Game Theoretical Formulation of Network Selection in Competing Wireless. Networks: An Analytic Hierarchy Process Model. Haris Pervaiz, John Bigham.
2009 Third International Conference on Next Generation Mobile Applications, Services and Technologies
Game Theoretical Formulation of Network Selection in Competing Wireless Networks: An Analytic Hierarchy Process Model
Haris Pervaiz, John Bigham School of Electronic Engineering and Computer Science Queen Mary University of London London, United Kingdom {harris.pervaiz, john.bigham}@elec.qmul.ac.uk Abstract—Network Selection mechanisms play an important role in ensuring quality of service for users in a multinetwork environment. These mechanisms handle the selection of an optimal wireless network to satisfy a user request. This paper proposes a radio resource management framework for integrated network selection mechanism control in multi- network environment as an interaction game between the service providers and customers in noncooperative manner to maximize their rewards. The proposed scheme comprises two steps. The first applies the analytic hierarchy process (AHP) to determine the relative weights of the evaluative criteria according to customer preferences and network condition. The second calculates the payoffs based on the relative weights calculated in the previous step and a utility function evaluation by each wireless network of each customer. Analytical and simulation results demonstrate the effectiveness of proposed model to achieve optimum network utility for the wireless networks along with optimizing the customer's satisfaction. The proposed model is preliminary and its contribution is to create an admission policy that can adapt to different coverage areas of a wireless network and depends on the priority of customers and their requirements.
networks show their ability to fulfill user requirements. The dynamic network selection is an optimization problem under certain objective function, which should be chosen to maximize their rewards. The outcome of the game is to decide which set of strategy must be selected independently by each network to maximize their rewards. In order to assure the desired QoS and avoid frequent handoffs in the heterogeneous systems, we integrate the Analytic Hierarchy Process (AHP) and non-cooperative game theory using utility functions into network selection algorithm to decide the best network for the mobile users. The rest of the paper is outlined as follows: in Section II, the related state of art work carried out in our research area is explained. In Section III, the system model and game theoretical formulation for network selection is described. Section IV and V describes the Simulation model and their results respectively. Finally, Section VI concludes the paper. II.
Game theory concepts have been applied to wireless networks on formulations for optimization purposes, namely, in flow and congestion control, network routing, load balancing, resource allocation and quality of service provisioning. A centralized algorithm is proposed in [3]. The network selection problem is formulated into an integer linear programming (ILP) problem to maximize the spectrum efficiency. This work only focuses on bandwidth usage; neither takes the user experience into account nor the fairness. The network selection problem has been mainly addressed in WLAN/cellular integrated environments [4, 7, 8]. Reference [8] addresses the network selection problem from network perspective. It also formulates this problem as a variation of Knapsack problem with multiple knapsacks. The best network for a user maximizes its total sum of admitted flows and also satisfies the QoS requirements. This approach does not consider the user satisfaction. In [5] the multi-agent system is used to collect dynamic information about networks and users. The multi-agent system is also responsible for network selection and resource allocation. Multiple criteria and user preference are both in the range of their consideration. The network selection algorithm is based on a cost function which makes decision depending on the weight of the attribute taken into consideration and the ability of network in accordance with that attribute. The network with the minimum overall cost is selected. In [6] Gazis et al. look at the complexity of being “Always Best Connected”. The focus is on user-centric
Keywords-Game Theory, Network Selection, WiMAX, Competitive networks, Analytic Hierarchy Process
I.
INTRODUCTION
Cellular systems have experienced exponential growth over the last decade and the demand for effective and careful resource allocation is greatly needed. To manage different QoS (Quality of Service) requirements, provide sufficient bandwidth and tolerable delays, and to guarantee a users’ service satisfaction, the CAC policies for cellular system need to consider not only the technical efficiency but also the tradeoff between this and a network provider’s profits [1]. Game theory [2] is a branch of mathematics that provides a suite of analytical tools to analyze the interactions of parties with conflicting interests. Each player has independent decision rights only over its own possible actions, which are confined to its strategy space. Hence, the network selection mechanism in multinetwork environment handles the selection of the best network to satisfy a user requirement. In this paper, we propose a network selection mechanism in which the QoS factors are decided according to user and network specific requirements. The criteria objectives comparisons show the importance of the particular requirements with respect to the mobile user. The comparisons between alternative 978-0-7695-3786-3/09 $26.00 © 2009 IEEE DOI 10.1109/NGMAST.2009.28
RELATED WORK
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activate the subscription or not. The competing networks are assumed and referred as network ‘i’ where i=1 to m.
benefit. The research involves identifying the network or combination of access networks from the available candidates that will best satisfy the current user requirements in their current circumstances. In our previous work [10] the game model is formulated between the different competing network providers based on the offered price. In that work, the providers try to offer the price strategy to the user independently in such a way that it maximizes the rewards for each competing network. The solution to the game is found using Nash Equilibrium. The sole objective of the model was monetary profit. This work is an extension of our previous work with focus on multi-objective problem of the network selection in heterogeneous wireless environment in accordance with user satisfaction. In this paper we have considered different user requirements and map these user requirements to the competing network conditions as a part of our heterogeneous network selection model. This paper also considers the avoidance of frequent vertical handoffs to minimize the loss of revenue for network providers. III.
Figure 1: Heterogeneous wireless environment scenario
We consider a non-cooperative game of multinetworks which has a finite number of pure strategies. In non cooperative game, no preplay communication is permitted between the networks. The players in this game are the WiMAX and two WLAN providers. The strategy of player ‘i’ (i.e. Provider) represented by Si is the set of the prices being offered by the respective network. The payoff for provider ‘i’ is the revenue which is denoted by Ri. The payoff for each player is directly related to a user generated preference value corresponding to that network. For a network provider to be selected it needs to satisfy user requirements of the Relative Value Vector for each criteria objective. Each user has a limited budget Puser for subscription. At the time of network selection, the user is supplied with a price offered Pioffered by each network for the service. If the offered price by provider is less (or more) than user budget it will gain a positive (or negative) reputation. Similarly degradation can be assumed such as it is between 0 and 1 depending on the type and load of the network. Each network is assigned the ratio of (probability to degrade) :( probability not to degrade) according to the type and load of the network. We assume that for higher network coverage area the probability of degradation for the particular network increases, because the network with higher coverage area cannot always guarantee better QoS. Availability is a measure of the ratio of allocated bandwidth to the total bandwidth. Further detail about user preference and provider’s payoff is explained in Subsection C and D respectively.
HETEROGENEOUS WIRELESS NETWORK SELECTION
A. System Model We consider a competitive heterogeneous wireless access network model in which multiple wireless networks operated by different service providers coexist and offer their services to users. Each provider is aware of the competitive nature but is not aware of other providers’ actions, and bases its actions on his own network’s condition. The integrated heterogeneous wireless access system model is shown below in Fig. 1 consists of one IEEE 802.16 WiMAX network provider and two IEEE 802.11 based WLAN providers. Since WiMAX has greater coverage area as compared to WLAN, we need to make sure users stay within a WLAN coverage for sensible time frame to be considered for selection in order to avoid frequent vertical handoffs. The user decision could be either maintaining the actual connection but with a more favorable price or moving to an alternative network which offer a better access service. In this work, we assume the latter decision. Each time a user wishes to receive a service, they can express their preferences for different criteria factors according to their requirements. When the user selects a provider, a contract is established with the provider. The pilot signal strength, (modeled as a function of distance in the simulations) is used as a measure of power consumed to serve a user is used to measure the quality of service provided. The network selection is divided into two steps: processing user preference data and make network selection based on network specific data best satisfying user preferences.
C. User Preference Every new user connection request has some parameters associated with it. Some users prefer the quality of service whereas some prefer low cost. The network should be able to provide the services requested by users. The probability of selection for a network is a measure of user satisfaction with respect to the services it requested. The user will always prefer a network with high probability of success AHP has already been applied to a number of areas such as predicting economic outcomes and resolving conflicts. Analytic Hierarchy Process (AHP) [9] is a Multi Criteria decision making method to derive ratio scales from paired comparisons. The input can be obtained from actual measurements (price, quality of service etc) or from
B. Game Formulation We assume the providers offer their prices simultaneously. For simplicity here, all traffic units are assumed to be assigned the same user grade. The provider makes the first move by deciding to accept or reject the new connection request. After that user decide whether to
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The relative importance of each criteria objective can be computed as normalized geometric means of the rows. The geometric means for criteria objective ‘j’ i.e. Reputation is computed as shown below in Eq. (1):
subjective opinion such as satisfaction feelings and preference. The decision factors of the problem are identified and inserted into the hierarchy. The overall objective is placed at the topmost node of the hierarchy. The subsequent nodes present the decision factors. The solution alternatives are located at the bottom nodes. For instance, if a user is making selection between ‘m’ networks namely as Network ‘1’, Network ‘2’ and Network ’m’. The user’s preference criteria are Cj (Availability), Cj+1 (Reputation), Cj+2 (Degradation) and Cj+3 (Price). The hierarchy on “choosing a network” is established as shown in Fig. 2. There are two comparison groups: a group of four criteria objectives and a group of ‘m’ alternatives.
m j = n 1 × n a j , j +1 × n a j , j + 2 × n a j , j +3
(1)
Similarly, the geometric means can be computed for the other criteria objectives i.e. simply multiplying all the entries in the corresponding row and taking their nth root. These groups of geometric means (m1, m2, m3, m4) for particular criteria objective divided by sum of all geometric means are called the Relative Value Vector (RVV). These four numbers correspond to the relative values of the Reputation (R), Degradation (D), Price (P) and Availability (A). The RVV can be computed as follows:
RVV j1 = m j / n j
(2)
4
Where
nj = ∑mj j =1
D. Provider’s Payoff Our next step is to evaluate all the alternative networks against each criteria objective. We need four sets of pair wise comparisons but this time in terms of how well alternative networks perform in terms of criteria objectives. Every competing networks (alternatives) in Level ‘2 is compared against each other for every criteria objectives in Level ‘1’and assigned a number between 1 to 9 based on the perceived intensity of importance. The more detail about assigning an importance to a network for a particular criteria objective is shown in Section 6. Let the Relative Value Vector of criteria objective ‘j’ for each available network ‘i’ represented as ‘RVVj, i2’is calculated similarly as shown before in Eq. (1) & (2). The RVV values of alternative networks (Level 2) in terms of the four criteria objectives i.e. Reputation (R), Degradation (D), Price (P) and Availability (A) is shown below in Table II:
Figure 2: Choose a Network
In the first step, every objective is compared against all objectives within the same parent to decide the relative importance of each criteria objective. The comparisons within the same parent result in a square matrix. The size of square matrix depends on the number of pair wise comparisons within the same parent (e.g. “choosing a network” a square matrix of 4*4 is created). Each pair wise comparison is based on the importance and the factor by which it is important. A 1 to 9 scale is used to allow the decision maker to express the strength of preference. The numbers from 1 to 9 are used to respectively present equally, weakly moderately, moderately, moderately plus, strongly, strongly plus, very strongly, very very strongly and extremely important to the objective. Comparing criteria factors ‘j’ and ‘j+1’ gives a value aj, j+1. If the value of aj,j+1=k then the value of aj+1,j=1/k. All the diagonal values ‘aj, j’ in the square matrix are set to ‘1’.The smaller preference in a pair is chosen as a unit and the larger one is estimated as a multiple of that unit and assigned a number based on the perceived intensity of importance. Similarly, the reciprocals of these numbers are used to show the inverted comparison results. We thus obtain a reciprocal matrix where the entries are symmetric. The square matrix for the Analytic Hierarchy process (mentioned in Figure 1) is shown as below in Table I:
TABLE II: WEIGHT OF ALTERNATIVE NETWORKS IN ACCORDANCE WITH CRITERIA OBJECTIVES
TABLE I: CRITERIA OBJECTIVE COMPARISON
Reputation
Degrad ation
Price
Availability
R
1
aj, j+1
aj, j+2
aj, j+3
D
aj+1,
j
1
aj+1, j+2
aj+1, j+3
P
aj+2,
j
aj+2, j+1
1
aj+2, j+3
A
aj+3,
j
aj+3,
j+1
aj+3,
j+2
NW I
R
D
P
A
RVVj, i2
RVVj+1,i2
RVVj+2,i2
RVVj+3,i2
i+1
RVVj,i+12
RVVj+1,i+12
RVVj+2,i+12
RVVj+3,i+12
M
RVVj, m2
RVVj+1,m2
RVVj+2,m2
RVVj+3,m2
In the final step, the reward index for each available network is calculated. The reward index is the respective abilities of alternative networks to achieve the desired criteria objective. For each available network, the RVV values of each criteria objective calculated in level ‘1’ is multiplied with corresponding RVV values calculated in level ‘2’. The decision about network selection is based on the reward index for each network. We assume there are ‘m’ networks and ‘n’ criteria objectives. The revenue for each network compromises of two parts: 1) The network reward index
1
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2) Within the overlapping coverage area of network 1 and 2 3) Within the overlapping coverage area of network 1,2 and 3
2) The utility ‘Ui’ to be gained if the user select the network The reward index for network ‘i’ is given as follows:
ri =
n
∑
RVV
1
j
× RVV j2,i
V.
(3)
The revenue for each network in a particular cell is shown below in Eq. (4):
Ri = ri × U i
(4)
In this case, the utility in fact depends on the location of the mobile unit as the resources required depend on the location. U is defined as a number between 0 and 1such that it is ‘1’ when the user is close to the base station (or AP) and ‘0’ when the user is far from the base station (or AP). In the simulation the modified utility value decreases with the perceived distance from the particular base station (or AP). U i = 1 − α (d max − d min ) (5) U is defined for each network to serve the minimum distance between the user and the base station whereas the maximum distance can be up to 1.5km depending on the network type. From network perspective, the less transmitting power will be needed to serve a user at d=dmin as com pared to user at d= dmax. α, dmin and dmax is chosen so that U ranges from ‘1’ to ‘0’ according to the wireless net-work being used. However there are situations where it is possible to configure the antenna propagation so the network operator can affect the value of U. The details of how this can be done are not described here, but are described in [11]. The Eq. (4) can be rewritten as shown below in Eq. (6)
Ri = ri × (1 − α (d max − d min )) IV.
(6)
THE SIMULATION MODEL
Simulations are based on cellular WiMAX network and three AP’s of each WLAN provider. All BSs and AP’s are in the centre of the belonging cell. The network which satisfies the user requirements and the requested QoS is selected. We assume that the coverage of WLAN provider ‘1’ (A), WLAN provider ‘2’ (B) and WiMAX BS’s are 200m, 400m and 1000m respectively. In the simulation scenario, a mobile user is moving clockwise at a constant speed of 10metre per second throughout the simulation scenario shown in Fig 1. The network selection decision for this scenario can be divided into three cases: 1) When there is only one network TABLE III: CRITERIA OBJECTIVE COMPARISON
R
D
P
A
RVV1
R
1
1/3
5
1
0.232
D
3
1
5
1
P
1/5
1/5
1
A
1
1
5
RESULTS
User’s preference on criteria objectives are defined in Table III. The pair wise comparison of alternatives for each criteria objectives are done based on original network parameters shown in Table IV which decide the preferred network and intensity of importance. Example For every pair wise comparison between alternative networks, the respective price being offered is considered. When both the prices being offered is well above (or well less) than user expected value, they are equally preferred. When both prices being offered are less than user expected value, a $1 difference in price does not matter, but a $2 difference is strongly important, and a $4 difference is extreme. Whenever a network that is less than user expected value is compared with one that is well above user expected value, the former is extremely preferred. The network prices being offered above or below the user expected value determine the preferred network whereas their difference decides the relative importance. The relative importance of each network for every criteria objective (Degradation, Price, Reputation and Availability) is defined in Table V (a),(b),(c) and (d) respectively. The Relative value vectors for alternative networks for every criteria objective is shown below in Table VI. The network selection results based on reward index for each competing networks are shown below in Figure 3. The results show that network 3 never gets selected because its reward index is less than the other two competing networks. The network selection results with user preference based on criteria objective Reputation is shown below in Figure 4. In Figure 5, the network selection is shown with user preference on price while Figure 6 and 7 show network selection with user preferences on Degradation and Availability respectively. It is also noted that mobile user selects high reliable WLAN 3 (NW3), when WiMAX (NW1), WLAN 2 (NW2) and WLAN3 (NW3) are simultaneously available. Similarly the mobile user selects low price WLAN2, when WiMAX (NW1), WLAN 2 (NW2) and WLAN3 (NW3) are simultaneously available. However the network selection result would change if the user changes his preference as shown in Figure 8. Increase in the Relative Value Vector for price enhances the selection of Network ‘2’.Similarly increase in the Relative Value Vector for Degradation and Availability enhances the selection of Network ‘1’.
j =1
TABLE IV: NETWORK PARAMETERS
NW1
NW2
NW3
R
0.3
0.4
0.5
0.402
D
0.2
0.3
0.5
1/5
0.061
P
$1.2
$0.8
$0.9
1
0.305
A
0.6
0.35
0.25
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TABLE V: NETWORK COMPARISONS WITH RESPECT TO CRITERIA OBJECTIVES (DERIVED FROM TABLE IV)
D NW1 NW2 NW3
NW1 NW2 NW3 1 1 5 1 1 3 1/5 1/3 1 (a) Degradation
P NW1 NW2 NW3
NW1 NW2 1 1/9 9 1 5 1/2 (b) Price
R NW1 NW2 NW3
NW1 NW2 NW3 1 1/3 1/9 3 1 1/3 9 3 1 (c) Reputation
A NW1 NW2 NW3
NW1 NW2 NW3 1 5 9 1/5 1 3 1/9 1/3 1 (d) Availability
NW3 1/5 2 1
TABLE VI: RANKING VECTOR FOR ALTERNATIVES WITH RESPECT TO EACH ATTRIBUTE
R
D
P
A
ri
NW1
0.077
0.480
0.066
0.751
0.392
NW2
0.231
0.406
0.615
0.178
0.406
NW3
0.692
0.114
0.319
0.071
0.204
Figure 3: Network Selection based on Reward Index
Figure 4: Network Selection with user preference on Reputation
Figure 5: Network Selection with user preference on Price Figure 6: Network Selection with user preference on Degradation
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Reward Index for Alternative Networks w.r.t Relative Value Vector for price 0.6
Reward Index
0.5 0.4 NW1
0.3
NW2 NW3
0.2 0.1 0 0
Figure 7: Network Selection with user preference on Availability
0.2
0.3
0.4
0.5
0.6
0.7
Relative Value Vector for Price
Figure 8: Reward Index for Alternative networks with respect to Relative Value Vector for Price
Network selection mechanism is a process of balancing user preferences and network condition. VI.
0.1
[2] T. Basar and G. J. Olsder, Dynamic Non-cooperative Game Theory, 2nd ed. SIAM, 1998 [3] Huiling Jia, Zhaoyang Zhang, Peng Cheng, Hsiao-Hwa Chen, and Shiju Li, “Study on Network Selection for NextGeneration Heterogeneous Wireless Networks,” Personal, Indoor and Mobile Radio Communications, 2006 IEEE 17th International Symposium on, 2006, pp. 1-5. [4] V. Gazis, N. Alonistioti, and L. Merakos, “Toward a generic "always best connected" capability in integrated WLAN/UMTS cellular mobile networks (and beyond),” Wireless Communications, IEEE, vol. 12, 2005, pp. 20-29. [5] A. Iera, A. Molinaro, C. Campolo, and M. Amadeo, “An Access Network Selection Algorithm Dynamically Adapted to User Needs and Preferences,” Personal, Indoor and Mobile Radio Communications, 2006 IEEE 17th International Symposium on, 2006, pp. 1-5. [6] V. Gazis, N. Houssos, N. Alonistioti, and L. Merakos, “On the complexity of "Always Best Connected" in 4G mobile networks,” Vehicular Technology Conference, 2003. VTC 2003-Fall. 2003 IEEE 58th, 2003, pp. 2312-2316 Vol.4. [7] Q. Song, A. Jamalipour, “Network Selection in an integrated wireless LAN and UMTS environment using mathematical modeling and computer techniques.” IEEE Wireless Communication Magazine; Volume 12, Number 3, Page 42-48, 2005. [8] Q. Song and A. Jamalipour, “Quality of Service Provisioning in WirelessLAN/UMTS Integrated Systems Using Analytic Hierarchy Process and Grey Relational Analysis,” in Proc. of IEEE GLOBECOM, Dallas, TX, USA, Nov./Dec. 2004. [9] T.L.Saaty,“The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation,” McGrawHill, NewYork, 1980. [10] Haris Pervaiz, John Bigham, Peng Jiang. and Mei Pou Chen, “A Game Theoretic based Call Admission Control Scheme for Competing WiMAX networks,” in Proc of The Second IEEE International Conference on Computer, Control and Communication, IEEE-IC4-2009 ,Karachi, Pakistan, 17th-18th Feb 2009. [11] L. Du, J. Bigham, and L. Cuthbert, “A Bubble Oscillation Algorithm for Distributed Geographic Load Balancing in Mobile Networks,” The Twenty-third Annual Joint Conference of the IEEE Computer and Communications Societies, IEEE INFOCOM'2004,Hong Kong, March 2004.
CONCLUSION
In this paper, we have presented a modeling approach for network selection in heterogeneous networks environment. The proposed scheme considered multiple decision factors and multiple optimization objectives. The network selection between competing networks based on decision factors derived using AHP is modeled as a game between non-cooperative players illustrated here using a WiMAX network and two WLAN networks. A wireless environment where user commitment to particular network depends on parameters like reputation, degradation, availability and price, each of which contributes to the provider’s utility is considered. This is used to give a theoretical formulation of a game representing the conflict situation between the network provider and the users. The solution of the game can be used to define a specific strategy set for a user lying in a particular coverage area. The simulation results of our proposed network selection mechanism shows the variation in policy depending on changes in user preferences. However, there are still some issues that need further consideration. Firstly, our proposed scheme should be able to decide whether the networks should compete for a particular user or not. Secondly, our proposed scheme should be able to enforce cooperation between networks in overloaded or emergency scenarios. Finally, the proposed scheme should be able to promise QoS for high priority users without degrading the existing users. ACKNOWLEDGMENT Haris Pervaiz is a research student at School of Electronic Engineering & Computer Science, Queen Mary University of London, United Kingdom funded by National University of Science & Technology, Islamabad, Pakistan for his PhD studies. REFERENCES [1] L. Badia and M. Zorzi, “Dynamic utility and price based radio resource management for rate adaptive traffic,” Wireless Networks, vol. 14, Dec. 2008, pp. 803-814.
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