Journal of Network and Computer Applications 34 (2011) 1263–1271

Contents lists available at ScienceDirect

Journal of Network and Computer Applications

1084-80

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/jnca

A bidding model and cooperative game-based vertical handoffdecision algorithm

Xingwei Liu a,b,n, Xuming Fang b, Xu Chen a, Xuesong Peng a

a School of Mathematics and Computer Engineering, Xihua University, Chengdu, Chinab Key Laboratory of Information Coding and Transmission, Southwest Jiaotong University, Chengdu, China

a r t i c l e i n f o

Article history:

Received 21 October 2010

Received in revised form

8 January 2011

Accepted 28 January 2011Available online 5 February 2011

Keywords:

Vertical handoff decision

Network selection

Bidding model

Cooperative game

Load balancing

45/$ - see front matter & 2011 Elsevier Ltd. A

016/j.jnca.2011.01.012

esponding author. Tel.: +86 028 87720584.

ail addresses: lxwphd@gmail.com, lxw@mail.x

a b s t r a c t

The next-generation wireless network is envisioned as a convergence of different wireless access

technologies, and can offer mobile users the best service anywhere anytime. While mobile users roam

between heterogeneous access networks, vertical handoff may take place and vertical handoff decision

(network selection) would be a clear challenge. Because game theory is an effective mathematical

theory to deal with models for studying interaction among decision makers, in this paper, the

competition between mobile users and heterogeneous access networks can be formulated as a

multi-tenderee bidding model; at the same time, the competition among heterogeneous access

networks can be formulated as a cooperative game process to seek for larger total payoff. Then, the

proposed algorithm is evaluated by network utility and standard deviation through simulation, and the

experimental results show that it is effective to achieve the load balancing and meet the quality of

service (QoS) requirements of various applications.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The next-generation wireless network is envisioned as aconvergence of different wireless networks such as Wi-Fi, WiMAXand Universal Mobile Telecommunications Systems (UMTS),which can offer mobile users the best service anywhere anytime.Therefore, supporting terminal seamless handoff across hetero-geneous access networks is a clear challenge and becomes one ofthe most critical mechanisms for next-generation wireless net-work. Currently, numerous mobility management protocols havebeen proposed by IETF for IP-based wireless networks (McNairand Zhu, 2004). IEEE 802.21 working group has been working onstandard development to enable handoff between heterogeneousaccess networks including both 802 and non-802 networks.Unlicensed Mobile Access (UMA), along with Generic AccessNetwork (GAN), has been providing fixed-mobile convergencebetween cellular and unlicensed spectrum technologies such asWi-Fi and Bluetooth.

Handoff is often defined as a process by which a mobile node(MN) moves from one network to another. Handoff can beprimarily classified into homogeneous and heterogeneous hand-off. Homogeneous handoff (horizontal or traditional handoff)process occurs to provide an uninterrupted service when a mobile

ll rights reserved.

hu.edu.cn (X. Liu).

node moves between two homogeneous access networks or cells(Chen et al., 2004). Heterogeneous handoff (vertical handoff)process is generally described in three phases (Kassar et al.,2008): handoff initiation, handoff decision and handoff execution.The handoff initiation (network discovery) phase is used to collectall the information required from candidate networks. The hand-off decision phase is used to determine whether and how toperform the handoff by evaluating and selecting the most appro-priate access network. It is also called network selection phase.The handoff execution phase is used to change channels andassociate with the target network. Therefore, handoff decision isan important and intelligent part of vertical handoff process, andin this paper our study will mainly focus on the network selectionalgorithm (which network it should connect to and which criteriathis choice is based on?).

Generally, horizontal handoff decision takes into account somelink quality condition parameters such as received signal strengthindicator (RSSI), signal-to-noise ratio (SNR) and so on drop belowa specified handoff threshold. In a heterogeneous wireless envir-onment, mobile users can move between different wireless accessnetworks, and they will benefit from different network character-istics (coverage, bandwidth, power consumption, cost, etc.) thatcannot be compared directly. Therefore, the handoff decisionmaking (network selection) becomes more difficult in such anenvironment than the homogeneous one. It usually needs to takeinto account not only the aforementioned network characteristicsbut also the user preferences and the traffic classes. In this paper,

X. Liu et al. / Journal of Network and Computer Applications 34 (2011) 1263–12711264

we formulate handoff decision problem as a multi-tendereebidding model and cooperative game process, where mobile usersselect the most appropriate network to meet QoS requirements ofvarious applications and networks act cooperatively with eachother in order to achieve the load balancing.

The rest of the paper is organized as follows. In Section 2,related work about vertical handoff decision algorithms isreviewed. Then, two typical vertical handoff scenarios acrossheterogeneous networks of Wi-Fi and WiMAX are introducedin Section 3. A novel vertical handoff decision algorithm based onmulti-tenderee bidding model and cooperative game is discussedin Section 4. Section 5 shows experimental studies for verifyingthe proposed handoff decision algorithm. Section 6 providesconclusion.

2. Related work

Traditional handoff algorithms are usually based on thereceived signal strength (RSS), and subsequent algorithms furtherconsider hysteresis and dwelling-timer. In Liu et al. (2006), a self-adaptive vertical handoff algorithm (SAVA) is proposed, whichconsiders the long term movement region and short term move-ment trend of mobile node. SAVA algorithm outperforms tradi-tional hysteresis and dwelling-timer based handoff algorithms.

The policy-enabled vertical handoff model is proposed firstlyin Wang et al. (1999). Each candidate network is associated with acost function in the decision making, which depends on band-width, power consumption and monetary cost. The network withthe lowest cost is selected as the target network. In Lee et al.(2009), a generalized vertical handoff decision algorithm isproposed, which seeks to optimize a combined cost functioninvolving the battery lifetime of the mobile node. The proposedalgorithm not only balances the overall load among all attach-ment points, but also maximizes the collective battery lifetime ofmobile nodes.

Multiple Attribute Decision Making (MADM) is also used toselect a target network from a set of candidate networks that arecharacterized in terms of their attributes in the decision making.The classical MADM algorithms include Simple Additive Weight-ing (SAW), Technique for Order Preference by Similarity to IdealSolution (TOPSIS), Analytic Hierarchy Process (AHP) and GreyRelational Analysis (GRA). In Song and Jamalipour (2005), net-work selection algorithm based on AHP and GRA is proposed. AHPis used to decompound the network selection problem to severalsubproblems and assign each subproblem a weight value. Then,candidate networks are ranked using GRA and the network withthe highest ranking is selected as the target network. In Stevens-Navarro and Wong (2006), a comparison of algorithms above-mentioned is established with attributes such as bandwidth,delay, jitter and bit error rate (BER). SAW and TOPSIS providesimilar performance to the traffic classes used. Meanwhile, GRAprovides a slightly higher bandwidth and lower delay for inter-active and background traffic classes.

The classical MADM methods usually cannot efficiently handlea decision problem with imprecise information. However, fuzzylogic does it very well, and can combine and evaluate multipleattributes simultaneously. In Nie et al. (2007), a bandwidth basedadaptive fuzzy logic handoff algorithm is proposed in the hybridof Wi-Fi and WiMAX, which can adapt itself with the dynamicconditions of the heterogeneous networks. In Ali and Celal (2010),an adaptive fuzzy logic and an Adaptive Network Fuzzy InferenceSystem (ANFIS) based vertical handoff decision making algorithmare proposed with integrating with GSM/GPRS, Wi-Fi, UMTS andWiMAX technologies. This algorithm shows better performancethan typical fuzzy based algorithm in terms of number of handoff,

decision time, etc. In Krishnamurthy et al. (2000), a neuralnetwork-based approach is proposed to detect the received signaldecay and make handoff decision across heterogeneous networksof GPRS and Wi-Fi. However, because of the complex neuralnetwork topology this algorithm is difficult to realize in practice.An MDP-based vertical handoff decision algorithm is presentedin Stevens-Navarro et al. (2008), and it has formulated handoffdecision as a Markov decision process with the objective ofmaximizing the total expected payoff per connection. Basedon Stevens-Navarro et al. (2008), Sun et al. (2008) introduce aConstrain Markov Decision Process (CMDP) to describe verticalhandoff decision, which further takes into account user’s velocityand location information. Recently, game theory is used to modelnetwork selection. In Antoniou and Pitsillides (2007), networkselection is modeled using a game theoretic approach that definesa game between the access networks, and then, networks com-pete in a non-cooperative manner to maximize their payoffs.In Malanchini and Cesana (2008), network selection problem isformulated as a non-cooperative game where mobile users andaccess networks play selfishly strategy profiles to achieve max-imum payoff (maximization of the perceived QoS for the mobileusers, and maximization of the number of customers for theaccess network operators). In Niyato and Hossain (2009), con-sidering user-driven load balancing in a heterogeneous wirelessnetwork, network selection problem is formulated as a dynamicevolutionary game where two algorithms, namely, populationevolution and reinforcement-learning algorithms, for networkselection are presented. In Kun et al. (2010), the network selectionproblem is formulated as a Bayesian game with incompleteinformation and the solution of the game is Bayesian Nashequilibrium.

3. The typical handoff scenario

In the literature, most researches on convergence of hetero-geneous networks are for interworking between Wi-Fi and 3Gnetworks. Not much attention has been paid to the integration ofWi-Fi and WiMAX. This is because, currently, Wi-Fi and cellularnetworks are commonly available and many cellular devices havedual radio-frequency (RF) interfaces for Wi-Fi and cellular access.However, WiMAX is a promising next-generation broadbandwireless access network. It provides the last mile solution andsupports high-speed multimedia services. The combination ofWi-Fi and WiMAX can effectively complement each other interms of coverage and provision of seamless mobility support.

In the loosely coupled interworking architecture for Wi-Fi andWiMAX, each network is connected to the all-IP CN via itscorresponding gateway. Each mobile node is equipped with twoindependent radio interfaces, which can operate and connect tothe different radio access networks simultaneously, one is forWi-Fi, and the other is for WiMAX. In dense urban areas, a mobilenode is often simultaneously within the overlap coverage areas ofboth WiMAX and Wi-Fi, and multiple Wi-Fi coverage areas areusually contained within a WiMAX coverage area. Depending onthe network condition and user preference such as in a situationof network congestion, the vertical handoff may take place notonly at the network edge, but also anywhere anytime (even whenthe MN does not move).

In the first typical handoff scenario (which is shown in Fig. 1),the MN currently connects to a WiMAX. When the MN is movinginto the overlap coverage areas of the WiMAX BS and three Wi-FiAPs, the vertical handoff process may take place, and the MNneeds to determine which network it should connect to.

In the second typical handoff scenario (which is shown inFig. 2), multiple MNs currently connect to a WiMAX. At any given

Internet

WiMAX BS

Wi-Fi AP Wi-Fi AP

Wi-Fi AP

MN

MN

Gateway

Gateway

Fig. 1. First typical handoff scenario.

Internet

Gateway

Wi-Fi AP

MNMN

WiMAX BS

Gateway

Fig. 2. Second typical handoff scenario.

X. Liu et al. / Journal of Network and Computer Applications 34 (2011) 1263–1271 1265

instant, once all MNs are simultaneously moving into the overlapcoverage areas of the WiMAX BS and a Wi-Fi AP, they areconfronted with the problem that in order to provide QoS supportto as many users as possible and equitably distribute the trafficload across available APs and BSs, the admission control for a newconnection should be made by the network jointly with verticalhandoff decision by the MNs.

Because the two problems are strictly related, in this paper weconsider them jointly and formulate them as a multi-tendereebidding model and cooperative game process. Furthermore, ourproposed model is not limited to the interworking between Wi-Fiand WiMAX, and it can potentially extend to other integratedheterogeneous networks. The detailed algorithm is described inthe following section.

4. The vertical handoff decision algorithm

4.1. Bidding model

Bidding is a market dealing process in which the tendereeproposes the conditions for purchasing commodities or servicesand invites bidders to bid for selecting the trading object underthe given procedure. In a standard bidding model, there is a singletenderee and multiple competing bidders. Bidders submit theirbids to tenderee, then the tenderee selects winning bidderaccording to procedure (Liu and Xi, 2000).

In dense urban areas, multiple MNs are often simultaneouslywithin the overlap coverage areas of multiple WiMAX BSs andmultiple Wi-Fi APs. There exists the competition between MNs

and heterogeneous access networks, which may be formulated asa multi-tenderee bidding model.

Tenderee: a finite set of MNs.Bidders: a finite set of candidate access networks.Project: an application service applied by MN.Winning bidder: an access network is selected by a MN andprovides the application service to MN.

Assumption 1. ci is an anticipated cost of a bidder for a project,which is unknown to the other bidders and defined as

ci ¼XN

k ¼ 1

wkrik ð1Þ

where N denotes the number of network parameters includingbandwidth, delay, jitter, packet loss ratio and price, wk denotesthe weight of parameter k, w1+w2+?+wk+?+wN¼1 and rik

denotes the value of parameter k in network i.

Assumption 2. B is a strictly monotone increasing function, bi

denotes a bid. Generally speaking, the bid could be composed ofcost and expected payoff. Here, according to symmetric BayesianNash Equilibrium strategy, a bid is defined as

bi ¼ BðciÞ ð2Þ

B�1ðbiÞ ¼ ci ð3Þ

Assumption 3. The cost ci is the private information of a bidder,and it is distributed according to the continuously differentiabledistribution function F defined over the support [cl, ch], wherecl and ch denote the lowest and highest bid, respectively.

The bidder with the lowest bid wins the project, and theexpected payoff of the bidder is defined as

Epi ¼ ðbi�ciÞYja i

½probðbiob�j Þ�

¼ ðbi�ciÞf1�prob½B�1ðbiÞ�gn�1

¼ ðbi�ciÞf1�F½B�1ðbiÞ�gn�1

ð4Þ

where prob(biobj*) denotes the probability that bidder i bids

below bidder j and n denotes the number of winning bidder.Because each bidder is rational, its objective is to maximize itsexpected payoff Epi. Applying first-order derivative of Epi withrespect to bi, we may obtain

@Epi

@bi¼ 1�F B�1ðbiÞ

� �� ��ðbi�ciÞðn�1ÞFu B�1ðbiÞ

� �Bu�1ðbiÞ ð5Þ

Let @Epi

@bi¼ 0, then

f1�F½B�1ðbiÞ�g�ðbi�ciÞðn�1ÞF u½B�1ðbiÞ�Bu�1ðbiÞ ¼ 0 ð6Þ

Replace bi, ci in (6) with (2) and (3), respectively, we mayobtain

1�FðciÞ½ ��ðbi�ciÞðn�1ÞFuðciÞ@ci

@bi¼ 0 ð7Þ

According to Assumption 3, we may obtain

FðciÞ ¼ci�cl

ch�clð8Þ

Solving (7) and (8), we may obtain

ch�ci

ch�cl�ðbi�ciÞðn�1Þ

1

ch�cl

1@bi@ci

¼ 0

ðch�ciÞ@bi

@ci�ðbi�ciÞðn�1Þ ¼ 0

X. Liu et al. / Journal of Network and Computer Applications 34 (2011) 1263–12711266

@bi

@ci�ðbi�ciÞ

ðch�ciÞðn�1Þ ¼ 0

@bi

@ci�ðn�1Þ

ðch�ciÞbi ¼ðn�1Þ

ch�cið�ciÞ ð9Þ

Solving the differential (9), we may obtain

bi ¼ eR

n�1ch�ci

dci

Z�ðn�1Þci

ch�cieR� n�1

ch�cidci

� �dciþe

�

¼ elnðch�ciÞ1�n

Z�ðn�1Þ

ci

ch�cielnðch�ciÞ

n�1

� �dciþe

�

¼ ðch�ciÞ1�n

Z�ðn�1Þ

ci

ch�ciðch�ciÞ

n�1

� �dciþe

�

¼ ðch�ciÞ1�n ciðch�ciÞ

n�1þðch�ciÞ

n

nþe

�

¼ ciþðch�ciÞ

nþeðch�ciÞ

1�nð10Þ

Let e¼ 0, the solution is obtained

bi ¼ ciþ1

nðch�ciÞ ð11Þ

If a bidder wins the project, its payoff is (ch�ci)/n, contrarily,the payoff of the bidder losing is zero. Generally speaking, thebidder with the lowest bid wins the project, so each accessnetwork would be forced to decrease its bid in the next roundbidding process. Finally the total payoff of all the bidders woulddecline. To seek for larger total payoff, each access network needsto cooperate with each other, and the cooperative process will bedescribed in the next section.

4.2. Cooperative game process

Game theory is an effective mathematical theory to deal withmodels for studying interaction among decision makers. Coop-erative game theory and non-cooperative game theory are twomajor branches in game theory. In non-cooperative game theory,each player chooses selfishly the best strategy to maximize itsown payoff. On the contrary, in cooperative game theory, all theplayers act cooperatively in order to come to an agreement andseek for larger total payoff. Generally, a model of cooperativegame often has the following elements (Niyato and Hossain,2009):

K

A finite set of decision makers, i.e. the game players. K A non-empty set of pure strategies for each player. K A set of payoff functions for each player with the player’s

strategies.

Taking this cooperative behavior into account, the competitionamong heterogeneous access networks to achieve the load balan-cing of networks as well as the QoS requirements of variousapplications may be formulated as a cooperative game, and theequilibriums of the cooperative game is considered to be thesolution to this game.

4.2.1. Players

In dense urban areas, a mobile node is often simultaneouslywithin the overlap coverage areas of multiple WiMAX BSs andmultiple Wi-Fi APs. There exists the competition among hetero-geneous access networks. Therefore, the game players are definedas a finite set {BS-1, y, BS-n, AP-1, y, AP-n}, where BS-n denotesa WiMAX BS, AP-n denotes a Wi-Fi AP, etc. At the same time, thegame players are also defined as the set of bidders in biddingmodel introduced in previous section.

4.2.2. Strategy

The strategy of each network in a round is defined as a finiteset si¼{b1, b2, y, bn}, where each element denotes a bid to acorresponding tenderee in bidding model calculated by (2). Allpotential strategies of each network are defined as a set Si¼{si},where si denotes a special strategy of this network in a round.The strategies of all players in a round are defined as a set{s1, s2, y, sn}, and all strategies of all players are defined as a set{S1, S2, y, Sn}.

4.2.3. Payoff

The payoff function of each access network is determined bythe bid according to (2). ui denotes the payoff function of networki. The value of ui is equal to the sum of the bids received by MNswhich select network i. Then the total payoff of all the accessnetworks is defined as

T ¼Xn

i ¼ 1

ui ð12Þ

where T denotes the total payoff of all the access networks, and n

denotes the number of the game players.Thus, our cooperative game model can be defined as G¼{n;

S1, y, Sn; u1, y, un}, where n denotes the number of the gameplayers, and the game would be played in rounds. In every roundof the game process, each player independently chooses itsstrategy from set Si, and obtains its payoff ui(s1, s2, y, sn). More-over, each player also calculates its network utility, which couldbe defined as

Ri ¼U_Bi

T_Bið13Þ

where Ri denotes network utility, U_Bi denotes the used band-width of this network and T_Bi denotes the total bandwidth of thisnetwork. Because the bandwidth is the most precious and limitedresources in the wireless network, for convenience’s sake, weoften use the network utility to denote the traffic load of eachattachment point.

In every round of the game process, each network as a gameplayer acts cooperatively in order to seek for larger total payoff,and tries to achieve well load balancing, which depends on thedifferences between each player’s network utility. If any one islarger than a default value x in a round game, the equilibriumdoes not achieve, and then the next round game continues to beplayed, as well as all players cooperatively adjust their strategiesin the direction of the agreement.

The details on how to adjust the strategies in the direction ofthe agreement is described in the followed manner. The gameplayer with higher network utility will increase the bid in order todecline the chance to win the bid. On the contrary, the player withlower network utility will decrease the bid in order to increaseprobability of winning the bid. In this way, it finally achieves theload balancing after the limited rounds, and obtains larger totalpayoff.

For evaluating the performance of the proposed algorithm, thestandard deviation of the network utility is defined as

D¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni ¼ 1

ðRi�EÞ2

n

vuuutð14Þ

where D denotes the standard deviation of the network utility, n

denotes the number of the access networks and E denotes theaverage value of the network utility, which is calculated by

E¼

Pni ¼ 1

Ri

nð15Þ

Table 3Weights of various parameters.

Parameter Video VoIP Background Best-effort

Bandwidth 0.0276 0.2983 0.0881 0.1118

Delay 0.3149 0.0804 0.0881 0.0233

Jitter 0.3149 0.2983 0.0196 0.0233

PER 0.0276 0.0246 0.5555 0.5809

Price 0.3149 0.2983 0.2484 0.2604

Fig. 3. Network selection results using the proposed algorithm.

X. Liu et al. / Journal of Network and Computer Applications 34 (2011) 1263–1271 1267

5. Experimental results

Our experimental environment is the aforementioned twotypical handoff scenarios (which are shown in Figs. 1 and 2,respectively), where multiple MNs are simultaneously movinginto the overlap coverage areas of a WiMAX BS and three Wi-FiAPs (which are named as AP-1, AP-2 and AP-3) (Table 1).

Suppose there are 20 MNs that are named as MN-1, MN-2,MN-3, etc. and Table 2 shows the QoS requirements of each MNfor various applications in our experiments. Moreover, AHP isapplied to figure out the weights of various parameters (Yanget al., 2008) and the results are shown in Table 3.

The network selection results in the final round using theproposed algorithm are shown in Fig. 3, where 1 of the verticalordinate means WiMAX BS network, 2 means AP-1 network,3 means AP-2 network, etc. The MN-1 selects the AP-2 network,the MN-6 selects the WiMAX BS, etc.

Furthermore, the network selection results in the final roundusing non-cooperative game strategy are shown in Fig. 4, where1 of the vertical ordinate means WiMAX BS network, 2 means AP-1 network, 3 means AP-2 network, etc. Comparing Figs. 3 and 4, itis clear that all the MNs in Fig. 3 are allocated equitably in accessnetworks. However, in Fig. 4, AP-2 and AP-3 networks areselected by the most MNs, but no MN selects AP-1 network.

Suppose the service provided by the network can meet the QoSrequirement of the application; the lower the bid is, the greaterthe chance that the network can be selected. Each MN has fourbids came from BS, AP-1, AP-2 and AP-3, but only the networkwith the lowest bid wins the project and provides service to the

Table 1Parameter values of various traffic classes.

Parameter Traffic class Value

Bandwidth VoIP 21–106 kbps

Video More 20% than one stream

Delay VoIP o150 ms

Video o200–300 ms

Jitter VoIP o30 ms

Video o30 ms

Loss ratio VoIP o1%

Video o1%

Table 2MNs’ QoS requirements for various applications.

No. Bandwidth (kb/s) Delay (ms) Traffic class

1 42.490 94.390 VoIP

2 8.230 414.000 Background

3 60.210 122.200 VoIP

4 10.410 324.170 Background

5 410.290 232.370 Video

6 9.940 562.020 Background

7 620.030 242.560 Video

8 9.500 323.150 Background

9 609.580 231.350 Video

10 22.020 261.950 Best-effort

11 35.090 120.160 VoIP

12 11.230 322.130 Background

13 109.170 100.340 VoIP

14 19.770 260.930 Best-effort

15 98.720 119.140 VoIP

16 18.320 349.740 Best-effort

17 88.260 90.300 VoIP

18 455.040 238.510 Video

19 14.680 469.120 Background

20 444.590 249.690 Video

Fig. 4. Network selection results using non-cooperative game strategy.

MN. The bids of each network in the final round using theproposed algorithm and non-cooperative game strategy areshown in Figs. 5 and 6, respectively. In the cooperative gameprocess, each access network submits its bid in every round underan agreement (i.e. in this paper, that is to balance the networkload). However, in the non-cooperative game strategy, eachaccess network chooses selfishly the best strategy to maximizeits own payoff and submits its bid just according to the require-ments applied by MNs. Because of that, some networks’ bids arealways relative high. In Fig. 6, the bids came from AP-1 networkare always not the smallest one in four bids, so no MN selects it toprovide services.

The cooperative game process plays in rounds. If the agree-ment is not achieved in this round, then all the players

Fig. 5. Bid of each network in the final round using the proposed algorithm.

Fig. 6. Bid of each network in the final round using non-cooperative game

strategy.

Fig. 7. Cooperative game process.

Fig. 8. Network payoff in the cooperative game process.

Fig. 9. Total payoff in the cooperative game process.

X. Liu et al. / Journal of Network and Computer Applications 34 (2011) 1263–12711268

cooperatively adjust their bids to enter the next round game. Inthis example, it lasts 23 rounds or times, and the cooperativegame process is shown in Fig. 7.

When every round game process is at end, each player canobtain the payoff. The change of each player’s payoff with theadjusted bids is shown in Fig. 8, and the change of the total payoff

with the adjusted bids is shown in Fig. 9. When the load balancingis achieved, it obtains larger total payoff. The total payoff usingthe proposed algorithm is 14.153985. However, the total payoffusing non-cooperative game strategy is 12.58293.

The comparison of network selection between the proposedalgorithm and other algorithms, including non-cooperative gamestrategy, SAW, TOPSIS and GRA is shown in Fig. 10, where 1 of thevertical ordinate means WiMAX BS network, 2 means AP-1network, 3 means AP-2 network, etc. While using SAW andTOPSIS, most MNs would prefer to select AP-2 network. It isunwise because the network utilities of AP-2 with SAW andTOPSIS are 0.99662 and 0.99697, but the network utilities ofWiMAX BS with SAW and TOPSIS are only 0.95146 and 0.95146.Meanwhile, while using GRA, most MNs would prefer to selectAP-1 network, the network utility of AP-1 is 0.99431, but that ofWiMAX BS is only 0.95171. While using non-cooperative gamestrategy, most MNs would prefer to select AP-2 and AP-3. TheAP-1 is not selected by any MN. On the other hand, while usingthe proposed algorithm, MNs would prefer to select WiMAX BSnetwork. The network utility of AP-1 with the proposed is0.971543, and that of AP-2 is 0.970806, they are very approx-imate. Furthermore, the standard deviations of network utilitieswith non-cooperative game strategy, SAW, TOPSIS and GRA are0.01330, 0.01699, 0.01718 and 0.01787, respectively; however,that of the proposed algorithm is only 0.007488.

Fig. 10. Comparison of network selection between the proposed algorithm and other algorithms.

Fig. 11. Trend comparison of network utilities between the proposed algorithm and non-cooperative game.

X. Liu et al. / Journal of Network and Computer Applications 34 (2011) 1263–1271 1269

When non-cooperative game strategy and some classical algo-rithms such as SAW, TOPSIS and GRA are used to network selection,the network utilities seem unsatisfactory to some extent because oflack of well load balancing mechanism. It implies that somenetworks would be selected by too many MNs; on the other hand,other networks would be rarely selected. As time goes on, the trendof polarization will continue and it might cause networks conges-tion. On the contrary, in the proposed algorithm, each network as agame player acts cooperatively in order to come to an agreement,

and tries to achieve well load balancing of networks. Therefore, theutilities of all networks with the proposed algorithm become moreand more approximate (that is, the traffic load is equitably dis-tributed across available APs and BSs), and it further implies that theheterogeneous wireless networks could provide sustainable servicesto MNs better. The trend comparisons of network utilities amongthe proposed algorithm, non-cooperative game strategy and someclassical algorithms such as SAW, TOPSIS and GRA are shown inFigs. 11–14, respectively.

Fig. 12. Trend comparison of network utilities between the proposed algorithm and SAW.

Fig. 13. Trend comparison of network utilities between the proposed algorithm and TOPSIS.

X. Liu et al. / Journal of Network and Computer Applications 34 (2011) 1263–12711270

6. Conclusion

Vertical handoff is one of the most critical mechanisms forconvergence of heterogeneous wireless networks. In a complexhandoff scenario, when multiple MNs simultaneously move intothe overlap coverage areas of multiple WiMAX BSs and multipleWi-Fi APs, vertical handoffs may take place, and we are con-fronted with the problem that which networks MNs shouldconnect to and which criteria these choices are based on. Wehave studied this issue. In summary, the competition betweenmobile users and heterogeneous access networks can be

formulated as a multi-tenderee bidding model; at the same time,the competition among heterogeneous access networks toachieve the load balancing and meet the QoS requirements ofvarious applications can be formulated as a cooperative game.Moreover, our proposed model is not limited to the interworkingbetween Wi-Fi and WiMAX, and it can potentially extend to otherintegrated heterogeneous networks.

In this paper, our introduced integrated heterogeneous net-works operate in an infrastructure mode between the MN and theAP or BS. However if we consider the multi-hop ad hoc mode,there would exist cooperative or non-cooperative game between

Fig. 14. Trend comparison of network utilities between the proposed algorithm and GRA.

X. Liu et al. / Journal of Network and Computer Applications 34 (2011) 1263–1271 1271

MNs. Therefore, vertical handoff decision algorithm in thiscomplex situation becomes an open issue.

Acknowledgements

This research was partly supported by the Sichuan ProvincialBasic Research Fund under Grant no. 2009JY0063 and the OpenResearch Fund of Key Laboratory of Information Coding andTransmission, Southwest Jiaotong University.

References

Antoniou J, Pitsillides A. 4G converged environment: modeling network selectionas a game. In: Proceeding of the MWCS, Budapest; 2007.

Ali C, Celal C. An adapative neuro-fuzzy based vertical handoff decision algorithmfor wireless heterogeneous networks. In: Proceeding of the PIMRC, Istanbul;2010.

Chen WT, Liu JC, Huang HK. An adaptive scheme for vertical handoff in wirelessoverlay networks. In: Proceedings of the ICPADS, USA; 2004.

Krishnamurthy P, Hatami A, Ylianttila M, Makela JP, Pichna R, Vallstron J. Handoff inhybrid mobile data networks. IEEE Personal Communications 2000;7:34–47.

Kassar M, Kervella B, Pujolle G. An overview of vertical handover decisionstrategies in heterogeneous wireless networks. Computer Communications2008;31:2607–20.

Kun Z, Dusit N, Ping W. Network selection in heterogeneous wireless networks:evolution with incomplete information. In: Proceeding of the WCNC, Sydney;2010.

Liu XJ, Xi YM. Putting auction theory to work. Beijing. China Machine Press; 2000.

Liu M, Li ZC, Guo XB, Dutkiewicz E, Wang MH. SAVA: a novel self-adaptive verticalhandoff algorithm for heterogeneous wireless networks. In: Proceeding of theGLOBECOM, San Francisco; 2006.

Lee S, Sriram K, Kim K, Kim YH, Golmie N. Vertical handoff decision algorithms forproviding optimized performance in heterogeneous wireless networks. IEEETransactions on Vehicular Technology 2009;58:865–81.

McNair J, Zhu F. Vertical handoffs in fourth-generation multinetwork environ-ments. IEEE Transactions Wireless Communications 2004;11:8–15.

Malanchini I, Cesana M. Modelling network selection and resource allocation inwireless access networks with non-cooperative games. In: Proceeding of theMASS, Atlanta; 2008.

Nie J, Zeng LY, Wen JCA. Bandwidth Based adapative fuzzy logic handoff in IEEE802.16 and IEEE 802.11 hybrid networks. In: Proceeding of the ICCIT,Gyeongju; 2007.

Niyato D, Hossain E. Dynamics of network selection in heterogeneous wirelessnetworks: an evolutionary game approach. IEEE Transactions on VehicularTechnology 2009;58:2008–17.

Song QY, Jamalipour AA. Network selection mechanism for next generationnetworks. In: Proceeding of the ICC, Seoul Korea; 2005.

Stevens-Navarro E, Wong VWS. Comparison between vertical handoff decisionalgorithms for heterogeneous wireless networks. In: Proceeding of the VTC,Australia; 2006.

Stevens-Navarro E, Lin YX, Wong VWS. An MDP-based vertical handoff decisionalgorithm for heterogeneous wireless networks. IEEE Transaction on VehicularTechnology 2008;57:1243–53.

Sun C, Stevens-navarro E, Wong VWS. A constrained MDP-based vertical handoffdecision algorithm for 4G wireless networks. In: Proceeding of the ICC, Beijing;2008.

Wang HJ, Kata RH, Giese J. Policy-enabled handoffs across heterogeneous wirelessnetworks. In: Proceeding of the WMCSA, New Orleans; 1999.

Yang SF, Wu JS, Huang HH. A vertical media-independent handover decisionalgorithm across Wi-FiTM and WiMAXTM networks. In: Proceeding of theWOCN, Surabaya; 2008.