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Mobility Management Approaches for Mobile IP Networks: Performance Comparison and Use Recommendations
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INTRODUCTION
IP multimedia applications are becoming popular in the
packet-based wireless networks. The integration of these
applications in wireless networks requires the support of
seamless terminal mobility. Mobile IP (MIP) has been
proposed by the Internet Engineering Task Force (IETF) to
provide global mobility in IP networks [1]. It allows
maintaining mobile terminals ongoing communications
while moving through IP network [1], [2].
In the MIP protocol, Mobile Terminal (MT) registers with
its home network from which it gets a permanent address
(home address). This address is stored in the Home Agent
(HA). It is used for identification and routing purpose. If
MT moves outside the home network visiting a foreign
network, it maintains its home address and obtains a new
one from the Foreign Agent (FA). This Foreign address is
called Care-of-Address (CoA). To allow continuity of
ongoing communications between the MT and a remote
end point, the MT shall inform the HA of its current
location when it moves outside the home network. The HA
delivers to MT the intercepted packets by tunneling them to
the MT’s current point of attachment.
IP mobility in wireless networks can be classified into
macro- and micromobility. The macromobility is the MT
mobility through different administration domains. The
micromobility is the MT movements through different
subnets belonging to a single network domain. For
micromobility where the MT movement is frequent, the
MIP concept is not suitable and needs to be improved [3].
Indeed, the processing overhead related to location update
could be high specifically under high number of MTs and
when MTs are distant from the HAs yielding to highmobility
signaling delay [4].
Hierarchical Mobile IP (HMIP) has been proposed to
reduce the number of location updates to HA and the
signaling latency when an MT moves from one subnet to
another [5], [6]. In this mobility scheme, FAs and Gateway
FAs (GFAs) are organized into a hierarchy. When an MT
changes FA within the same regional network, it updates its
CoA by performing a regional registration to the GFA.
When an MT moves to another regional network, it
performs a home registration with its HA using a publicly
routable address of GFA. The packets intercepted by the
HA are tunneled to a new GFA to which the MT is
belonging (e.g., GFA2 following MT handoff from FA3 to
FA5 in Fig. 1). The GFA checks its visitor list and forwards
the packets to the FA of the MT (FA5 in Fig. 1). This
regional registration is sensitive to the GFAs failure because
of the centralized system architecture [7], [8]. Moreover, a
high traffic load on GFAs and frequent mobility between
regional networks degrade the mobility scheme performance
[4]. In order to reduce the signaling load for
interregional networks, mobility dynamic location management
approaches for MIP have been proposed: A Hierarchical
Distributed Dynamic Mobile IP (HDDMIP) and
Dynamic Hierarchical Mobile IP (DHMIP).
In the HDDMIP approach, each FA can act either as an
FA or GFA according to the user mobility. The traffic load
1312 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 8, NO. 10, OCTOBER 2009
. The author is with INRS Energy, Materials et Telecommunications (INRSEMT),
Place Bonaventure, 800, de La Gauchetie`re West, Gate North-West,
Suite 6900, Montreal, Quebec, Canada, H5A 1K6.
E-mail: kara[at]emt.inrs.ca.
Manuscript received 21 Sept. 2007; revised 4 Jan. 2009; accepted 21 Jan. 2009;
published online 6 Feb. 2009.
For information on obtaining reprints of this article, please send e-mail to:
tmc[at]computer.org, and reference IEEECS Log Number TMC-2007-09-0290.
Digital Object Identifier no. 10.1109/TMC.2009.36.
1536-1233/09/$25.00 2009 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS
in a regional network is distributed among the FAs. The
number of FAs attached to a GFA is adjusted for each MT.
Thus, the regional network boundary varies for each MT.
This number is computed according to the MT mobility
characteristics and the incoming packet arrival rate. This
number is adjustable from time to time according to the
variation of the mobility and the packet arrival rate for each
MT. In [9] and [10], analytic models are proposed to
compute this number such as the total signaling traffic for
location update and packet delivery is transferred with
minimal network resource and low delay, respectively.
Nevertheless, this approach requires that each FA is able to
act as an FA and a GFA. Moreover, it adds processing load
on the MT to estimate the average packet arrival rate and
the subnet residence time. Hence, the main advantage of
this approach is the system robustness enhancement since
the GFA failure affects only the packets routing to MTs
belonging to this GFA. The disadvantages are the system
infrastructure and MTs costs which could be high.
The DHMIP approach has been proposed to reduce the
location update messages to the HA by registering the new
CoA to the previous FA and building a hierarchy of FAs .
Hence, the user’s packets are intercepted and tunneled
along the FAs hierarchy to the MT. The hierarchy level
numbers are dynamically adjusted based on mobile user’s
mobility and traffic load information. Fig. 2 illustrates an
example of DHMIP approach with a maximum of hierarchy
level number equal to 3. When MT is attached to FA2, FA3,
FA5, or FA6, the CoA update is sent to the previous FAs. If
the MT becomes attached to FA4 the level number reach the
threshold and the MT will set up a new hierarchy. The MT
registers its new CoA directly to the HA. In this approach,
the location update to the new FA, which is close to the
previous FAs, could be less expensive than that to the HA.
In [11], authors propose an analytic performance model to
evaluate the signaling transmission, the packet delivery, and
the total costs of HMIP, HDDMIP, and DHMIP mobility
approaches using a one-dimensional random walk model.
The performance analysis shows that the DHMIP scheme
outperforms compared to the HMIP and HDDMIP ones.
Despite that, the DHMIP approach still requires the new
location update and packet route processing in FAs
belonging to the hierarchy increasing the mobility signaling
and packet delivery delay. Moreover, the path extension
through the FAs hierarchy increases the network resources
used for packet delivery and location update signaling for
an ongoing communication.
In [12], another inter-FAs tunneling approach has been
proposed to optimize the route between the remote end
point and the MT. This approach enables remote end point
to get the CoA associated to the MT and to use it to reach
the MT through the foreigner network without passing
through the home network. When the MT moves from one
foreigner network to another, it communicates its new CoA
to its previous FA through its new FA. The previous FA
tunnels the received traffic from the remote end point to the
MT’s new location. At the same time, it sends a message to
the HA requesting that the remote end point be notified of
the MT’s new CoA. Upon receiving this new CoA, the
remote end point uses it to reach the MT through the new
foreigner network without passing through its previous
foreigner network. This approach requires to restore an
optimized route after each CoA change. It aims to transfer
packets through the resulting route with smaller delay than
that experienced when these packets transit through the
home network. However, this may not be always the case,
and such performance will depend on the route optimization
mechanism used and a set of influencing factors such
as remote end point to FAs distance, the loads of the
networks the optimized route should pass through, and the
MT inter-FAs mobility frequency. Such analysis is needed
to compare this approach with the existing ones, but it is out
of the scope of this paper.
Another alternative that reduce the signaling load in
Mobile IP network is to use a multicast-based mobility
approaches. These approaches have been proposed to
reduce the mobility signaling delay by setting a multicast
group (see Section 2). The MTs address update processes
are concentrated into the multicast network nodes (e.g.,
routers). They are reachable under these multicast group
addresses. However, these approaches could be resource
consuming except for next-generation IP-based radio access
technologies such as 3rd Generation Partnership Program
KARA: MOBILITY MANAGEMENT APPROACHES FOR MOBILE IP NETWORKS: PERFORMANCE COMPARISON AND USE... 1313
Fig. 1. MIP and DHMIP mobility approaches.
Fig. 2. DHMIP mobility approaches.
(3GPP) and 3GPP2 future cellular communication system
called Long Term Evolution (LTE) [13], [14]. In LTE
systems, where small cells deployment is expected, MT
with high mobility will be able to access different wireless
networks frequently yielding to increase traffic overhead
due to MIP signaling and tunneling. This signaling includes
not only location update signaling but also security
association signaling required for MIP support [14], [15].
HAs could be signaling traffic bottleneck for such future
mobile networks with high-mobility MTs. Hence, MHMIP
mobility approach is proposed to reduce the signaling delay
using multicast groups. The MT with high mobility could
reuse the multicast resources for signaling and packet
delivery for several handoff events that occur during its call
holding time. From that we expect that the resource usage is
no greater than that of the DHMIP mobility approach.
Hence, we propose to compute the mean bandwidth per
call and the mean handoff delay per call used for signaling
and packet delivery according to the MT mobility and call
holding time duration, and to compare the performance of a
Multicast Hierarchical Mobile IP approach (MHMIP) with
those of the DHMIP and MIP mobility strategies. We derive
a set of recommendations for the usage of these mobility
management approaches according to the MTs mobility.
The main contribution of this paper is the analytic model
that allows performance evaluation of three mobility
management approaches.
This paper is organized as follows: Section 2 discusses
the multicast-based mobility approaches. Sections 3 and 4
present the analytic model and the numerical results,
respectively. Section 5 gives the conclusions.
2 MULTICAST-BASED MOBILITY APPROACHES
2.1 Overview
The multicast has been proposed to be used for mobility
support and specifically in wireless networks with small
radio cells and high mobility of MTs. Several multicastbased
mobility approaches have been proposed. They can
be classified into multicast-based mobility in connectionoriented
and connection-less networks. For connectionoriented
networks, Acampora and Naghshineh propose a
virtual tree concept, where a multicast connection tree is
preestablished. This tree is a collection of radio base stations
and ATM network switches connected to the tree’s root. The
signaling delay is limited to the activation and deactivation
of preestablished branch in the tree [16].
For Connection-less network, Seshan, in [17], proposes to
apply a multicast to Mobile IP to reduce the handoff delay.
The HA encapsulates the intercepted packets into multicast
packets and sends them to the targeted MT over multiple
FAs. In [18], Ghai and Singh propose to divide the wireless
network into regions controlled by a supervisor host. Each
region includes groups of cells such as each cell may be part
of several of these groups. A unique IP multicast ID is
assigned to each of these groups. In [19], authors extend this
work by considering multiple wireless networks and cases
where mobile device is not able to use channel characteristics
to trigger handoffs due to the frequent network
interface change.
Different Mobile IP multicast protocols have been
proposed. In [20], Mobility Supporting Agents (MSA)-based
architecture has been proposed using IGMPv2 and PIM SM
IP multicast protocols. In [21], an Core Based Trees (CBT)-
based multicast mobile IP approach has been proposed for
micromobility. In [22], authors propose a set of multicast
mobility protocols called Candidate Access Router set (CARset).
The performance of multicast mobility approaches has
been evaluated through simulation or through analytic
models [22], [23]. In [22], a set of performance metrics (such
as handoff delay, packet loss, and bandwidth overhead due
to handoff) have been identified and evaluated for multicast
mobility approaches that have been simulated using NS2
network simulator. In [23], a software platform, set up
testbeds, has been used to analyze multicast mobility
protocols in terms of handoff delay, packets losses and
duplications, and relative TCP throughput. There is a large
number of multicast approaches that could be used to
implement mobility into MIP networks. The analysis of these
approaches and their design is not the focus of this paper.We
refer the reader to [23], where four case studies for multicastbased
mobility are presented based on different multicast
service models and protocols. In this paper, we focus on
usage of the multicast hierarchical architecture for IP
mobility support and its performance in terms of bandwidth
usage and handoff delay. The example used in this paper of
such architecture is given in Section 2.2.
2.2 Multicast Hierarchical Mobile IP
In this approach, we propose to build hierarchical multicast
groups. In each group, FAs are connected to each other
through a GFA. A set of GFAs are connected to an HA.
When an MT moves through FAs belonging to the same
group, the GFA of this group multicasts the received packet
(coming from the HA) to the MT. When the MT moves
outside a group, the new CoA is registered to the GFA of
the new group to which the MT is currently belonging. This
GFA sends this CoA to the HA. This latest tunnels the
packet to the new GFA which will multicast the received
packets within the new FAs group. This approach reduces
the frequency of the location update to the HA. This update
is performed every inter-GFAs mobility rather than every
inter-FAs mobility limiting the location update processing
only at the GFA. In this example, the group creation is static
in the sense that the numbers of groups and FAs do not
change and remain fix.
In Fig. 3, when the MT moves from FA2 to FA5, the
location registration is performed between HA and GFA2.
GFA2 multicasts packets to FA4, FA5, and FA6. Thus,
when MT moves to FA6 or FA4 there is no need for the MT
location registration. Hence, this approach allows reducing
the mobility signaling delay compared to the HMIP and
DHMIP mobility approaches specifically for high-mobility
MTs. However, it is network resources consuming approach
due to multicast protocol use. Consequently, it is
required for comparison purpose to evaluate the performance
not only in term of handoff signaling delay but also
in term of bandwidth use. This latest is the bandwidth used
for signaling transfer and packet delivery.
If we take the same MIP network architecture for the
three mobility management approaches, the bandwidth
used by MHMIP signaling is smaller than that of MIP or
1314 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 8, NO. 10, OCTOBER 2009
DHMIP approaches because the path reestablishment is
performed only between HA and GFAs. However, the
bandwidth used by an MT for packet delivery is high
because several connections are used for packets’ transfer to
the MT. It is clear that the total bandwidth used for
signaling and packet delivery in MHMIP approach is higher
than that used by the other approaches. Nevertheless, in
case of MTs with high mobility (high handoff requests), the
multicast resource in the GFA groups are reused by the MT
every handoff event that occurs during its call holding time.
Consequently, we expect that the MHMIP mean bandwidth
per call for MTs with high mobility is no greater than that of
the DHMIP and MIP mobility approaches. We also expect
that the MHMIP mean handoff delay (including signaling
and packet delivery delays) is smaller than that of the
DHMIP and MIP mobility approaches.
Hence, we propose to derive an analytic model that
allows computation of mean bandwidth and mean handoff
delay per call for MIP, DHMIP, and MHMIP mobility
approaches. These performance measurements are computed
according to the MTs mobility type (high or low) and
the call holding time duration. The model description and
the performance comparison of the three mobility approaches
are discussed in the following sections.
3 ANALYTIC MODEL
This section describes the analytic model and the set of
established assumptions.
3.1 Assumptions
Generally, during each handoff, a path reestablishment is
required to maintain or to improve call quality. This
reestablishment uses signaling messages and involves a
change in the number of links of the mobile connection.
Note that the three mobility approaches described here
are based on a mobile connection path reestablishment
which leads to perform the following operations:
. CoA update with the HA,
. new path establishment from HA to FA for DHMIP
and MIP, and from HA to GFA for MHMIP,
. user data traffic transfer from the previous path to
the new one,
. previous path discard.
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
holding time depends on the MT dwelling time in a radio
cell and the traffic type: voice or data. Several voice traffic
researches have supposed that the dwelling time in a radio
cell is an exponential distribution [24], [25]. In fact, this
assumption depends on the shape of the radio cell and the
specific distributions of the mobile’s speed and direction
which are difficult to characterize. In [26], [27], [28], [29],
[30], authors have demonstrated that the exponential
distribution for the dwelling time in radio cell is not
appropriated. They propose to replace it with complex
distributions such as Phase-Type, Lognormal, Hyperexponential,
and HyperErlang requiring the identification of
several parameters related to the selected traffic model. In
order to simplify the computation of the mean bandwidth
and mean delay per call, we consider that the time between
the handoff events and the call duration is a geometric
distribution of mean 1=qa
1 and 1=qf , respectively.
For data traffic, researches have addressed the problem
of the persistent congestion periods with non-negligible
packet losses [31], [32], [33], [34]. They show that these losses
do not allow the usage of Poisson model to model the TCP
traffic. In [33], [34], authors have demonstrated that the Self-
Similar processes are better models for TCP traffic modelization
than the exponential ones. However, in this study,
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
for the data traffic.
The proposed discrete time model is a generalization of
the one proposed in [35]. The novelty of this model consists
in the definition of generic analytical model that applies to
more than one handoff approach and that allows to
compute not only mean bandwidth due to handoff but also
mean handoff delay of the analyzed handoff approaches.
The temporal diagram given in Fig. 4 is used to compute
these means. First, we compute the bandwidth and the
delay within each interval and their means over the handoff
events. Then, we compute the bandwidth and the delay
sums over the total call holding time. Finally, we evaluate
their means over all the call durations. In order to
understand the modelization mechanism, we illustrate by
taking as an example the mean bandwidth computation. In
this figure, the holding time of ongoing call is divided into
KARA: MOBILITY MANAGEMENT APPROACHES FOR MOBILE IP NETWORKS: PERFORMANCE COMPARISON AND USE... 1315
1. The respective temporal means are obtained while multiplying by the
interval duration.
Fig. 3. Hierarchical handoff scheme.
time intervals small enough that we may assume that in
each time interval i; i þ 1, at most one handoff may occur.
In each interval, let
. n be the number of intervals for a call,
. Bl
i be the bandwidth used by a call during the time
interval i; i þ 1,
. Bsi
be the signaling bandwidth used by a call during
handoff that occurred in the time interval i; i þ 1, and
. Bi be the total bandwidth used by a call during the
time interval i; i þ 1;
Bl
i and Bsi
are random variables with values that depend on
the occurrence or not of a handoff during the interval i; i þ 1
and on the possible path reestablishment once the handoff
occurs. The variable Bl
i can take two values. When a handoff
occurs for a call in the interval i; i þ 1, Bl
i represents the sum
of the allocated bandwidth over the original path and the
one allocated over the links of the new established path.
Otherwise, it represents the bandwidth used on the link of
the ongoing connection. Bi represents the sum of the
bandwidth used by the ongoing call (Bl
i) and the bandwidth
used for signaling (Bsi
). Otherwise, it represents the allocated
bandwidth to the ongoing call (Bl
i). Then, we obtain
Bi ¼
Bl
i þ Bsi
; if a handoff occurs in i; i þ 1;
Bl
i; otherwise:
ð1Þ
The mean of Bi over the handoff events is given by
EBi
¼ EBl
i
þ EBsi
: ð2Þ
For fixed value of n, the total mean bandwidth BðnÞ used
by an ongoing call during the n time intervals is
BðnÞ ¼ BlðnÞ þ BsðnÞ ¼
Xn1
i¼0
EBl
i
þ
Xn1
i¼0
EBsi
: ð3Þ
As the call duration n is a random variable, the mean
bandwidth B is computed over all the call durations
n ¼ 1; . . . ;1. With our assumptions, the probability that a
call runs n periods is defined as PðnÞ:
PðnÞ ¼ qf ð1 qf Þn1 n ¼ 1; 2; . . . ð4Þ
such as
n ¼
X1
n¼1
nPðnÞ ¼
X1
n¼1
nqf ð1 qf Þn1
¼ qf
X1
n¼1
nð1 qf Þn1 ¼ 1=qf
represents the mean number of intervals during a call.
Then, we obtain
B ¼ B
l
þ B
s
¼
X1
n¼1
BlðnÞ þ BsðnÞ PðnÞ
¼
X1
n¼1
BlðnÞPðnÞ þ
X1
n¼1
BsðnÞPðnÞ:
ð5Þ
Let E½Bxi
; x 2 fs; lg, a variable that designates the E½Bl
i or
E½Bsi
entity. In the bandwidth computations given later,
E½Bxi
could be variable or not during a call. If variable, then
we obtain
Bx ¼
X1
n¼1
BxðnÞPðnÞ ¼
X1
n¼1
Xn1
i¼0
EBxi
PðnÞ
¼ qf
X1
n¼1
ð1 qf Þðn1ÞXn1
i¼1
EBxi
;
ð6Þ
otherwise, we have
Bx ¼
X1
n¼1
BxðnÞPðnÞ ¼
X1
n¼1
Xn1
i¼0
EBxi
PðnÞ
¼
X1
n¼1
EBx
i
Xn1
i¼0
PðnÞ ¼ EBx
i
X1
n¼1
nPðnÞ
¼ qfEBxi
X1
n¼1
nð1 qf Þðn1Þ ¼
EBxi
qf
:
ð7Þ
The same procedure applies for the mean handoff delay
computation by substituting to variable B the variable D
which represents the delay. Note that B and D are random
variables due to handoff.
In the following sections, the mean bandwidth per call is
the network bandwidth needed to support a mobile
connection over its total duration, and it is given by the
sum of the bandwidth used on the paths’ links of the
ongoing connection and the signaling bandwidth due to
handoffs. Likewise, the mean handoff delay per call is the
network handoffs’ durations to support a mobile connection
which is given by the sum of the duration of the
resource establishment on the paths’ links and the signaling
duration due to handoff. The paths’ links are the total
network links of all paths used by the ongoing connection
during its holding time. Let
. BPD be the allocated bandwidth on each link for
packet delivery of a call,
. BPE be the signaling bandwidth used per call for
each path extension,
. BPR be the signaling bandwidth used per call for
each path reestablishment,
. DPD be the duration per call to allocate bandwidth
BPD on a link of a new extended path and/or a
reestablished path,
. DPE be the signaling duration per call for a path
extension, and
. DPR be the signaling duration per call for a path
reestablishment.
Note that BPD and DPD are, respectively, the bandwidth
and the duration for packet delivery on each link of a path
1316 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 8, NO. 10, OCTOBER 2009
Fig. 4. Discrete diagram of a call holding time.
for an ongoing call. The BPD can take different fixed values
according to the traffic type carried through the path links:
voice or data (e.g., 64 kbps). A link is the network
connection between two network entities such as an FA
and a router (e.g., in Fig. 3, there is three links between the
FA1 and HA). The signaling duration is the time taken for
the transmission and the execution of the different handoff
signaling messages. The parameters BPE and DPE are,
respectively, the bandwidth and the duration necessary to
set up the path extension between two FAs involved in a
handoff. The parameters BPR and DPR include the
bandwidth and the duration, respectively, for 1) CoA
registration, 2) setting up the new portion of connection
between HA and FA in case of DHMIP and MIP, and
between HA and GFA in case of MHMIP (e.g., path between
HA and FA4 in Fig. 2), and 3) terminating the old portion of
a connection (e.g., path between HA and FA3 in Fig. 2).
3.2 DHMIP Analytic Model
The DHMIP mobility approach combines the path reestablishment
and the connection extension protocols. The
path reestablishment protocol is invoked to set up a new
FAs hierarchy. This protocol allows a path establishment
between the HA and a new FA in the new hierarchy. In
this latest, the path extension is used to maintain the
mobile connection when mobile moves through the FAs
belonging to this hierarchy. The path reestablishment may
occur after each new FAs hierarchy setup. Events that may
occur at each time i ¼ 1; 2; . . . are 1) path reestablishment,
2) path extension, and 3) call termination. Let
. p be the probability that a new FA hierarchy is set and
consequently a path reestablishment is performed,
. L be the number of links between the FA to which
the MT is attached and the remote end point with
which the MT communicates,
. Lp be the number of links between the HA and the
initial FA through which a new hierarchy is set (e.g.,
FA1 and FA4 in Fig. 2), and
. H be the number of links of the path extension
(e.g., in Fig. 2, this number is equal to 1 when MT
moves from FA1 to FA2 and becomes connected
to FA2).
L, Lp, and H are random variables with general distributions
and with mean L, Lp, and H, respectively.
The mean bandwidth per call is
Bp ¼
L
qf
BPD þ
qað1 pÞð1 qf ÞH
qf ½1 ð1 pqaÞð1 qf Þ
BPD
þ
qa
qf
ðBPE þ pBPRÞ;
ð8Þ
while the mean handoff delay per call is
Dp ¼
qa
qf
DPD½ð1 pÞH þ pLp
þ
qa
qf
½DPE þ pDPR:
ð9Þ
In (8), the first term (L
qf
BPD) represents the bandwidth
used on the original path and the paths resulting from the
reestablishment. The second term ( qað1pÞð1qf ÞH
qf ½1ð1pqaÞð1qf Þ
BPD)
represents the additional bandwidth due to the path
extensions. The last term (qa
qf
ðBPE þ pBPRÞ) represents the
signaling bandwidth due to the extensions and path
reestablishments.
In (9), the term qa=qf represents the mean number of
handoffs of a call. The second term ½DPD½ð1 pÞH þ pLp þ
DPE þ pDPR represents the handoff delay which is the sum
of the resource reservation delay on the links of the extended
and the reestablished paths (DPD½ð1 pÞH þ pLp), and the
signaling delay due to the path extensions and the path
reestablishments (DPE þ pDPR).
The reader is referred to Appendix A.1 and B.1 for a
detailed demonstration of these formulas.
3.3 MIP Analytic Model
The MIP mobility approach is based only on the path
reestablishment protocol. This latest allows maintaining
the call connectivity when the MT moves between FAs. In
this case, events that may occur at each time i ¼ 1; 2; . . .
are 1) path reestablishment and 2) call termination. Let
. qa be the probability that there is an inter-FAs
handoff and thus a partial reestablishment,
. L be the number of links between the FA to which
the MT is attached and the remote end point with
which the MT is communicating, and
. Lr be the number of links between the HA and the
new FA to which the MT moved (e.g., the number of
links between the HA and the FA3 following the
handoff from FA1 to FA3 in Fig. 1).
L and Lr are random variables with general distributions
and with mean L and Lr, respectively.
The mean bandwidth per call is
Br ¼
1
qf
LBPD þ
qa
qf
BPR
: ð10Þ
In (10), the first term 1
qf
LBPD is the bandwidth of the
original connection and the reestablished paths. The second
term qa
qf
BPR is the signaling bandwidth due to the path
reestablishments.
The mean handoff duration per call is
Dr ¼
qa
qf
ðLrDPD þ DPRÞ: ð11Þ
In (11), the term qa
qf
represents themeannumberof handoffs
for a call. The term LrDPD þ DPR represents the handoff
delay which is the sum of the delay for resource allocation on
the reestablished path (LrDPD) and the signaling delay (DPR).
Details on these computations are given in Appendix A.2
and B.2.
3.4 MHMIP Analytic Model
The MHMIP mobility approach is based on the path
reestablishment and the multicast protocols. When the MT
moves within a GFA group, the mobile connection is
maintained using the multicast protocol. When the MT
moves outside this hierarchy, a combination of the path
KARA: MOBILITY MANAGEMENT APPROACHES FOR MOBILE IP NETWORKS: PERFORMANCE COMPARISON AND USE... 1317
reestablishment and the multicast protocols allows maintaining
the call’s connection. Events that may occur at
each time i ¼ 1; 2; . . . are 1) path reestablishment and
2) call termination.
We define q0a
as the probability that there is an inter-
GFAs handoffs and thus path reestablishments such as
q0a
¼ qa with 0 1. is the fraction of inter-GFAs
MHMIP handoffs on the whole possible handoffs qa (intraand
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 theGFAhierarchies.
Lh, Lhp, and Lhs are random variables with general
distributions and with means Lh, Lhp, and Lhs, respectively.
The mean bandwidth per call is
Bh ¼
1
qf
LhBPD þ LhrBPD þ
q0
a
qf
BPR: ð12Þ
In (12), the first term 1
qf
LhBPD is the bandwidth used on
the original path and the reestablished paths. The second
term LhrBPD is associated to the multicast resources used by
the call in the GFA hierarchies. The last term q
0
a
qf
BPR is the
signaling bandwidth due to the path reestablishment
following the GFA handoffs.
The mean call duration per call is
Dh ¼
q0
a
qf
½LhpDPD þ DPR: ð13Þ
In (13), the term q
0
a
qf
is the mean number of handoffs of a
call. The second term ½LhpDPD þ DPR is the handoff delay
which is the sum of the delay of resource allocated on the
reestablished path (LhpDPD) and the signaling delay (DPR).
The details on these computations are given in
Appendix A.3 and B.3.