater
architecture is considered (Fig. 5). Symmetric architecture        than this value, the mean bandwidth and the mean handoff
means that the number of links between the HA and each             delay are high.
FA is the same (e.g., there is five links between the HA and           We rewrite (8), (12), (10), (9), (13), and (11) to obtain the
each F Ai ; fi ¼ 1; . . . ; 32g in Fig. 5). The example given in   ratios Bj R ¼ Bj =BP R and Dj R ¼ Dj =DP R , where j ¼ p; r; h.
                                                                           P                   P
KARA: MOBILITY MANAGEMENT APPROACHES FOR MOBILE IP NETWORKS: PERFORMANCE COMPARISON AND USE...                                                       1319




Fig. 6. Mean bandwidth per call Bp R and Bh R for voice traffic with 1=qf ¼
                                 P        P                                   Fig. 7. Mean bandwidth per call variation Bp R for voice traffic with 1=qf ¼
                                                                                                                         P
60 seconds, BP D =BP R ¼ 0:5.                                                 60 seconds, BP D =BP R ¼ 0:5.


Thus, these equations contain the following ratios: BP D =BP R ,
BP E =BP R , DP D =DP R , and DP E =DP R . We expect that the
signaling bandwidth for the path extension in DHMIP is
smaller than that of the path reestablishment (BP R > BP E
and DP R > DP E ). Then, BP R =BP E < 1 and DP R =DP E < 1.
As an example, we take BP R =BP E ¼ DP R = DP E ¼ 0:2.
Moreover, we expect that BP R > BP D and DP R > DP D .
Indeed, the BP R represents the sum of the allocated
bandwidth on each link of the path over which the handoff
signaling is transferred (the path between HA and FA for
DHMIP and MIP, and between HA and GFA for MHMIP).
This bandwidth could be greater than BP D which is the
                                                                              Fig. 8. Mean bandwidth ratio Bp R =Bh R and Br R =Bh R for voice traffic
bandwidth allocated on a path link for packet transfer.                                                         P P        P     P
                                                                              with p ¼ qa =2; BP D =BP R ¼ 0:8.
According to the BP D and the signaling bandwidth values,
we could have 0 < BP D =BP R < 1. In the same way, DP R                       bandwidth represents a performance measurement that an
represents the sum of the delays for bandwidth allocation on                  IP network operator can use to determine the needed
each link of the path carrying the signaling traffic and the                  resources to be deployed in the network to service a certain
delay for signaling messages processing. It is greater than                   number of MTs. The MHMIP mobility management
DP D , which represents the delay for BP D allocation. Thus, we               approach is the method that allows cost reduction in terms
take 0 < DP D =DP R < 1. In this analysis, we show an example                 of resources usage compared to the DHMIP approach.
of the results for BP D =BP R ¼ DP D =DP R ¼ 0:5 and 0.8.                        Fig. 7 illustrates the Bp =BP R ratio variation for different
                                                                              values of the probability p. We note that lower is p higher is
4.2    Numerical Results
                                                                              the mean bandwidth per call. Moreover, we note a different
We propose to compare the performance of the MHMIP                            behavior of this bandwidth between the intervals qa 0:3
handoff approach with those obtained with DHMIP and                           and 0:3 qa 1. For 0:3 qa 1, the mean bandwidth
MIP approaches in terms of mean bandwidth and mean                            value decreases while it increases in the interval qa 0:2 for
handoff delay per call. For summarization purpose, we                         different values of p (p ¼ qa =6; qa =4; qa =2) and still increasing
compute the ratios Bp R =Bh R , Br R =Bh R , Dp R =Dh R , and
                         P     P     P    P     P     P                       in the interval 0:2 qa 0:3 for p ¼ qa =6. This is in fact due
Dr R =Dh R . These ratios allow a simple and direct reading of
  P     P                                                                     to the low probability of path reestablishment p and the
the different performance between the tree mobility                           frequent use of path extension in the interval qa 0:3.
management approaches.                                                        Hence, less frequent path reestablishment usage for DHMIP
   Figs. 6 and 7 give an example of mean bandwidth                            mobility management approach involves a high mean
variation per call Bp R and Bh R for the DHMIP and MHMIP
                     P         P
                                                                              bandwidth per call consumption.
handoff approaches.
                                                                              4.2.1 Mean Bandwidth
   Fig. 6 illustrates the mean bandwidths per call for
MHMIP and DHMIP mobility management approaches. It                            Figs. 8 and 9 show examples of the mean bandwidth ratio
shows that the MHMIP mean bandwidth per call is smaller                       variation Bp R =Bh R and Br R =Bh R for the realistic and the
                                                                                           P     P          P P
than that obtained with the DHMIP approach. This mean                         critical cases, respectively.
1320                                                                 IEEE TRANSACTIONS ON MOBILE COMPUTING,     VOL. 8,   NO. 10,   OCTOBER 2009


                                                                                                         TABLE 2
                                                                                                        Mean Delay




                                                                               the partial reestablishment is more frequently used due to
                                                                                                      0
                                                                               the high probability qa of inter-GFAs handoffs.
Fig. 9. Mean bandwidth ratio Bp R =Bh R and Br R =Bh R for data traffic with
                              P     P        P     P
p ¼ qa =2; BP D =BP R ¼ 0:8.                                                   4.2.2 Delay Comparison
                                                                               The ratio values of the mean delay per call Dp R =Dh R and
                                                                                                                                 P    P
   Note that the ratio Bp R =Bh R is much higher than the
                           P    P
                                                                               Dr R =Dh R are summarized in Table 2 for the Realistic Case
                                                                                 P      P
ratio Br R =Bh R for different call holding time duration
         P    P
                                                                               (RC) and the Critical Case (CC). These values represent the
(1=qf ¼ 60; 90; 120 seconds) specifically for small probabil-
                                                                               arithmetic average of the ratios Dp R =Dh R and Dr R =Dh R
                                                                                                                    P     P          P     P
ity qa . This means that the combination of the path
                                                                               over the set of qa values. In the realistic case, the MHMIP
extension and the path reestablishment for handoff
                                                                               mean delay is smaller than those of the DHMIP and MIP
management involves higher mean bandwidth per call
                                                                               approaches. The mean delay differences are 8 and 21
than that used by the approaches based only on the path
                                                                               compared to DHMIP and MIP, respectively. They become
reestablishment (such as MHMIP and MIP). This behavior
                                                                               high, if we consider the configuration 2 where this difference
is noticed in all the analyzed cases. The main obtained
                                                                               reaches 40. This result was expected because in the MHMIP
results are summarized in Table 1 that give the ratio values
                                                                               approach, the path reestablishment is performed through a
of the mean bandwidth per call for the Realistic Case (RC)
                                                                               shorter path than that of the DHMIP and MIP approaches.
and the Critical Case (CC) for both Types of Configuration                        The mean delay per call of the MHMIP approach in the
(ToC). These values represent the arithmetic average of the                    critical case is smaller than that of the MIP and DHMIP
ratios Bp R =Bh R and Br R =Bh R over the set of qa values
          P    P         P    P                                                approaches unless for configuration 1 where this delay is
(0 qa 1). These results show that the MHMIP mean                               greater than that of the DHMIP approach, because the
                                                                                                                                       0
bandwidth is smaller than those of the DHMIP and MIP                           path reestablishment is not only more frequent (qa ¼ qa )
approaches. This bandwidth difference is higher in the                         but also the number of links involved in the path
configuration 2 than in the configuration 1 because the                        reestablishment is greater than that of configuration 2
MHMIP reestablishment is performed over small number                           (Lh ¼ 3 compared to Lh ¼ 1).
of links in the configuration 2, yielding to a smaller mean
                                                                               4.3 Recommendation
bandwidth per call than that computed with the config-
                                                                               Hence, we can derive the following recommendations that
uration 1. However, this mean bandwidth difference is
                                                                               indicate when one would use the MHMIP, the DHMIP, or
small in the critical case than in the realistic case because                  the MIP mobility management approaches:

                                                                                 .    The MHMIP versus DHMIP usage:
                              TABLE 1
                           Mean Bandwidth                                             1.   If the inter-GFAs handoffs are not frequent then
                                                                                           we suggest to use the MHMIP approach that
                                                                                           provides a best mean handoff delay and mean
                                                                                           bandwidth per call for voice and data traffic.
                                                                                      2.   If the inter-GFAs handoffs occur frequently
                                                                                                      0
                                                                                           (such as qa ¼ qa ), then we have two cases. If the
                                                                                           mean handoff delay per call is more important
                                                                                           than the mean bandwidth per call and if the
                                                                                           number of links involved in MHMIP path
                                                                                           reestablishment is high, then we suggest using
                                                                                           the DHMIP handoff approach; otherwise, we
                                                                                           suggest using the MHMIP handoff approach.
KARA: MOBILITY MANAGEMENT APPROACHES FOR MOBILE IP NETWORKS: PERFORMANCE COMPARISON AND USE...                                               1321


    .    The MHMIP versus the MIP usage: We suggest                     The mean bandwidth used by a call in a time interval
         using the MHMIP handoff approach that gives a best        Ši; i þ 1Š is given by
         mean handoff delay per call and a mean bandwidth
         per call for voice and data traffic, and for both                     Bl ¼ Bl ½ð1 À Ki Þ þ Ki ð1 À Ji ފ
                                                                                i    iÀ1

         frequent and nonfrequent GFAs handoffs.                                    þ BKi ½Ji Li ðiÞ þ ð1 À Ji ÞHi ðiފ
                                                                                                                                             ð16Þ
                                                                                       ¼ Bl ½1 À Ki Ji Š
                                                                                          iÀ1
5       CONCLUSION                                                                       þ BKi ½Ji Li ðiÞ þ ð1 À Ji ÞHi ðiފ:
In this paper, we have proposed an analytical model                We define new random variables sj ¼ ðKj ; Jj Þ, where sj
which evaluates the mean handoff delay per call and the            represents the pair of variables K and J at the period j and
mean bandwidth per call of three mobility management               the vector sj ¼ ½s1 ; s2 . . . sj Š.
approaches: MIP, DHMIP, and MHMIP. Numerical results                  At each interval, Li and Hi represent, respectively, the
show that the MHMIP mobility approach compares very                number of links of the original path or a path resulting
favorably with the previously considered mobility ap-              from a path reestablishment and the number of links of
proaches. More specifically, our analysis gives in almost all      the extended path. In general, these values are depen-
cases a lower mean handoff delay per call and a mean               dent in complex way of events that occurred before the
                                                                   instant i. They are generally random variables which
bandwidth per call than those offered by the DHMIP and
                                                                   should be designated by Li ðsi Þ and Hi ðsi Þ. Then, we can
MIP approaches. It also shows the robustness of the                rewrite (16) more explicitly such as
MHMIP approach in the sense that for critical scenario
corresponding to the extreme situation where all handoff                     Bl ðsi Þ ¼ Bl ðsiÀ1 Þ½1 À Ki Ji Š
                                                                              i          iÀ1
                                                                                                                                             ð17Þ
events are localized at the multicast group borders, this                                   þ BKi ½Ji Li ðsi Þ þ ð1 À Ji ÞHi ðsi ފ:
approach essentially yields to 1) a lower mean bandwidth
per call than the DHMIP and MIP approaches; 2) a lower             As the events are independent in each interval, we can write
                                                                   for si
mean handoff delay per call than that offered by the MIP
approach; 3) a lower mean handoff delay than that offered                                   pðsi Þ ¼ pðsiÀ1 ÞpðKi ; Ji Þ;
by the DHMIP except in case of frequent inter-GFAs
                                                                   where pðKi ; Ji Þ is the probability to have a given config-
handoffs with a network configuration having a high
                                                                   uration of the random variables Ki and Ji . Note that
number of links involved in MHMIP path reestablishment             pð0; 1Þ ¼ 0 because we could have a path reestablishment
such as the configuration 2. Since we expect a diversity of        only after a handoff. Let define the two auxiliary entities:
multimedia applications for future IP mobile networks, we
recommend using the MHMIP approach in networks parts                                          gðKi ; Ji Þ ¼ ½1 À Ki Ji Š;                    ð18Þ
carrying delay sensitive and/or low mean bandwidth                                        Â                               Ã
consumption type of applications and this according to                        hðsi Þ ¼ BKi Ji Li ðsi Þ þ ð1 À Ji ÞHi ðsi Þ :                 ð19Þ
the mobility type.                                                    The mean bandwidth over the handoff events is
                                                                   given by
APPENDIX A                                                                  Â Ã X i          X
                                                                          E Bl ¼
                                                                              i    pðs ÞZi ¼   pðsiÀ1 ÞpðKi ; Ji ÞZi
EVALUATION OF THE MEAN BANDWIDTH PER CALL                                                  s  i                            i
                                                                                           X                       Xs                        ð20Þ
                                                                                                           iÀ1
By using the discrete time model given in Fig. 4, we                                   ¼           pðs           Þ  pðKi ; Ji ÞZi ;
estimate the mean bandwidth per call for the DHMIP, MIP,                                    siÀ1                  Ki ;Ji

and MHMIP mobility management approaches.                          where Zi ¼ ½BiÀ1 ðsiÀ1 ÞgðKi ; Ji Þ þ hðsi ފ. As Li and Hi are
A.1 DHMIP Approach                                                 dependent on si in a complex way and for computation
                                                                   simplification purpose, a set of assumptions are made. We
In this case, we take into account the following events: the       suppose these variables constant from the fact that in
inter-FAs handoffs (path extension) that occur with prob-          general we can expect that the connection paths and the
ability qa and the path reestablishment which is executed          path extensions do not vary a lot from one handoff to
with probability p.                                                another. From this assumption, we can continue our
   For each time interval Ši; i þ 1Š, we define two random         computations such as (20) becomes
variables corresponding to the occurrence or not of a                  Â Ã X iÀ1                       X
handoff event and the path reestablishment.                           E Bl ¼
                                                                          i        pðs ÞBiÀ1 ðsiÀ1 Þ       pðKi ; Ji ÞgðKi ; Ji Þ
                                                                               siÀ1                                        Ki ;Ji
                      &                                                            X                       X
                Ki ¼
                        1; a handoff occurs;
                                                        ð14Þ                   þ            pðsiÀ1 Þ                pðKi ; Ji ÞhðKi ; Ji Þ
                        0; otherwise:                                              siÀ1                    Ki ;Ji
                                                                                   Â          ÃX                                             ð21Þ
               &                                                             ¼E        Bl
                                                                                        iÀ1                pðKi ; Ji ÞgðKi ; Ji Þ
                   1; a path reestablishment is executed;                          X
                                                                                                  Ki ;Ji
        Ji ¼                                                ð15Þ
                   0; otherwise:                                               þ            pðKi ; Ji ÞhðKi ; Ji Þ;
                                                                                   Ki ;Ji
We also suppose that E½Ki Š ¼ qa and E½Ji Š ¼ p.
1322                                                                  IEEE TRANSACTIONS ON MOBILE COMPUTING,             VOL. 8,   NO. 10,   OCTOBER 2009

       P                                                                                    X
                                                                                            1                      X
                                                                                                                   1
with        siÀ1   pðsiÀ1 Þ ¼ 1. We can compute the two terms:                                    
 n P ðnÞ ¼ qf         
 n ð1 À qf ÞnÀ1
       X                                                                                    n¼1                    n¼1
            pðKi ; Ji ÞgðKi ; Ji Þ ¼ ð1 À qa Þgð0; 0Þ þ qa pgð1; 1Þ                                             qf X 1
   Ki ;Ji                                                              ð22Þ                                ¼            ½
ð1 À qf ފn                 ð31Þ
                                                                                                             1 À qf n¼1
                                     þ qa ð1 À pÞgð1; 0Þ;                                                                      !
                                                                                                                       

                                                                                                           ¼ qf                  :
   X                                                                                                             1 À 
ð1 À qf Þ
            pðKi ; Ji ÞhðKi ; Ji Þ ¼ ð1 À qa Þhð0; 0Þ þ qa phð1; 1Þ
   Ki ;Ji                                                              ð23Þ      By replacing in (30), we obtain
                                     þ qa ð1 À pÞhð1; 0Þ;                                                                            !
                                                                                            l      M         1             qf 

                                                                                          B ¼            þK      1À
with gð0; 0Þ ¼ 1; gð1; 1Þ ¼ 0, gð1; 0Þ ¼ 1, hð1; 1Þ ¼ L, hð1; 0Þ ¼                                qa pqf    qa p     1 À 
ð1 À qf Þ
                                                                                                                                !
H, and hð0; 0Þ ¼ 0. By replacing each of these terms in (21),                                      M         1        qa p
                                                                                                ¼        þK                                           ð32Þ
we obtain                                                                                         qa pqf    qa p 1 À 
ð1 À qf Þ
                                                                                                                                    !
    Â Ã                  Â    Ã                                                                    M                   1
  E Bl ¼ ð1 À qa pÞE Bl                                PD                                       ¼        þK                           :
       i                   iÀ1 þ qa ½ð1 À pÞH þ pLŠB      : ð24Þ                                  qa pqf     1 À ð1 À qa pÞð1 À qf Þ

If we suppose that E½Bl Š ¼ LBP D , we can solve the
                           0
                                                                                 By replacing M with its value and by reorganizing the
recurrence (24) and we obtain                                                 terms we finally find
      Â Ã                                                                                                                              !
    E Bl ¼ ð1 À qa pÞi LBP D                                                      l  L                     1        qa ð1 À qf Þ
         i                                                                       B ¼ BP D þ BP D ð1 À pÞH                                :
                                                                                     qf                   qf ð1 À ð1 À qa pÞð1 À qf ÞÞ
                      þ ½1 þ ð1 À qa pÞ þ Á Á Á þ ð1 À qa pÞiÀ1 ŠM
                                                                       ð25Þ                                                                           ð33Þ
                                                         i
                                           1 À ð1 À qa pÞ
                   ¼ ð1 À qa pÞi LBP D þ                  M;                  Using (28) and (33), we compute Bp ¼ Bl þ Bs
                                                qa p
                                                                                           L PD       qa ð1 À pÞð1 À qf ÞH
where M ¼ ½qa ð1 À pÞH þ qa pLŠBP D .                                               Bp ¼      B þ                              BP D
                                                                                           qf     qf ð1 À ð1 À qa pÞð1 À qf ÞÞ
                                                                                                                                                      ð34Þ
   The mean signaling bandwidth due to handoff in the                                         qa
                                                                                           þ ðBP E þ pBP R Þ:
interval Ši; i þ 1Š is given by                                                               qf

                     Bs ¼ Ki ðBP E þ Ji BP R Þ;
                      i                               i ! 1;           ð26Þ   A.2 MIP Approach
                                                                              An inter-FAs handoff occurs with probability qa . For each
with the mean of Bs over the handoff events is
                  i                                                           time interval Ši; i þ 1Š, we define the random variable
                    E½Bs Š ¼ qa ðBP E þ pBP R Þ;       i ! 1:          ð27Þ                          &
                       i                                                                                1; a handoff occurs;
                                                                                                Ii ¼                                  ð35Þ
                                                                                                        0; otherwise;
As E½Bs Š is not a variable, then we use (7) and (27) to
      i
           s
compute B .                                                                   which corresponds to the occurrence of a handoff followed
                             Â Ã                                              by a path reestablishment of the MT’s ongoing connection.
                       s    E Bsi                     1                       Note that E½Ii Š ¼ qa .
                     B ¼          ¼ qa ðBP E þ pBP R Þ :               ð28Þ
                             qf                       qf                         The mean signaling bandwidth due to mobility in the
                                                                              interval Ši; i þ 1Š is given by
   We use (25) such as
                                                                                                     Bs ¼ Ii BP R ;
                                                                                                      i                      i ! 1:                   ð36Þ
                            X
                            nÀ1                       !X
                                                       nÀ1
                                 M                M                           The mean bandwidth corresponding to the handoff events
                   Bl ðnÞ ¼           þ LBP D À            
i
                            i¼0
                                 qa p            qa p i¼0                     is given by
                                                  !                  ð29Þ
                            Mn               M 1 À 
n                                        Â Ã
                          ¼       þ LBP D À                   ;                            E Bs ¼ qa BP R ;
                                                                                               i              i ! 1:            ð37Þ
                            qa p             qa p     qa p
                                                                              The bandwidth used in the time interval Ši; i þ 1Š is
where 
 ¼ ð1 À qa pÞ.                                                         given by
   Using (6) and (29), we find
                                                                                        Bl ¼ ð1 À Ii ÞBl þ Li ðiÞIi BP D ;
                                                                                         i             iÀ1                               i ! 1:       ð38Þ
                      X
                      1                X Â Ã
                                       nÀ1
            l
        B ¼ qf          ð1 À qf ÞðnÀ1Þ     E Bl                               Note that Bl depends on all the random variables Ij ; j ¼
                                                                                                 i
                                              i
                      n¼1               n¼1                                   1; . . . ; i À 1 and on the variable Ii of the current interval.
                                                                       ð30Þ
                  MX    1
                                       1 X  1                                 The length Li ðiÞ depends in complex manner on the events
                ¼          nP ðnÞ þ K          ð1 À 
 n ÞP ðnÞ;               that occurred before i. It is represented by Li ðsi Þ with
                  qa p n¼1            qa p n¼1
                                                                              si ¼ ½I1 ; I2 ; . . . ; Ii Š. We can then rewrite (38) as
where K ¼ ½LBP D À qMpŠ. We evaluate the following
                    a                                                           Bl ðsi Þ ¼ ð1 À Ii ÞBl ðsiÀ1 Þ þ Li ðsi ÞIi BP D ;
                                                                                 i                   iÀ1                                     i ! 1:   ð39Þ
equation:
KARA: MOBILITY MANAGEMENT APPROACHES FOR MOBILE IP NETWORKS: PERFORMANCE COMPARISON AND USE...                                                                 1323


Let pðsi Þ ¼ pðsiÀ1 ÞpðIi Þ, where pðIi Þ is the probability of the                                  A.3 MHMIP Approach
occurrence or not of a handoff such as pð1Þ ¼ qa and                                                 In this case, two types of handoff can occur in each time
                                                                                                     interval: inter and intra-GFAs handoffs. From the fact that
pð0Þ ¼ 1 À qa , and let the auxiliary entities gðIi Þ ¼ ð1 À Ii Þ
                                                                                                     intra-GFAs handoff doesn’t generate signaling traffic. This
and hðsi Þ ¼ BP D Ii Li ðsi Þ. The mean value on the handoff
                                                                                                     type of events is not considered in our computations.
events is given by                                                                                      In each time interval Ši; i þ 1Š, we define a random
             Â Ã X i        X                                                                        variable corresponding to the inter-GFAs handoff occur-
           E Bl ¼
               i   pðs ÞF ¼   pðsiÀ1 ÞpðIi ÞF
                                    i                           i
                                                                                                     rence and consequently to a path reestablishment.
                                  s
                                  X                       Xs                                  ð40Þ                   &
                                                  iÀ1
                              ¼          pðs            Þ   pðIi ÞF ;                                                  1; an inter-GFAs handoff occurs;
                                                                                                                Ii ¼                                        ð49Þ
                                  siÀ1                    Ii                                                           0; otherwise:
where F ¼ ½BiÀ1 ðsiÀ1 ÞgðIi Þ þ hðsi ފ. As Li depends in com-                                       with a mean value E½Ii Š ¼ qa .
                                                                                                                                    0



plex manner on si , we assume that Li is constant. This                                                 The computation of the mean bandwidth per call follows
assumption is valid since the connection length after a path                                         the same steps than those explain for the MIP handoff
                                                                                                                                     0
                                                                                                     approach by replacing qa by qa and Li by Lh .
                                                                                                                                               i
reestablishment doesn’t change a lot from one handoff to
                                                                                                        The mean bandwidth per call for the MHMIP handoff
another. Consequently, we can write                                                                  approach is given by
      Â Ã X iÀ1                   X
    E Bl ¼
         i      pðs ÞBiÀ1 ðsiÀ1 Þ   pðIi ÞgðIi Þ                                                                              1 h PD
                      siÀ1                                          Ii
                                                                                                                       Bh ¼      ðL B þ qa BP R Þ:             ð50Þ
                          X                        X                                                                          qf
                                        iÀ1
                      þ           pðs         Þ          pðIi ÞhðIi Þ                         ð41Þ
                           siÀ1                    Ii
                                                                                                     To this bandwidth, we add a fixed bandwidth due to
                          Â        ÃX                                    X                           resources allocation in the GFAs hierarchies Bhs given by
                ¼ E Bl
                     iÀ1                       pðIi ÞgðIi Þ þ                 pðIi ÞhðIi Þ;
                                         Ii                              Ii
                                                                                                                              Bhs ¼ Lhs BP D :                 ð51Þ
       P              iÀ1
with     siÀ1   pðs Þ ¼ 1. We can compute the two terms                                              Lhs is the number of links in the GFAs hierarchies. Then,
                 X
                    pðIi ÞgðIi Þ ¼ ð1 À qa Þgð0Þ þ qa gð1Þ; ð42Þ                                     the mean bandwidth per call is given by
                 Ii
                                                                                                                       1 h PD                1
                                                                                                                Bh ¼      L B þ Lhs BP D þ qa BP R :           ð52Þ
                X                                                                                                      qf                    qf
                          pðIi ÞhðIi Þ ¼ ð1 À qa Þhð0Þ þ qa hð1Þ;                             ð43Þ
                 Ii
                                                                                                     APPENDIX B
with gð0Þ ¼ 1; gð1Þ ¼ 0; hð0Þ ¼ 0, and hð1Þ ¼ L. By replacing
                                                                                                     EVALUATION OF MEAN HANDOFF DELAY PER CALL
these terms in (41), we find
              Â Ã            Â    Ã                                                                  As in Appendix A, we consider the temporal diagram given
            E Bl ¼ ð1 À qa ÞE Bl
                 i             iÀ1 þ qa LB
                                           PD
                                              :                                               ð44Þ   in Fig. 4. The handoff delay is defined as the sum of the
Let E½Bl Š ¼ LBP D , we can solve the recurrence and we                                              delay due to bandwidth allocation BP D on the new path
       0
obtain                                                                                               links and the signaling delay. In each interval Ši; i þ 1Š, let

                                                                                                       .     Dl be the delay to allocate the bandwidth BP D on a
      Â Ã                      1 À ð1 À qa Þi                                                                  i
     E Bl ¼ ð1 À qa Þi LBP D þ
        i                                     X ¼ LBP D ;                                     ð45Þ           link of the new path resulting from a handoff event
                                    qa                                                                       during a call,
with X ¼ qa LBP D .                                                                                     . Ds be the signaling delay due to a handoff that
                                                                                                               i
  As E½Bs Š given in (37) is not variable, then we compute
         i
                                                                                                             occurred in the time interval Ši; i þ 1Š, and
 s
B using (7):                                                                                            . Di be the total delay for a call in the time
                                                                                                             interval Ši; i þ 1Š.
                                          s                     1                                       Dl and Ds are the random variables which depend on the
                                        B ¼ qa BP R                :                          ð46Þ        i       i
                                                                qf                                   occurrence of handoff events in the interval Ši; i þ 1Š. Di
Since E½Bs Š given in (45) is not variable, we use (7) and (45)                                      represents the sum of the delay due to the bandwidth
         i
                      l                                                                              allocation on the new path following a handoff event and
to compute B .
                                                                                                     the signaling delay.
                                               l               1
                                              B ¼ LB                                          ð47Þ
                                                               qf                                                             Di ¼ Dl þ Ds :
                                                                                                                                    i    i                     ð53Þ

We use (46) and (47) to compute the mean bandwidth per
                                                                                                     B.1 DHMIP
call such as
                                                                                                     We reuse the same procedure than that used for the
                                                    1                                                computation of the DHMIP mean bandwidth per call
                 Br ¼ Bl þ Bs ¼                        ðLBP D þ qa BP R Þ:                    ð48Þ
                                                    qf                                               (Appendix A.1) by replacing B by D.
1324                                                              IEEE TRANSACTIONS ON MOBILE COMPUTING,           VOL. 8,   NO. 10,   OCTOBER 2009


   The signaling delay due to handoff event in the time                   The mean handoff delay per call is given by
interval Ši; i þ 1Š is given by
                                                                                      X
                                                                                      1
                                                                                                                       qa p P D
                                                                                 D¼         ðDs ðnÞ þ Dl ðnÞÞP ðnÞ ¼      ½L D þ DP R Š:        ð65Þ
               Ds
                i    ¼ Ki ðDP E þ Ji DP R Þ;             i ! 1:    ð54Þ                                                qf
                                                                                      n¼1

The mean Ds , on the handoff events is given by
          i                                                               B.3 MHMIP
            Â Ã                                                           The handoff delay computation procedure is similar to that
         E Ds ¼ qa ðDP E þ pDP R Þ;
               i                         i ! 1:                    ð55Þ
                                                                          of MIP approach. By replacing Lp by Lhp , the mean handoff
   The delay for bandwidth Bl allocation in the time
                                i
                                                                          delay per call becomes
interval Ši; i þ 1Š is given by
                                                                                                       X
                                                                                                       1
              Dl ¼ Hi DP D Ki ð1 À Ji Þ þ Lp DP D Ki Ji :
               i                           i                       ð56Þ                         Dp ¼     ðDs ðnÞ þ Dl ðnÞÞP ðnÞ
                                                                                                       n¼1                                      ð66Þ
Note that Dl depends on the random variables Ki and Ji in                                           qa
            i                                                                                      ¼ ½Lhp DP D þ DP R Š:
the current interval. If we assume that Lp and Hi do not
                                          i                                                         qf
change a lot according to i and in general they remain
constant, we obtain                                                       REFERENCES
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