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a specific network or cell. As the mobile node moves to another cell or changes wireless technology, the new cell or network may have limited resources that ...
RADIO RESOURCE ALLOCATION IN HETEROGENEOUS WIRELESS NETWORKS USING COOPERATIVE GAMES Isameldin M. Suliman, Carlos Pomalaza-R´aez, Ian Oppermann and Janne Lehtom¨aki Centre for Wireless Communications P.O. Box 4500 90 014 University of Oulu Finland A BSTRACT Next generation wireless networks are expected to be heterogeneous consisting of several wireless technologies including, but not limited to, UMTS, GPRS, Satellite and WLAN networks. These networks provide bandwidths that range from tenth hundreds of Kbits/sec provided by technologies such as GPRS, to tens of Mbits/sec provided by Broadband wireless LANs such 802.11a. Here we study the problem of resource allocations in heterogeneous wireless networks, where the demand for bandwidth is growing at an enormous rate. Wireless networks may cooperate either because they can not deal with resource allocation demands alone or because they can reduce their cost by working together. We formulate our approach as an optimization problem that allocates resources to mobile users and maximizes benefits for networks. In addition, we employ an exponential cost function to balance load across multiple heterogeneous networks. A resource allocation model made of the three wireless networks and a user is presented. Cooperative game-theory concepts are used to identify stable resource allocations, under which all three networks find it beneficial to cooperate. The results suggest that an allocation that maximizes revenues exists, which makes this cooperation attractive to all networks.

I.

I NTRODUCTION

Users of future mobile networks will be able to choose from different radio access technologies. These networks vary widely in service capabilities such as coverage area, bandwidth, and error characteristics. In such a heterogeneous environment, a mobile user may negotiate quality of service requirements and have resources allocated on a specific network or cell. As the mobile node moves to another cell or changes wireless technology, the new cell or network may have limited resources that would not allow it to provide the same quality of services that was negotiated and allocated in the originating network. In order to cope with limited bandwidth and other constraints, an effective multi-network resource allocation algorithm is required to deal with such a situation and provide guaranteed radio resources if possible. While motivated by the move towards heterogenous wireless networks, where several network technologies are expected to support a variety of multimedia applications, the work presented in this paper tries to address the growing radio resources demand and performance requirements of multimedia applications. This increasing demand for high bandwidth makes it appropriate for wireless networks to cooperate

with each other to meet resource allocation requests and handle stringent bandwidth constraints. In this paper, we investigate the problem of resource allocation in a heterogenous network environment by using using cooperative Stackelberg [1] games. Formulating the problem as a cooperative Stackelberg game allows individual networks to cooperate with each other by forming coalitions. Therefore the objective of each network is to maximize the the overall objective of the heterogeneous network and to fulfill the resource allocation requests from users. Every member of the coalition provides some of the requested resources according to its own operation constraints. Resource allocation in heterogenous network has been previously addressed in [2]. Therein, services were delivered via the network that is most efficient for that service. In [3], the authors introduced a fault tolerance architectures to provide continuous QoS support in case of network failures. They found that it is possible to achieve a certain level of fault tolerance by allowing users to access one of several wireless networks. They also propose that when multiple access networks are available, a mobile user can decide, based on priorities, to handoff to one of these networks. In [4] a resource reservation strategy that enables scheduling and allocation of resources at an early stage in time has been studied. However, these approaches to resource allocation rely on single network to handle resource demands and may results in an inefficient resource allocation or perhaps single network cannot alone fulfill user requests. To overcome the limitations of these approaches, one solution is to spread applications among several networks. The idea of using game theory in wireless communications is not completely novel. For example, the authors of [5] present some of the basic concepts of game theory and show why it is an appropriate tool for analyzing some communication problems. They provide some insights into how communication systems should be designed. One of the game theory approaches that has been used in network optimization problem is the Stackelberg [6, 7] cooperative games. It is a multi-level game wherein a dominant player (Stackelberg leader) chooses a strategy in the first stage, which takes into account the likely reaction of the followers. In the second stage, the Stackelberg followers choose their own strategies having observed the Stackelberg the leader decision i.e., they react to leader’s strategy. Figure 1 shows a Stackelberg games on which the network/player 1 assumes the rule of the leader and the remainder networks assume the rule of the followers.

The leader will begin the game by announcing its policy, the followers will take the decision of the leader and will optimize their objective functions. In [8], a Stackelberg routing strategy has been used to improve the overall system performance. A cooperative approach to resource allocation has been treated in [9] where the authors investigated a fair and efficient resource allocation scheme on ATM networks for two traffic types contending for a shared network resource.

Level one (the leader)

Level two (the followers)

Player 3

Player n

Figure 1: Stackelberg Multilevel Decision This paper proposes a cooperative game model that addresses the problem of the resource allocation in heterogeneous wireless networks. In this model, wireless networks cooperate with each other to fulfill resource allocation requests by forming coalitions among themselves. The propose model enables a mobile user to split its application between the coalition members when the applications can not be handled by a single network. The paper is organized as follows. In section II we introduce some game theory concepts and definitions. In section III, we mode resource allocation as a cooperative game among heterogeneous networks. Section IV deals with load balancing across heterogenous networks. Section V provides an illustrative example. Finally section VI concludes the paper and provides direction for future work.

II.

The Core: The core is the set of all feasible outcomes that no player or coalition can improve upon by acting for themselves. It was developed as a solution concept for cooperative games. It consists of all undominated allocations in the game. An allocation in the core of a game will always be an efficient allocation. Pareto-optimal: Pareto optimality is a measure of efficiency. An outcome of a game is Pareto optimal if there is no other outcome that makes every player at least as well off and at least one player strictly better off. That is, a Pareto-optimal outcome cannot be improved upon without hurting at least one player.

Player 1

Player 2

denoted v(S).

C OOPERATIVE G AME C ONCEPTS

In this section we briefly summarize the basic concepts of cooperative game theory. A cooperative game is a game in which the players have the option of planning as a group in advance of choosing their actions. In this game, players are able to make enforceable contracts. There are no restrictions on the agreement that may be reached among the players. A cooperative game consists of two elements: a set of players, and a characteristic function specifying the value created by different subsets (coalitions) of the players in the game. Coalitions: Let N = {1, ..., n} be a set of n players, Non-empty subsets of N , S, T ⊆ N are called a coalition. The coalition form of an n player game is given by the pair (N, v), where v is the characteristic function.

Imputation: The division of the payoff which can be achieved by all player cooperating is called an imputation of the game. The elements x = (x1 , x2 , ..., xn ) represent the payoff to each player (the imputation) i under coalition structure P . The (x, P ) is called solution configuration. III.

R ESOURCE ALLOCATION AS A COOPERATIVE GAME AMONG HETEROGENEOUS NETWORKS

We consider a resource allocation problem for a mobile user having access to a heterogeneous wireless network (equipped with multiple network interfaces). Let N = 1, ..., n denote the set of possible wireless access networks available for the mobile user to request resources from, i.e., the finite player set. Let R denote the radio resource required by the mobile user to run its multiple independent applications. The basic coalition problem can be described as: Given a set of wireless networks N and a resource allocation demand R they have to satisfy, if the resource demand can’t be satisfied by a single network or when a single network handles the request inefficiently, it is necessary for the wireless networks to cooperate with each other to fulfill the resource demand. With cooperation between networks (by forming coalitions among themselves), resource can be allocated by splitting the applications over the N networks. We assume that each player Ni has resource capacity ci . The capacity configuration of wireless networks is given by c = (c1 , c2 , ..., cn ), and the resource of the wireless Ptotal n networks is given by C = i=1 ci . Each network can use its available resource ci for contribution ri ≥ 0 to the resource allocation request R, such that ri ≤ ci . In the original Stackelberg games, each player attempts to optimize its own objective with respect to decisions made by other players in the game. The objective of each player can be given by the optimization problem below max

ui (ri )

such that

ri ≤ ci , ri ≥ 0,

ri

Grand Coalition: A grand coalition is a coalition that include all of the players. Characteristic Function: The characteristic function is a function, denoted v, that assign each coalition S its maximum gain, the expected total income of the coalition,

(1)

where ui is the utility function of player i and ri is the resource allocated by player i. Allocating resources according to individual networks capabilities without considering the overall heterogeneous network conditions will not

typically results in a Pareto-optimal solution. Achieving Pareto-optimal allocation may require cooperation among individual networks by forming a coalition among themselves. LetTP = P1 , P2 , ..., Pj denote a coalition structure, where Pi Pj = ∅ for all i 6= j. As a result of coalition formation, individual players now act for the benefit of the coalition. Therefore the objective of each member in the coalition becomes the optimization of the coalition objective subjected to operating constraints. The coalition objective function can be formulated as follows: u0Pj (R) =

X i∈Pj

u i (ri )

(2)

where u0i is the coalition utility function that maximizes the total payoff for the coalition for allocating R resource. Then the overall resource allocated to the mobile Pm user in the heterogenous network is given by: R = i=1 ri . We assume that there is a transferable utility (means that each coalition can achieve a certain total amount of utility with no restriction on how the total payoff may be divided among coalition members). IV.

L OAD BALANCING

It is of the interest for the coalition to take into account the goals of resource allocation and payoff maximization simultaneously with load balancing on the networks and to minimize the delays experienced by user data over the multiple networks. Load balancing in distributed systems has been formulated [10, 11] using game theoretic approaches. In [10], with cooperative approach, the authors have shown that the Nash Bargaining Solution provides a Pareto optimal allocation for the distributed system and it is also a fair solution. However, in [11], the authors follow the noncooperative approach for obtaining a user-optimal load balancing scheme in heterogeneous distributed systems. It is shown that the scheme guarantees the optimality of allocation for each user in the distributed system. Here, we employ an exponential cost function to assign congestion factor (which is a measure of the utilization of a network) to the networks. Using the exponential cost function, the congestion factor is computed for each network with li

cfi = e ci

(3)

where li is the network load and ci is the network capacity. 2.8 2.6

Based on the congestion factor, networks decide whether to allocate resources or not. We use the congestion factor to optimize network performance, e.g., to minimize maximum load or network delay. Figure 2 shows the plot of the congestion factor. With the congestion factor, the payoff for resource allocation will be different on each network, based on how much resource is already used. We allocate resource on networks where the sum of the payoff is maximized. If the request can not be satisfied on any network, then the request is rejected. Let λi = cf1i , then the payoff for allocating resource on network i is given by xi = λi ∗ri . The coalition is characterized by the maximum total payoff denoted by vector x = (x1 , x2 , ..., xn ), where xi is the payoff allocated to player i. V.

I LLUSTRATIVE E XAMPLE

Consider a cooperative game with three networks/players. Let r = (r1 , r2 , r3 ) be an 3−dimensional vector representing the amount of resources allocated to the user by the three players. The objective is to allocate the resources so that the total utility of the coalition is maximized, subjected to resource capacity constraints in each network. We assume that the user bandwidth demand equal 100 Mbits/s. Therefore r1 + r2 + r3 = 100. Let λ = (λ1 , λ2 , λ3 ) be an 1 3−dimensional vector representing cf for the multiple networks. Vector x = (x1 , x2 , x3 ) represents the total payoff is given by x = λrT . Let the characteristic function of the game given by Table 1: Coalition structure Coalition {∅} {1} {2} {3} {1,2} {1,3} {2,3} {1,2,3}

Coalition value 0 10 10 20 50 40 70 100

The imputations are the points (r1 , r2 , r3 ) such that r1 + r2 + r3 = 100 and r1 ≥ 10, r2 ≥ 10, r3 ≥ 20. The set of the imputations for the game is represented graphically as shown in Figure 3. The figure shows the core and various other solution points for the game. The core consists of all imputations in the trapezoidal area.

congestion factor

2.4 Accepted load or congestion level

2.2

VI.

C ONCLUSIONS

2 1.8 1.6 1.4 1.2 1

0

0.2

0.4 load / capacity

0.6

Figure 2: Congestion factor

0.8 1 no contribution

In this paper, we studied resource allocation in heterogeneous wireless network where users are able to split parallel applications over multiple heterogenous networks. Our main contribution is to apply cooperative game concepts to solve the problem of resource allocation in heterogenous wireless networks. We have presented a coalition structure that enable multiple networks to cooperate to fulfill resource allocation demands. A core allocation has been shown to exist for heterogeneous networks. We have shown

(70, 10, 20)

IEEE/ACM Transactions on Networking, 5(1):161– 173, February 1997. [9] X. Chang and K. R. Subramanian. A cooperative game theory approach to resource allocation in wireless ATM networks. In Proceedings of the NETWORKING 2000, volume 4, pages 969–978, 2000.

r1+r2=50

(40, 10, 50) r1+ r3=40

(30, 50, 20)

r2+r3=70 (30, 10, 60)

The Core

(20, 60, 20)

[10] D. Grosu and A.T. Chronopoulos. A game-theoretic model and algorithm for load balancing in distributed systems. In Proceedings of the International Parallel and Distributed Processing Symposium, pages 146– 153, 2002.

(10, 10, 80)

(10, 70, 20) (10, 60, 30)

(10, 40, 50)

Figure 3: The core of the three player cooperative game that such a resource allocation approach results in higher utilization of network resources and maximizes the outcome while potentially satisfying user performance requirements. We used an exponential cost function to balance the load on the networks. Our results for resource allocation are preliminary, and more work should be done to model resource allocation for multiple users and to study coalition formation strategies. R EFERENCES [1] H. von Stackelberg. The Theory of the Market Economy. Oxford University Press, Oxford, 1952. [2] P. J. M. Havinga, G. J. M. Smit, L. Vognild, and G. Wu. The SMART project: Exploiting the heterogeneous mobile world. In Proceedings of the 2nd International Conference on Internet Computing IC’2001, pages 346–352, 2001. [3] R. Jain and U. Varshney. Supporting quality of service in multiple heterogeneous wireless networks. In Proceedings of the IEEE IVehicular Technology Conference, pages 952–956, 2002. [4] A. Schill, S. K¨uhn, and F. Breiter. Resource reservation in advance in heterogeneous networks with partial ATM infrastructures. In Proceedings of the IEEE INFOCOM, pages 612–619, 1997. [5] A. B. MacKenzie and S. B. Wicker. Game theory in communications: Motivation, explanation, and application to power control. In Proceedings of the IEEE GLOBECOM, volume 2, pages 821–826, 2001. [6] W. F. Bialas. Cooperative n-person Stackelberg games. In Proceedings of the 28th IEEE Conference on Decision and Control, volume 3, pages 2439– 2444, 1989. [7] M. Simaan and Jr. Cruz, J. A Stackelberg solution for games with many players. IEEE Transactions on Automatic Control, 18(3):322–324, June 1973. [8] Y. A. Korilis, A.A. Lazar, and A. Orda. Achieving network optima using Stackelberg routing algoriths.

[11] D. Grosu, A.T. Chronopoulos, and Ming-Ying Leung. Load balancing in distributed systems: an approach using cooperative games. In Proceedings of the International Parallel and Distributed Processing Symposium, pages 52–61, 2002.