IEEE TRANSACTIONS ON MOBILE COMPUTING, …vikramk/YK07.pdfCDMA core network in the same manner as other CDMA radio access networks. In this approach, WLANs and CDMA networks would

Optimal Joint Session Admission Controlin Integrated WLAN and CDMA

Cellular Networks with Vertical HandoffFei Yu, Member, IEEE, and Vikram Krishnamurthy, Fellow, IEEE

Abstract—This paper considers optimizing the utilization of radio resources in a heterogeneous integrated system consisting of two

different networks: a wireless local area network (WLAN) and a wideband code division multiple access (CDMA) network. We propose

a joint session admission control scheme for multimedia traffic that maximizes overall network revenue with quality of service (QoS)

constraints over both the WLAN and the CDMA cellular networks. The WLAN operates under the IEEE 802.11e medium access

control (MAC) protocol, which supports QoS for multimedia traffic. A novel concept of effective bandwidth is used in the CDMA network

to derive the unified radio resource usage, taking into account both physical layer linear minimum mean square error (LMMSE)

receivers and characteristics of the packet traffic. Numerical examples illustrate that the network revenue earned in the proposed joint

admission control scheme is significantly larger than that when the individual networks are optimized independently with no vertical

handoff between them. The revenue gain is also significant over the scheme in which vertical handoff is supported, but admission

control is not done jointly. Furthermore, we show that the optimal joint admission control policy is a randomized policy, i.e., sessions

are admitted to the system with probabilities in some states.

Index Terms—Mobile communication systems, algorithm design and analysis, Markov processes, linear programming.

Ç

1 INTRODUCTION

WIRELESS local area network (WLAN)-based systems are

emerging as a new means of wireless public access.

Recent studies show that WLANs and wide area networks,

such as code division multiple access (CDMA) cellular

networks, will coexist to offer Internet services to users [1],

[2], [3], [4], [5]. WLANs offer relatively high data rates.

However, WLANs can only cover smaller areas (hotspots),such as hotels and airports. On the contrary, CDMA cellular

networks support low data rates, but offer a much wider

area of coverage that enables ubiquitous connectivity. The

complementary characteristics of WLANs and CDMA

cellular networks make it attractive to integrate these two

wireless access technologies. By offering integrated WLAN/

CDMA services, operators can attract a wider user base and

facilitate the introduction of high-speed wireless dataservices. Users would benefit from the lower overall cost

and the enhanced performance of the combined services.In integrated WLAN/CDMA systems, these two networks

can use the same or share a subscriber database for functionssuch as security, billing, and customer management. There-fore, a mobile user of a laptop/handheld that supports bothWLAN and CDMA access capabilities can connect to bothnetworks by roaming agreements [1], [2]. Vertical handoff (alsoreferred as handover in the literature) between WLANs andCDMA networks can be seen as the next evolutionary step

from roaming in this integrated environment. The support ofvertical handoff provides mobile users ongoing sessioncontinuity, in spite of movements across and betweenWLANs and CDMA networks [1], [4].

Although some work has been done to integrate WLANsand CDMA networks, most of the previous work concen-trates on architectures and mechanisms to support roamingand vertical handoff, and how to utilize the overall radioresource optimally subject to quality of service (QoS)constraints has not been studied in detail in this coupledenvironment. As a consequence, WLAN and CDMA net-works are studied and optimized separately in theliterature. However, the interplay between WLANs andCDMA networks plays an important role in designing theintegrated systems. Therefore, the schemes optimized foronly one network (a WLAN or CDMA network) may resultin unsatisfactory performance for the overall integratedsystems. In order to fully utilize the best of these twowireless access technologies, it is important to consider theradio resource jointly. Luo et al. [3] and Zhuang et al. [5]make fine attempts in this direction by proposing archi-tectures and schemes for joint radio resource managementand QoS provisioning. Particularly, a joint session admissioncontrol (JSAC) function is identified as a crucial unit toutilize the overall radio resource efficiently in integratedWLAN/CDMA systems. However, no further developmentabout an optimal JSAC scheme is reported in [3], [5].

In this paper, we propose an optimal joint session admissioncontrol scheme for multimedia traffic in an integrated WLAN/CDMA system with vertical handoff, which maximizes overallnetwork revenue while satisfying several QoS constraints in boththe WLAN and the CDMA network. The distinct features ofthe proposed scheme are as follows:

IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 1, JANUARY 2007 1

. The authors are with the Department of Electrical and ComputerEngineering, University of British Columbia, 2356 Main Mall, Vancouver,BC, Canada V6T 1Z4. E-mail: {feiy, vikramk}@ece.ubc.ca.

Manuscript received 20 July 2004; revised 26 July 2005; accepted 3 May 2006;published online 15 Nov. 2006.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference IEEECS Log Number TMC-0229-0704.

1536-1233/07/$20.00 � 2007 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS

. It can optimally control whether or not to admit aswell as to which network (WLAN or CDMAnetwork) to admit a new session arrival or a verticalhandoff session between the WLAN and the CDMAnetwork.

. The model takes into account the different revenuerates in the WLAN and CDMA networks, and theoverall network revenue can be maximized.

. A novel concept of effective bandwidth [6] is used inthe proposed scheme to measure the unified radioresource usage, taking into account both linearminimum-mean square error (LMMSE) receiversand varying the statistical characteristics of thepacket traffic in the CDMA network. QoS constraintsare the signal-to-interference (SIR) and SIR outageprobability in the CDMA network.

. IEEE 802.11e [7], which is a new standard forWLANs to provide QoS, is considered in ourscheme. Throughput and packet delay are consid-ered as QoS constraints in the WLAN.

. At the network layer of the integrated system, QoSconstraints are blocking probabilities of sessions,including new and vertical handoff sessions in bothnetworks. All of the above QoS constraints can beguaranteed in the proposed scheme.

We compare our scheme with two other WLAN/CDMAintegration schemes using numerical examples. It is shownthat the proposed scheme results in significant revenue gainover the scheme in which optimization is done indepen-dently in individual networks and no vertical handoff issupported between the WLAN and the CDMA network.The revenue gain is also significant when it is comparedwith the scheme in which vertical handoff is supported, butno joint admission control is used in the system. In addition,we show that the optimal policy obtained from our schemeis a randomized policy, i.e., sessions are admitted to thesystem with some probabilities when the system is incertain states.

The rest of the paper is organized as follows: Section 2describes integrated WLAN/CDMA systems and the jointsession admission control problem. Section 3 describes theQoS considerations in WLANs and CDMA networks.Section 4 presents our new approach to solve the jointsession admission control problem. Some numerical exam-ples are given in Section 5. Finally, we conclude this studyin Section 6.

2 JOINT SESSION ADMISSION CONTROL IN

INTEGRATED WLAN/CDMA SYSTEMS

In this section, we introduce the integrated WLAN andCDMA cellular networks considered in this paper. Then,we present the joint admission control problem in thisintegrated environment. We also give an overview of theproposed joint admission control algorithm.

2.1 Integrated WLAN/CDMA Systems

There are two different ways of designing an integratedWLAN/CDMA network architecture, defined as tightcoupling and loose coupling interworking [1], [2]. Fig. 1

shows the architecture for WLAN/CDMA integration,where UMTS is used as a specific example of CDMAnetworks.

In a tightly coupled system, a WLAN is connected to aCDMA core network in the same manner as other CDMAradio access networks. In this approach, WLANs andCDMA networks would use the same authentication,mobility, and billing infrastructure, and the WLAN gate-way needs to implement all the CDMA protocols requiredin the CDMA radio access network. The main advantage ofthis solution is that the mechanism for authentication,mobility, and QoS in the CDMA core network can be reuseddirectly over the WLAN. However, this approach requiresthe modifications of the design of CDMA networks toaccommodate the increased traffic from WLANs.

In the loose coupling approach, a WLAN is notconnected directly to CDMA network elements. Instead, itis connected to the Internet. In this approach, WLANs andCDMA networks use different mechanisms and protocols tohandle authentication, mobility, and billing, and the WLANtraffic would not go through the CDMA core network.Nevertheless, as peer IP domains, they can share the samesubscriber database for functions such as security, billing,and customer management.

Since mobile users are free to move in integratedWLAN/CDMA systems, the support of handoff betweenthese two networks, which provides ongoing servicecontinuity and seamlessness, is needed in this integration[1], [4]. Handoff in a heterogeneous network environment isdifferent from that in a homogeneous wireless accesssystem, where it occurs only when a mobile user movesfrom one base station (or access point) to another. While

2 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 1, JANUARY 2007

Fig. 1. Integrated WLAN and CDMA cellular networks.

handoff within a homogeneous system is called horizontalhandoff, handoff between different wireless access technol-ogies is referred to as vertical handoff [4].

2.2 The Joint Session Admission Control Problem

To support QoS in WLANs, an efficient admission control

scheme is required in IEEE 802.11e WLANs [8], [9], whereas

admission control is also crucial in designing CDMA

networks [11], [12], [13]. Since joint radio resource manage-

ment in integrated WLAN/CDMA systems is largely

ignored in most of the previous work, the admission

control schemes in these two networks are studied and

optimized separately. In the coupled WLAN/CDMA

environment, the schemes optimized for only one network

(WLAN or CDMA network) may not be optimal for the

overall integrated system. Moreover, although the session

arrivals in a WLAN coverage area normally connect to the

WLAN, there is also the alternative that some session

arrivals in the WLAN area are admitted to the CDMA

network to avoid the potential congestion in the WLAN. In

order to utilize the overall radio resource efficiently, a joint

session admission control (JSAC) is important in the

integration of these two wireless access technologies [3], [5].The problem of JSAC in the integrated WLAN/CDMA

systems is whether or not to admit and to which network(WLAN or CDMA network) to admit a new or verticalhandoff session arrival. An optimal JSAC should maximizethe average network revenue and guarantee QoS con-straints in both WLANs and CDMA networks.

Since the charging method in WLANs is usually different

from that in CDMA networks, we should consider the

different revenue rates in the design of a JSAC. For the QoS

constraints in WLANs, throughput and packet delay are

important metrics [8], [9]. Throughput should be kept above

a target value and packet delay should be kept below a

target value for a certain class of traffic. In CDMA networks,

QoS requirements are usually characterized by SIR. How-

ever, guaranteeing SIRs of all classes of traffic at all time

instants may result in low network utilization for bursty

traffic. Therefore, besides the SIR, we use another QoS

metric, namely, the SIR outage probability. Instead of

guaranteeing the SIR at all the time, we can guarantee the

SIR outage probability below some target value. In addition,

at the network layer of the integrated WLAN/CDMA

systems, QoS metrics are blocking probabilities of new and

vertical handoff sessions in both networks, which should

also be guaranteed.

2.3 Overview of the Proposed Algorithm

We propose an optimal joint session admission controlalgorithm that maximizes the overall network revenue withQoS constraints in both WLANs and CDMA networks. Anoverview of the proposed algorithm is as follows:

. The QoS Constraints in WLANs and CDMA net-works are formulated in Section 3.

. The joint session admission control problem isformulated as a semi-Markov decision process(SMDP) in Section 4. The state space of the SMDP

is defined using the QoS constraints in WLANs andCDMA networks.

. The network layer blocking probability QoS con-straints are formulated in Section 4.5.

. An optimal linear-programming-based solution tothe SMDP is presented in Section 4.6.

3 QOS IN WLANS AND CDMA CELLULAR

NETWORKS

In this section, we formulate the QoS metrics in WLANs

and CDMA cellular networks separately. These QoS metrics

will be used in the design of the optimal joint session

admission control scheme.

3.1 QoS in WLANs

Medium access control (MAC) protocols in IEEE 802.11

WLANs have great effects on the QoS metrics. We first

introduce the IEEE 802.11 MAC protocol, and then derive

QoS metrics, throughput, and packet delay in WLANs.

3.1.1 Medium Access Control in 802.11 WLANs

There are two medium access control (MAC) protocols in

IEEE 802.11 WLAN, namely, the mandatory distributed

coordination function (DCF) and the optional point co-

ordination function (PCF). DCF is a carrier sense multiple

access with a collision avoidance (CSMA/CA) mechanism.

A station that intends to transmit a packet has to sense the

channel as idle for a minimum duration called DCF

interframe space (DIFS). The station can immediately

transmit the packet if the channel is sensed idle for DIFS.

Otherwise, the station will generate a backoff time counter,

which is randomly selected from the range ð0; CWÞ, where

CW is the contention window. At the first transmitting

temp, CW is assigned a value CWmin. If the transmission is

not successful due to collision, the value of CW is increased

up to a maximum value CWmax ¼ 2mCWmin, where m is the

maximum backoff stage. Although CDF is a simple and

robust MAC protocol, it is not suitable for multimedia

applications with QoS requirements, such as video and

voice. The optional PCF is designed to support some forms

of QoS. However, PCF has not been widely implemented

and deployed due to some serious limitations [14].To support QoS in WLAN, a new MAC protocol, IEEE

802.11e, is proposed [7]. The IEEE 802.11e MAC employs a

channel access function called the hybrid coordination

function (HCF), which includes a contention-based HCF

part and a contention-free part. The contention-based HCF

part is also called the enhanced distributed coordination

function (EDCF). EDCF provides differentiated access to the

wireless medium for up to eight priorities. An access

category (AC) mechanism is defined to support the

priorities. There are four access categories (ACs). For access

category j; j ¼ 1; 2; 3; 4, there is a set of parameters, including

transmission opportunity (TXOPj), arbitration interframe

space number (AIFSNj), minimum contention window

(CWj;min), maximum contention window (CWj;max), and

maximum backoff stage (mj), which are announced by the

access point (AP).

YU AND KRISHNAMURTHY: OPTIMAL JOINT SESSION ADMISSION CONTROL IN INTEGRATED WLAN AND CDMA CELLULAR NETWORKS... 3

3.1.2 Throughput and Packet Delay Constraints

Throughput and packet delay are important QoS metrics formultimedia traffic in WLANs. Our goal here is to formulatethroughput and packet delay constraints, which will beused in Section 4 to formulate a constrained joint admissioncontrol problem. We adopt the derivation of throughputand packet delay for IEEE 802.11e in [9] in this paper. Let �denote the length of a time slot, M denote the average bitrate of WLAN, TSIFS denote the duration of a shortinterframe space (SIFS), TRTS , TCTS , TACK , TPHY , andTMAC denote the time required to transmit a request-to-send (RTS), a clear-to-send (CTS), an ACK, a physical layerheader, and an MAC header. Assume that all packets have aconstant propagation delay �. There are J classes of trafficwith distinct QoS requirements in the system. The numberof class j; j ¼ 1; 2; . . . ; J stations in the WLAN is nw;j.Assume that a class j; j ¼ 1; 2; . . . ; J packet has a constantprobability of collision, pj, all class j packets have the samelength, Sj, and the propagation delay of all packets isconstant, �. The average backoff counter of the class j

station E½BOj� is [9]

ð1� 2pjÞðCWj;min � 1Þ þ pjCWj;minð1� ð2pjÞmjÞ=2ð1� 2pjÞ:

The probability for a class j station to transmit a packet is

qj ¼ 2ð1� 2pjÞ=ð1� 2pjÞðCWj;min þ 1þAIFSNjÞþ pjCWj;min½1� ð2pkÞmj �:

The probability of collision can be calculated as

pj ¼ 1� ð1� qjÞðnw;j�1Þ Y1�i�J;i 6¼j

ð1� qjÞnw;i :

qj and pj can be obtained by solving the above equationsusing numerical techniques. The saturation bandwidth forclass j traffic is [9]

Bj ¼Vj

TI þ TC þ TS; ð1Þ

where Vj is the number of bits successfully transmitted forclass j during a transmission cycle. Vj can be computed asVj ¼ kjUjSj, where kj is the probability that a class j packetis successfully transmitted during a transmission cycle, Uj isthe number of class j packets that can be transmitted withinTXOPj, and Sj is the packet length.

Vj ¼ kjUjSj ¼nw;jqjð1� qjÞnw;j�1 Q

1�i�J;i 6¼jð1� qiÞnw;i

PJi¼1

nw;iqið1� qiÞnw;i�1 Q1�i�J;i6¼j

ð1� qiÞnw;iTXOPj þ TSIFSTSIFS þ Lj

M þ TACK

$ %Sj:

ð2Þ

TI in (1) is the average time of all idle periods during atransmission cycle,

TI ¼

Q1�i�J

ð1� qiÞnw;i

PJj¼0

nw;jqjð1� qjÞnw;j�1 Q1�i�J;i 6¼j

ð1� qiÞnw;i�: ð3Þ

TC in (1) is the average time of all collision periods during atransmission cycle,

TC ¼

1�Q

1�i�Jð1� qiÞnw;i �

PJj¼1

nw;jqjð1� qjÞnw;j�1 Q1�i�J;i6¼j

ð1� qiÞnw;i

PJj¼1

nw;jqjð1� qjÞnw;j�1 Q1�i�J;i 6¼j

ð1� qiÞnw;i

TRTS þ TSIFS þ �XJj¼0

kjAIFSj þ � !

:

ð4Þ

TS in (1) is the average time of the successful transmissionperiod during a transmission cycle,

TS ¼ 4TSIFS þ �XJj¼1

kjAIFSj þ TRTS þ 4�þ TCTS

þ TPHY þ TMAC þ

PJj¼1

Vj

Mþ TACK þ

XJj¼1

kjUj:

ð5Þ

The average packet delay of class j traffic is [9]

Dj ¼ bj þajpj

ð1� pjÞ2; ð6Þ

where

bj ¼ ð1=UjÞ½�E½BOj� þ 4TSIFS þ �AIFSNj þ TRTS þ 3�

þ TCTS þ TPHY þ TMAC þ Lj=M þ TACK þ ðNj � 1Þð2TSIFS þ TPHY þ TMAC þ Sj=M þ 2�þ TACKÞ�

and

aj ¼ð1=UjÞð�E½BOj� þ TSIFS þ �AIFSNj þ TRTS þ TSIFS þ �Þ:

The throughput constraints and average packet delayconstraints will be satisfied if the vector

xw ¼ ðnw;1; nw;2; . . . ; nw;JÞ

lies within the WLAN admissible set

XW ¼ xw 2 ZZJþ : Bj � TBj;Dj � TDj; j ¼ 1; 2; . . . ; J� �

; ð7Þ

where Bj is defined in (1), Dj is defined in (6), and TBj andTDj are the target throughput and average packet delay,respectively, for class j traffic.

Note that the above throughput and average packetdelay QoS constraints are derived under the assumption ofa saturated network, in which the maximum load is carriedin the system in stable conditions [10]. In practice, however,this assumption may not hold. Nevertheless, the jointadmission control scheme proposed in this paper is alsoapplicable to other QoS constraints in WLANs derivedunder different conditions as long as the admissible set canbe expressed explicitly.


3.2 QoS in CDMA Cellular Networks

In CDMA cellular networks, admission control is usually

designed independently of power control and access control;

this is a practically feasible and widely used methodology

[12], [13]. As a consequence, physical layer SIR and SIR

outage are important QoS constraints and are widely used in

solving the CDMA admission control problem [6], [12], [13],

[15]. Following these studies, we use SIR and SIR outage as

the QoS constraints in this paper. In order to derive the SIR

and the SIR outage probability, we present the asymptotic

system capacity and the minimum transmit power control

solution for CDMA networks with linear minimum mean

square error (LMMSE) receivers. We also introduce the

concept of effective bandwidth to incorporate both LMMSE

physical layer and characteristic of the packet traffic in the

derivation of SIR outage probability.

3.2.1 Fading Channel and Linear Multiuser Detector

Physical Layer Model

Consider a synchronous CDMA system with spreading

gain N and K users. There are J classes of traffic in the

system. An important physical layer performance measure

of class j users is the signal-to-interference, SIRj, which

should be kept above the target value !j. Note that we do

not need a specific mapping policy to map one class in

WLANs to another class in CDMA networks. Our proposed

scheme is general enough to be applicable to different

mapping policies. The signature sequences of all users are

independent and randomly chosen. Due to multipath

fading, each user appears as L resolvable paths or

components at the receiver. The path l of user k is

characterized by its estimated average channel gain �hkland its estimation error variance �2

k. Linear minimum mean

square error (LMMSE) detectors are used at the receiver to

recover the transmitted information. In a large system (both

N and K are large) with background noise �2, the SIR for

the LMMSE receiver of a user (say, the first one) can be

expressed approximately as [15]

SIR1 ¼P1

PLl¼1

j�h1lj2�

1þ P1�21�

; ð8Þ

where P1 is the attenuated transmitted power from user 1, �is the unique fixed point in ð0;1Þ that satisfies

� ¼ �2 þ 1

N

XKk¼2

ðL� 1ÞIð�2k; �Þ þ I

XLl¼1

j �hklj2 þ �2k; �

! !" #�1

;

ð9Þ

and

Ið�; �Þ ¼ �

1þ �� : ð10Þ

Assume that the all users in the same class have the same

average channel gain j�hjj2 ¼PL

l¼1 j�hjlj2; j ¼ q1; 2; . . . ; J . In

[13], it is shown that a minimum received power solution

exists such that all users in the system meet their target SIRs

if and only if

!j <j�hjj2

�2j

ð11Þ

and

1

N

XJj¼1

Xnc;ji¼1

Rij�j < 1; ð12Þ

where nc;j is the number of class j sessions in the CDMAcell, Ri

j is the number of signature sequences assigned to theith session of class j to make it transmit at Ri

j times the basicrate (obtained using the lowest spreading gain N), and

�j ¼ ðL� 1Þ!j�2j

j�hjj2þ!j 1þ �2

j

j�hjj2� �1þ !j

: ð13Þ

The minimum received power solution for a class 1 user is

P1 ¼!1�

2

j�h1j2 1� !1�2

1

j�h1j2� �

1� 1N

PJj¼1

Pnc;ji¼1

Rij�j

! : ð14Þ

3.2.2 Effective Bandwidth

The effective bandwidth of a traffic source in CDMAnetworks is defined as follows [6]:

Definition 3.1. Let L denote the number of resolvable paths thateach user appears at the receiver, j�hjj2 denote the estimatedaverage channel gain, and �2

j denote the channel estimationerror variance of class j sessions with a SIR target value !j ina CDMA system with spreading gain N . Let Rj½0; t� denotethe amount of work generated from a session of class j in thetime interval ½0; t�. The effective bandwidth of this session is

�jðL; h; �; !; s; tÞ ¼1

stlog E esRj½0;t��j=N

h i;

L 2 ZZþ; h; �; !; s; t 2 IRþ;ð15Þ

where �j is defined in (13).

Remark. The definition above incorporates both physicallayer LMMSE receivers and network layer packettraffic information. The physical interpretation of�jðL; h; �; !; s; tÞ is that, using the effective bandwidthconcept, we can have a unified measure of resourceusage given the physical layer wireless fading channelsin CDMA systems, statistical characteristics of thepacket traffic, and QoS requirements at both physicaland network layers. We assume that the effectivebandwidth of a session cannot be changed during thelifetime of that session in CDMA networks.

3.2.3 SIR Outage Probability

In this section, we derive the SIR outage probability usingeffective bandwidth, which will be used in Section 4. Thederivation is similar to that in [16]. SIR is an importantphysical layer QoS measure in CDMA networks. However,guaranteeing the SIR of all sessions at all time instants willresult in low network utilization, especially when the traffic


is bursty. This is similar to the philosophy in wireline

networks that allocating all sessions with their peak

bandwidths guarantees no packet loss, but results in the

lowest network utilization and no multiplexing gain. Most

bandwidth allocation and admission control schemes inwireline networks allow a small packet loss probability to

increase the network utilization [17]. Similarly, since most

applications in wireless networks can tolerate a small

probability of SIR outage, we introduce the SIR outage

probability in wireless packet CDMA networks. We assume

that there is a mix of a large number of different types of

sessions in CDMA networks.From (12), we can see that SIR outage probability can be

expressed as

P out ¼ P 1

N

XJj¼1

Xnc;ji¼1

Rij�j � 1

( ): ð16Þ

Using the Chernoff bound yields

logP out � log E e

sN

PJj¼1

Pnc;ji¼1

Rij�j�1

264

375: ð17Þ

In a packet bufferless CDMA system, the scaled

logarithmic moment generating function of the instanta-

neous work load of a class j session is

�j ¼ limt!0

�jðL; h; �; !;s

t; tÞ ¼ 1

slog E esRj�j=N

h i: ð18Þ

Therefore, (17) becomes

logP out � log E e

sN

PJj¼1

Pnc;ji¼1

Rij�j�1

264

375 ¼ s XJ

j¼1

nc;j�j � 1

!: ð19Þ

The SIR outage probability constraint P out � TP out will

be satisfied if the vector xc ¼ ðnc;1; nc;2; . . . ; nc;JÞ lies within

the admissible set

XC ¼ xc 2 ZZJþ : infs

sXJj¼1

nc;j�j � 1

!" #� logTP out

( ):

ð20Þ

Assume that s� attains the infimum in (20). An improved

bound can be derived using tilted approximations [16].

P out ¼ P 1

N

XJj¼1

Xnc;ji¼1

Rij�j � 1

( )�

exp s�PJj¼1

nc;j�j � 1

!" #

s� 2�N

PJj¼1

nc;j@2

@s2 ðs�jÞ" #2

:

ð21Þ

4 FORMULATION OF THE JOINT SESSION

ADMISSION CONTROL PROBLEM AS AN SMDP

In this section, the optimal session admission control (JSAC)problem is formulated as a semi-Markov decision process(SMDP) [18]. When a new or vertical handoff session

arrives, a decision must be made as to whether or not toadmit and to which network (WLAN or CDMA network) toadmit the arrival. These time instants are called decisionepochs and decisions are called actions in the SMDPframework. The action chosen is based on the current stateof the integrated system. The state information includes thenumber of sessions of each class of traffic in both the WLANand the CDMA network. The QoS constraints in bothnetworks described in Section 3 are incorporated bytruncating the state space to those points that satisfy theconstraints. The optimality criterion for the SMDP is thelong-run average reward per unit time. A linear program-ming (LP) algorithm is used to provide the optimal jointadmission control policy. Network layer blocking prob-ability QoS constraints are accommodated by addingadditional linear constraints to the LP. Since sample pathconstraints are included in the LP, the optimal policy will ingeneral be a randomized stationary policy [19].

For simplicity of the presentation, we consider anintegrated WLAN/CDMA system with a single WLANcell and a single CDMA cell shown in Fig. 1, where theWLAN coverage is within the CDMA cell. Note that theshapes of the cells do not necessarily need to be hexagonaland circle in our formulation. The generalization of ourscheme to multiple WLAN and CDMA cells is given inSection 4.7. We divide the CDMA cell into two areas,CDMA area and WLAN area. Mobile users in the WLANarea can access both the WLAN and the CDMA network,whereas mobile users in the CDMA area can only access theCDMA network. We assume that there are J classes oftraffic. Class j; j ¼ 1; 2; . . . ; J new sessions arrive accordingto a Poisson distribution with the rate of c;n;j (w;n;j) in theCDMA (WLAN) area. Class j vertical handoff sessionsdepart from the CDMA network (WLAN) to the WLAN(CDMA network) according to a Poisson distribution withrate of c;h;j (w;h;j). Session duration time for class j traffic isexponentially distributed with the mean 1=c;t (1=w;t) inthe CDMA (WLAN) area. For mathematical derivation, wehave the above Poisson handoff departure assumption. In[21], a necessary and sufficient condition is given for ourassumption to hold.

Remark. The Poisson arrivals are required to define theempirical blocking probability as a time average—thisfollows from the Poisson arrivals see time averages(PASTA) theorem. As a result, the blocking probabilitiesbecome an infinite horizon average constraint in theSMDP. The exponential holding time assumption isneeded for the SMDP formulation—otherwise, we wouldend up with a Generalized SMDP (GSMDP)—whichdoes not admit a linear program to obtain the optimalsolution. In the GSMDP (i.e., if we relax the Possionarrival and exponential holding time assumptions), theadmission control policies developed in this paper can beviewed as a suboptimal solution to an otherwise difficult(and intractable) problem.

In order to obtain the optimal solution, it is necessaryto identify the state space, decision epochs, actions, statedynamics, reward, and constraints in integrated WLAN/CDMA systems.


4.1 State Space

Define row vector xwðtÞ ¼ ½nw;1ðtÞ; nw;2ðtÞ; . . . ; nw;JðtÞ� 2 ZZJþ,where nw;jðtÞ denotes the number of class j sessions in theWLAN. Define row vector

xcðtÞ ¼ ½nc;1ðtÞ; nc;2ðtÞ; . . . ; nc;JðtÞ� 2 ZZJþ;

where nc;jðtÞ denotes the number of class j sessions in theCDMA cell. The state vector of the system at decisionepoch t is given by

xðtÞ ¼ ½xwðtÞ;xcðtÞ�¼ ½nw;1ðtÞ; nw;2ðtÞ; . . . ; nw;JðtÞ; nc;1ðtÞ; nc;2ðtÞ; . . . ; nc;JðtÞ�:

ð22Þ

The state space X of the system comprises of any statevector such that the throughput and average packet delayconstraints in the WLAN cell and the SIR outage probabilityconstraint in CDMA cell can be met. Therefore, the statespace of the SMDP can be defined as

X ¼n

x ¼ ½xw;xc� ¼ ½nw;1; nw;2; . . . ; nw;J ; nc;1; nc;2; . . . ; nc;J �

2 ZZ2Jþ ; Bj� TBj;Dj� TDj; P

out� TP out; j¼1; 2; . . . ; Jo;

ð23Þ

where Bj, Dj, and P out are defined in (1), (6), and (21),respectively.

4.2 Decision Epochs and Actions

When a new or vertical handoff session arrives, the JSACmakes an admission decision. The natural decision epochsfor the SMDP are the session arrival points. However, eachtime when a session departure occurs, the state of thesystem also changes. Therefore, similar to [12], we choosethe decision epochs to be the set of all session arrival anddeparture instances. Let t0 ¼ 0. The decision epochs aretaken to be the instances tk; k ¼ 0; 1; 2; . . . . At each decisionepoch tk, the network makes a decision for each possiblesession arrival that may occur in the time interval ðtk; tkþ1�.These decisions are collectively referred to as an action.Action aðtkÞ at decision epoch tk is defined as

aðtkÞ ¼ ½ac;nðtkÞ; ac;hðtkÞ; aw;nðtkÞ; aw;hðtkÞ�;

where ac;nðtkÞ, ac;hðtkÞ, aw;nðtkÞ, and aw;hðtkÞ are defined andinterpreted as follows:

. Define row vector

ac;nðtkÞ ¼ ½ac;n;1ðtkÞ; ac;n;2ðtkÞ; . . . ; ac;n;JðtkÞ� 2 f0; 1gJ ;

where ac;n;jðtkÞ denotes the action for class j newsession arrivals in the CDMA area at decisionepoch tk. If ac;n;jðtkÞ ¼ 1, a new class j session thatarrives in the CDMA area in the interval ðtk; tkþ1� isadmitted to the CDMA network. If ac;n;j ¼ 0, it isrejected.

. Define row vector

ac;hðtkÞ ¼ ½ac;h;1ðtkÞ; ac;h;2ðtkÞ; . . . ; ac;h;JðtkÞ� 2 f0; 1gJ ;

where ac;h;jðtkÞ denotes the action for class j verticalhandoff arrivals to the CDMA cell at decision epochtk. If ac;h;jðtkÞ ¼ 1, a vertical handoff class j session

that arrives in the CDMA area in the intervalðtk; tkþ1� is admitted to the CDMA network. Ifac;h;j ¼ 0, it is rejected.

. Define row vector

aw;nðtkÞ ¼ ½aw;n;1ðtkÞ; aw;n;2ðtkÞ; . . . ; aw;n;JðtkÞ� 2 f�1; 0; 1gJ ;

where aw;n;jðtkÞ denotes the action for class j newsession arrivals in the WLAN area at decisionepoch tk. If aw;n;jðtkÞ ¼ 1, a new class j session thatarrives in the WLAN area in the interval ðtk; tkþ1� isadmitted to the WLAN. If aw;n;j ¼ �1, it is admittedto the CDMA network. If aw;n;j ¼ 0, it is rejected.

. Define row vector

aw;hðtkÞ ¼ ½aw;h;1ðtkÞ; aw;h;2ðtkÞ; . . . ; aw;h;JðtkÞ� 2 f0; 1gJ ;

where aw;h;jðtkÞ denotes the action for class j verticalhandoff arrivals to the WLAN cell at decisionepoch tk. If aw;h;jðtkÞ ¼ 1, a vertical handoff class jsession that arrives in the WLAN area in the intervalðtk; tkþ1� is admitted to the WLAN network, ifac;h;j ¼ 0, it is kept in the CDMA network.

The action space can be defined as

A ¼�a ¼ ½ac;n; ac;h; aw;n; aw;h� : ac;n 2 f0; 1gJ ; ac;h 2 f0; 1gJ ;aw;n 2 f�1; 0; 1gJ ; an;h 2 f0; 1gJ ; j ¼ 1; 2; . . . ; J

�:

ð24Þ

For a given state x 2 X, a selected action should notresult in a transition to a state that is not in X. In addition,action ð0; 0; . . . ; 0Þ should not be the only possible action instate ð0; 0; . . . ; 0Þ. Otherwise, new sessions are neveradmitted into the network and the system cannot evolve.The action space of a given state x 2 X is defined as

Ax ¼ fa 2 A : aw;n;j 6¼ 1 and aw;h;j ¼ 0 if ½ðxw þ euj Þ;xc� 62 X;

ac;n;j ¼ 0 and ac;h;j ¼ 0 if ½xw; ðxc þ euj Þ� 62 X;

j ¼ 1; 2; . . . ; J; and a 6¼ ð0; 0; . . . ; 0Þ if x ¼ ð0; 0; . . . ; 0Þg;ð25Þ

where euj 2 f0; 1gJ denotes a row vector containing only

zeros except for the jth component, which is 1. xw þ eujcorresponds to an increase of the number of class j sessionsby 1 in the WLAN. xc þ euj corresponds to an increase of thenumber of class j sessions by 1 in the CDMA cell.

4.3 State Dynamics

The state dynamics of the system can be characterized bythe state transition probabilities of the embedded chain andthe expected sojourn time �xðaÞ for each state-action pair[21, p. 347], [22, p. 121]:

pxyðaÞ ¼4 Pðxðtkþ1Þ ¼ yjxðtkÞ ¼ x; aðtkÞ ¼ aÞ; ð26Þ

�xðaÞ ¼4 Efttþ1 � tkjxðtkÞ ¼ x; aðtkÞ ¼ ag: ð27Þ

The cumulative process consists of a session arrival

process with ratePJ

j¼1ðc;n;j þ w;h;jnw;j þ w;n;j þ c;h;jnc;jÞif class j new and vertical handoff sessions can

be admitted in both WLAN and CDMA cells (i.e.,


ac;n;j ¼ ac;h;j ¼ aw;n;j ¼ aw;h;j ¼ 1) and a session departure

process with ratePJ

j¼1ðc;t;jnc;j þ w;t;jnw;jÞ. The cumula-

tive event rate is the sum of the rates of all constituent

processes and the expected sojourn time is the inverse of

the event rate

�xðaÞ ¼"XJj¼1

ðc;n;jac;n;j þ w;h;jnw;j þ w;n;jjaw;n;jj

þ c;h;jnc;jaw;h;jÞ þXJj¼1

ðc;t;jnc;j þ w;t;jnw;jÞ#�1

:

ð28Þ

To derive the transition probabilities, we use the decom-position property of a Poisson process: An event of certaintype occurs (e.g., class j arrival) with a probability equal tothe ratio between the rate of that particular type of event andthe total cumulative event rate 1=�xðaÞ. Therefore, the statetransition probabilities of the embedded Markov chain are

pxyðaÞ ¼½c;n;jac;n;j þ w;n;j�ð�aw;n;jÞ��xðaÞ; if y ¼ ½xw;xc þ euj �w;n;j�ðaw;n;jÞ�xðaÞ; if y ¼ ½xw þ euj ;xc�w;h;jnw;jac;h;j�xðaÞ; if y ¼ ½xw � euj ;xc þ euj �c;h;jnc;jaw;h;j�xðaÞ; if y ¼ ½xw þ euj ;xc � euj �c;t;jnc;j�xðaÞ; if y ¼ ½xw;xc � euj �w;t;j þ w;h;jð1� ac;h;jÞ� �

nw;j�xðaÞ; if y ¼ ½xw � euj ;xc�0; otherwise;

;

8>>>>>>>>>>><>>>>>>>>>>>:

ð29Þ

where �ðxÞ is defined as

�ðxÞ ¼ 0; if x � 01; if x > 0:

�

4.4 Policy, Performance Criterion, and RewardFunction

For each given state x 2 X, an action a 2 Ax is chosenaccording to a policy ux 2 U, where U is a set of admissiblepolicies defined as

U ¼ u : X! A j ux 2 Ax; 8x 2 Xf g: ð30Þ

The average reward criterion is considered the performancecriterion in this paper. For any policy u 2 U and an initialstate x0, the average reward is defined as

Juðx0Þ ¼ limT!1

1

TE

Z T

0

rðxðtÞ; aðtÞÞdt�

; ð31Þ

where T is the time that the SMDP evolves. rðxðtÞ; aðtÞÞ isthe expected reward until the next decision epoch when aðtÞis selected in state xðtÞ. The aim is to find an optimal policyu� that maximizes Juðx0Þ for any initial state x0. We assumethat the embedded chain considered in this paper is aunichain, which is a common assumption in the CACcontext [12], [13]. With the unichain assumption, an optimalpolicy exists and can be obtained by solving the linearprogram associated with the SMDP. Based on the action ataken in a state x, a reward rðx; aÞ occurs to the network.

Proposition 4.1. The reward for state-action pair ðx; aÞ can beexpressed as

rðx; aÞ ¼XJj¼1

½wc;n;jac;n;j þ wc;h;jac;h;j þ ww;n;j�ðaw;n;jÞþ

wc;n;j�ð�aw;n;jÞ þ ww;h;jaw;h;j þ wc;n;jð1� aw;h;jÞ�;ð32Þ

where wc;n;j 2 IRþ, wc;h;j 2 IRþ, ww;n;j 2 IRþ, and ww;h;j 2IRþ are the weights associated with class j new sessions in theCDMA network, handoff sessions in the CDMA networks,new sessions in the WLAN, and handoff sessions in theWLAN, respectively.

Proof. See the Appendix. tu

4.5 Constraints

In the formulated problem, the SIR outage probabilityconstraint in the system can be guaranteed by restricting thestate space in (20). In addition, it is desirable for the networkoperator to put constraints on blocking probabilities of certainclasses of traffic. For example, in the case of networkcongestion, the network operator may want to have a smallblocking proability for premium classes and a large blockingprobability for economic classes. Therefore, we need to form-ulate session blocking probability constraints in our model.

Proposition 4.2. The new session blocking probability constraintsPbc;n;j � c;n;j in the CDMA networks can be addressed in the

linear programming formulation in (33) by defining a costfunction related to these constraints cbc;n;jðx; aÞ ¼ 1� ac;n;jðxÞ.Similarly, the cost function related to the vertical handoff sessionblocking probability constraints Pj

c;h;j � c;h;j in the CDMAnetwork are cbc;h;jðx; aÞ ¼ 1� ac;h;jðxÞ. The cost functionrelated to the new session blocking probability constraintsPjw;n;j � w;n;j in the WLAN are cbw;n;jðx; aÞ ¼ 1� jaw;n;jðxÞj.

The cost function related to the vertical handoff session blockingprobability constraints Pj

w;h;j � w;h;j in the WLAN arecbw;h;jðx; aÞ ¼ 1� aw;h;jðxÞ.

Proof. See the Appendix. tu

4.6 Linear Programming Solution to the SMDP

Due to the constraints in the above SMDP formulation, it isnatural to use the linear programming methodology to com-pute the optimal policy. The optimal policy u� of the SMDP isobtained by solving the following linear program [19]:

maxzxa�0;x2X;a2Ax

Xx2X

Xa2Ax

rðx; aÞ�xðaÞzxa;

subject toXa2Ay

zya �Xx2X

Xa2Ax

pxyðaÞzxa ¼ 0;y 2 X

Xx2X

Xa2Ax

zxa�xðaÞ ¼ 1;

Xx2X

Xa2Ax

ð1� ac;n;jðxÞÞzxa�xðaÞ � c;n;j; j ¼ 1; 2; . . . ; J;

Xx2X

Xa2Ax

ð1� ac;h;jðxÞÞzxa�xðaÞ � c;h;j; j ¼ 1; 2; . . . ; J;

Xx2X

Xa2Ax

ð1� jaw;n;jðxÞjÞzxa�xðaÞ � w;n;j; j ¼ 1; 2; . . . ; J;

Xx2X

Xa2Ax

ð1� aw;h;jðxÞÞzxa�xðaÞ � w;h;j; j ¼ 1; 2; . . . ; J:

ð33Þ


The decision variables are zxa;x 2 X; a 2 Ax. The termzxa�xðaÞ can be interpreted as the steady-state probabilityof the system being in state x and a is chosen. The firstconstraint is a balance equation and the second constraintcan guarantee that the sum of the steady-state probabil-ities to be one. The new blocking probabilities in theCDMA network, vertical handoff blocking probabilities inthe CDMA network, new blocking probabilities in theWLAN, and vertical handoff blocking probabilities in theWLAN are expressed in the third, forth, fifth, and sixthconstraints, respectively. Since sample path constraints areincluded in (33), the optimal policy obtained will be arandomized policy: The optimal action a� 2 Ax for state xis chosen probabilistically according to the probabilitieszxa=

Pa 2 Axzxa. Feasibility of the linear program can be

checked by well known “Phase 1” simplex methods [20].For large linear programs, Phase 1 methods based oninterior point methods can be used, which are availablein linprog in Matlab. We use linprog to solve the LP inthe numerical examples.

4.7 Computational Complexity andImplementation Issues

Here, we discuss the computational complexity of theproposed algorithm and some issues about the implemen-tation of the SMDP-based joint admission control scheme.

To obtain the optimal JSAC policy as the solution of LP(33), we need to 1) construct the state space X in (23) and2) solve the LP in (33). Both procedures are done offline.Constructing X involves a finite number of QoS constraintsfeasibility evaluations in both networks. Since if all actionsessions satisfy their QoS constraints, then the departure ofany active session results in the remaining users stillsatisfying their QoS requirements, the state space X iscoordinate convex. That is, X satisfies the following twoproperties: 1) if xþ euj 2 X for some j, then x 2 X, and 2) ifx =2 X, then xþ euj =2 X for all j. Therefore, not each point inX needs to be checked, which greatly simplifies theprocedure 1). The complexity of procedure 2) is polynomialin the number of decision variables in the LP, which can besolved in polynomial time by interior point methods. Thecomplexity of procedures 1) and 2) can be decreased byreducing the cardinality of the state space X, which can beachieved by reducing the number of traffic classes underconsiderations in integrated WLAN/CDMA systems.

Once we have the optimal JSAC policy, the JSACcontroller just checks the current system state (the numberof sessions of each class of traffic in both the WLAN and theCDMA network) whether there is a new (vertical handoff)session arrival and executes the policy (admit, reject, oradmit with a probability). In practice, we can implement acentralized JSAC controller that controls both the WLANand the CDMA network [3], which is suitable for a tightly

coupled WLAN/CDMA system. In this case, the JSACcontroller knows the state of two networks all the time. In aloosely coupled WLAN/CDMA system, our scheme can beimplemented in a distributed manner, i.e., a JSAC controllerin the WLAN and another one in the CDMA network. Inthis approach, exchanging status information between themis needed, which is a common technique in designingdistributed control schemes [24].

The structure of the SMDP-based optimal joint sessionadmission control scheme is shown in Fig. 2. When an event(either a session arrival or departure) occurs, a state x isidentified by getting the numbers of different sessions in thesystem. Then, an action aðxÞ is found according to the state.The controller executes the action (rejects or admits). Whenthe next event occurs, the process is repeated.

For real networks with multiple WLAN/CDMA cells,the state space and the computational complexity will beincreased dramatically. As a consequence, linear program-ming may not be a feasible method to solve the SMDP.Fortunately, recent advances in reinforcement learning [25]can be used to break the curse of dimensionality. Theformulations (e.g., the state space, actions, and decisionepochs) in this paper are still applicable in the reinforce-ment learning method.

5 NUMERICAL RESULTS

In this section, we illustrate the performance of theproposed optimal JSAC scheme by numerical examples.We show that the proposed scheme can achieve significantperformance improvement over two other WLAN/CDMAintegration schemes. In the first scheme, admission controlis done independently in individual networks and there isno vertical handoff between the WLAN and the CDMAnetwork. Due to the overlay of these two networks, weassume that half of the new session arrivals in the WLANarea will request admissions to the CDMA network, and therest will request to the WLAN network. When a mobile userwith a WLAN session moves from the WLAN area, it willbe dropped because there is no vertical handoff mechanismbetween these two networks. This scenario representscurrent systems in practice where WLANs and cellularnetworks are two isolated networks. In the second scheme,vertical handoff between these two networks can besupported. We assume that new session arrivals in theWLAN area will request admissions to the WLAN. When amobile user with a WLAN session moves from the WLANarea, it will handoff to the CDMA network if there is freebandwidth available in the CDMA network. On the otherhand, when a mobile user with a CDMA session moves intothe WLAN area, it will handoff to the WLAN if there is freebandwidth there. Otherwise, the mobile user will remain inthe CDMA network. Note that there is no joint sessionadmission control and joint radio resource management in


Fig. 2. The structure of the proposed optimal joint session admission control scheme.

this scheme. Moreover, we show that the QoS in differentnetworks can be guaranteed in the proposed scheme. Theoptimal policy obtained from the proposed scheme is alsogiven in this section.

One class of video traffic is considered in an integratedWLAN/CDMA system with a single WLAN cell and asingle CDMA cell. Each video flow is 1.17 Mbps in theWLAN, which is generated by a constant interarrival time10ms with a constant payload size of 1,464 bytes. Itcorresponds to a traffic-shaped constant bit rate (CBR)video flow. IEEE 802.11b physical layer is used and theaverage bit rate is assumed to be 11Mbps. The numericalvalues for the WLAN system parameters are given inTable 1. Because of the scarce bandwidth available incellular networks and the small screen of handsets, weassume that the bandwidth consumption of a video sessionis smaller in the CDMA network compared to that in theWLAN. This bandwidth adaptation can be achieved byadjusting compression parameters and coding techniquessuch as layered coding [26]. Specifically, the transmissionrate for the video traffic in the CDMA network is 240 Kbpsand corresponds to an equivalent spreading gain N ¼ 16,which can be interpreted as multiple code transmissionusing a higher spreading gain (say, N ¼ 256) to ensure theaccuracy of the asymptotic approximation of CDMA systemwith LMMSE receivers in (8). The numerical values for theCDMA network are given in Table 2. The new sessionarrival rates in the CDMA and the WLAN areas are c;n andw;n, respectively. The total new session arrival rate isn ¼ c;n þ w;n. c;t and c;h are the session termination rateand the session vertical handoff rate, respectively, in theCDMA network. w;t and w;h are the session termination

rate and the session vertical handoff rate, respectively, inthe WLAN.

5.1 Performance Improvement

We compare the average reward from the proposedscheme to that from two other WLAN/CDMA integrationschemes. Fig. 3 shows the average rewards earned indifferent schemes. In this example, 40 percent of the totalnew session arrivals in the system occur in the WLANarea. c;t ¼ w;t ¼ 0:005, c;h ¼ 0:004 and w;h ¼ 0:0005.wc;n ¼ wc;h ¼ 2. ww;n ¼ ww;h ¼ 1. From Fig. 3, we can seethat the reward earned in the proposed scheme is alwaysmore than that in two other schemes, and the reward is theleast in the scheme that vertical handoff is not supported.The percentage of reward gain is shown in Fig. 4. It isobserved that the higher the new session arrival rate, the lessthe percentage of reward gain. This is because the systembecomes saturated when the arrival rate is high, and theproposed scheme has no much room to select sessions toadmit based on the reward rate. Nevertheless, the rewardearned in the proposed scheme is about 27 percent percenthigher than that in the scheme without vertical handoffsupport even when the system is in high load.


TABLE 1WLAN Parameters Used in Numerical Examples

TABLE 2CDMA Network Parameters Used in Numerical Examples

Fig. 3. Average reward in different schemes.

5.1.1 Effects of the Percentage of Session Arrivals in the

WLAN Area

The percentage of session arrivals in the WLAN area may

not be a constant value. Fig. 5 shows the reward gain with

different percentages of traffic in the WLAN area (from 0

percent to 100 percent). n ¼ 0:01 and other parameters

remain the same in this example. We observe that the

proposed scheme is effective with different traffic load in

the WLAN area. It can be seen that the higher the

percentage of traffic in the WLAN area, the higher the

reward gain in the proposed scheme. This is because our

scheme can optimally admit some traffic in the WLAN area

to the CDMA network when the traffic load in the WLAN

area is high.

5.1.2 Effects of the Reward Rate Ratio between the

CDMA Network and WLAN

The reward rate ratio between CDMA networks and

WLANs will be different with different network operators.

If the ratio is less than 1, operators earn less reward when a

session is admitted to a CDMA network instead of a WLAN.Otherwise, operators earn equal reward (ratio is 1) or more

reward (ratio is greater than 1). Figs. 6 and 7 show the

reward gain with n ¼ 0:01 and n ¼ 0:03, respectively. It isinteresting to observe that the reward in the scheme with

vertical handoff but no joint admission control will be lessthan that in the scheme without vertical handoff support

when the ratio is larger than center values (3.8 in Fig. 6 and2.2 in Fig. 7). However, the proposed scheme can always

have reward gain with a large range of the ratio values.

5.1.3 Effects of User Mobility

The vertical handoff rates, c;h and w;h, represent how fast

mobile users move around in the CDMA network and theWLAN, respectively. Fig. 8 shows the effects of user

mobility on the reward gain. Since mobile users in WLANsusually have slow mobility compared to those in CDMA

networks, we set w;h ¼ c;h=5. We can see that our schemecan have significant reward gain over the other two

schemes with different user mobility rates.


Fig. 4. Percentage of reward gain versus new session arrival rate.

Fig. 5. Percentage of reward gain versus percentage of session arrivals

in the WLAN area.

Fig. 6. Percentage of reward gain versus reward rate ratio between the

CDMA network and the WLAN (n ¼ 0:01).

Fig. 7. Percentage of reward gain versus reward rate ratio between the

CDMA network and the WLAN (n ¼ 0:03).

5.2 QoS Provisioning in the Proposed Scheme

Besides the reward gain shown in the last section, the

proposed scheme can also guarantee QoS at different levels,

e.g., SIR outage probability in the CDMA network,

throughput and packet delay in the WLAN, and network

layer session blocking probabilities. Fig. 9 shows the

blocking probability of vertical handoff sessions from the

WLAN to the CDMA network. In this example, we set a

target vertical handoff session blocking probability, 1 per-

cent, two target SIR outage probabilities in the CDMA

network, 0 and 0.01, and two target throughputs, 1.3M and

1.12 M. The optimal joint admission scheme can guarantee

the vertical handoff session blocking probability in Fig. 9. It

is also observed that the blocking probability is higher with

the SIR outage probability of 0 and throughput 1.3M than

that with SIR outage probability of 0.01 and throughput

1.12M. This is because fewer sessions can be admitted to the

system to guarantee the tighter SIR outage probability and

throughput constraints. Fig. 10 shows the blocking prob-ability of new sessions in the CDMA network. Similarobservations in Fig. 10 show the better performance in ourscheme than two other ones.

5.3 Optimal Policy Obtained from the ProposedScheme

What does the optimal policy obtained from our schemelook like? Figs. 11 and 12 show the policies for verticalhandoff sessions and new sessions in the CDMA network,respectively. Two network layer QoS constraints areconsidered, new session blocking probability (0.03) andvertical handoff session blocking probability (0.01). It can beobserved that the optimal policy is a randomized policy,which means that a session will be admitted with a

probability in some states (two states in Figs. 11 and 12).For example, a vertical handoff or new session will beadmitted with probability 0.2208 when there are twosessions in the CDMA network and two sessions in theWLAN. We can also see that the number of state where a


Fig. 8. Percentage of reward gain versus vertical handoff rate in the

CDMA network.

Fig. 9. Blocking probability of vertical handoff sessions in the CDMA

network.

Fig. 10. Blocking probability of new sessions in the CDMA network.

Fig. 11. Optimal policy for vertical handoff sessions in the CDMA

network.

vertical handoff session can be admitted is more than thatwhere a new session can be admitted. This is because theQoS constraint for vertical handoff sessions (0.01) is tighterthan that for new sessions (0.03), and some bandwidth isreserved for vertical handoff sessions to guarantee thetighter QoS.

6 CONCLUSIONS AND FUTURE WORK

The complementary characteristics of WLANs and CDMAnetworks make it attractive to integrate them together toprovide mobile users seamless wireless access services. Inthis paper, we have presented an optimal joint sessionadmission control scheme in integrated WLAN/CDMAnetworks to utilize overall radio resource optimally. Theproposed scheme can maximize the network revenue withQoS constraints in both WLANs and CDMA cellularnetworks. An infinite horizon semi-Markov decision pro-cess formulation and linear-programming-based algorithmsfor computing the optimal joint admission control policyare presented. We illustrated the performance of theproposed scheme by numerical results. It was shown thatthe optimal joint session admission control scheme can havea very significant gain over the schemes in which admissioncontrols are done independently in individual networks.The optimal joint admission control policy obtained fromour scheme was found to be a randomized policy.

For the SMDP modeled in this work, some structuredpolicies (e.g., monotonic or threshold policies) may beobtained by showing supermodularity of the dynamicprogramming recursion using the methodologies in [27].Once such structured policies are obtained, they can beused in real networks with multiple WLAN-CDMA cells,since their implementation is very simple. Future study is inprogress in this direction. Nevertheless, such structuredresults make strong assumptions on the structure of thestate transition probabilities and the reward function. Thesestrong assumptions are relaxed in this paper. It is also veryinteresting to consider different QoS constraints in WLANsand CDMA cellular networks in future work.

APPENDIX

Proof of Proposition 4.1. Singh et al. [12] show that the

blocking probability can be expressed as an average cost

criterion in the CAC setting. Similarly, we use the

admitting probability (1 – blocking probability) as the

average reward criterion in this paper, and the proof in

[12] applies directly. The reward related to ac;n;j can be

expressed as wc;n;jac;n;j In addition, wc;h;jac;h;j is the

reward related to ac;h;j. Moreover, the reward is wc;n;j if

a new session in the WLAN cell is admitted to the

CDMA network (aw;n;j ¼ �1), and the reward is ww;n;j if it

is admitted to the WLAN (aw;n;j ¼ 1). Finally, if a class j

session is allowed to vertical handoff from the CDMA

network to the WLAN, i.e., aw;h;j ¼ 1, reward will occur

in the WLAN network; if aw;h;j ¼ 0, reward will occur in

the CDMA network. Therefore, the reward related to

aw;h;j is ww;h;jaw;h;j þ wc;n;jð1� aw;h;jÞ. Thus, the reward

for state-action pair ðx; aÞ is

rðx; aÞ ¼XJj¼1

½wc;n;jac;n;j þ wc;h;jac;h;j þ ww;n;j�ðaw;n;jÞ

þ wc;n;j�ð�aw;n;jÞ þ ww;h;jaw;h;j þ wc;n;jð1� aw;h;jÞ�:

tuProof of Proposition 4.2. Since we have derived the

expected sojourn time �xðaÞ for a given state-action pair,

the new blocking probability for class j in the CDMA

network can be defined as the fraction of time the system

is in a set of states Xbc;n;j � X and the chosen action is in

a set of actions Axbc;n;j� A, where xbc;n;j 2 Xb

c;n;j and

Axbc;n;j¼ fa 2 A : ac;n;j ¼ 0g,

Pbc;n;j ¼ lim

T!1

1

TE

Z T

0

ð1� ac;n;jðtÞÞ�xðtÞðaðtÞÞdt�

¼

Px2Xb

c;n;j

Pa2A

xbc;n;j

�xðaÞ

Px2X

Pa2A

�xðaÞ:

ð34Þ

The derivation of the above equation follows from the

Possion arrival see time averages (PASTA) theorem,

which requires Poisson arrivals. Therefore, the blocking

probability constraints in the system can be addressed in

the linear programming formulation in (33) by defining a

cost function related to these constraints. tu

ACKNOWLEDGMENTS

This work is supported by the Natural Science andEngineering Research Council of Canada.

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Fig. 12. Optimal policy for new sessions in the CDMA network.

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[14] S. Xu, “Advances in WLAN QoS for 802.11: An Overview,” Proc.IEEE Int’l Symp. on Personal Indoor and Mobile Radio Comm.,pp. 2297-2301, Sept. 2003.

[15] J. Evans and D.N.C. Tse, “Large System Performance of LinearMultiuser Receivers in Multipath Fading Channels,” IEEE Trans.Information Theory, vol. 46, pp. 2059-2078, Sept. 2000.

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Fei Yu received the PhD degree in electricalengineering from the University of British Co-lumbia in 2003. From 2002 to 2004, he was withEricsson (in Lund, Sweden), where he workedon the research and development of dual modeUMTS/GPRS handsets. Since 2005, he hasbeen working in Silicon Valley as an R&Ddirector at a start-up, where he conductsresearch and development in the areas ofadvanced wireless communication technologies

and new standards. Since receiving the PhD degree, he has been aresearch associate in the Department of Electrical and ComputerEngineering at the University of British Columbia. His research interestsinclude cross-layer optimization, QoS provisioning, and security inwireless networks. He is a member of the IEEE.

Vikram Krishnamurthy (S’90–M’91–SM’99–F’05) received the bachelor’s degree from theUniversity of Auckland, New Zealand, in 1988and the PhD degree from the Australian NationalUniversity, Canberra, in 1992. Since 2002, hehas been a professor and the Canada ResearchChair in the Department of Electrical Engineer-ing, University of British Columbia, Vancouver,Canada. Prior to this, he was a chaired professorin the Department of Electrical and Electronic

Engineering, University of Melbourne, Australia. His research interestsspan several areas, including ion channels and nanobiology, stochasticscheduling and control, statistical signal processing, and wirelesstelecommunications. Dr. Krishnamurthy has served as associate editorfor the IEEE Transactions on Signal Processing, IEEE TransactionsAerospace and Electronic Systems, IEEE Transactions Nanobioscience,IEEE Transactions Circuits and Systems II, Systems and Control Letters,and the European Journal of Applied Signal Processing. He was a guesteditor of a special issue of IEEE Transactions on NanoBioScience,March 2005, on bio-nanotubes. He is a fellow of the IEEE.

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IEEE TRANSACTIONS ON MOBILE COMPUTING, …vikramk/YK07.pdfCDMA core network in the same manner as other CDMA radio access networks. In this approach, WLANs and CDMA networks would