Game Theoretic Modeling of Cooperation among Service Providers in Mobile Cloud Computing Environments

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1 2012 IEEE Wireless Communications an Networking Conference: Services, Applications, an Business Game Theoretic Moeling of Cooperation among Service Proviers in Mobile Clou Computing Environments Dusit Niyato 1, Ping Wang 1, Ekram Hossain 2, Wali Saa 3, an Zhu Han 4 1 School of Computer Engineering, Nanyang Technological University (NTU), Singapore 2 Department of Electrical an Computer Engineering, University of Manitoba, Winnipeg, MB, Canaa 3 Electrical an Computer Engineering, University of Miami, FL, USA 4 Electrical an Computer Engineering, University of Houston, TX, USA Abstract Mobile clou computing aims at improving the performance of mobile applications an to enhance the resource utilization of service proviers. In this paper, we consier a mobile clou computing environment in which the service proviers can form a coalition to create a resource pool to support the mobile applications. First, an amission control mechanism is use to provie services of mobile applications to the users given the available long-term reserve resources in a pool. An optimization formulation is introuce to obtain the optimal ecision of amission control. Then, for a given coalition of service proviers, the revenue obtaine from utilizing the resource pool has to be share among the service proviers. A coalitional game moel is evelope for sharing the revenue. In aition, since the service proviers can ecie on shortterm capacity expansion of the resource pool, a game moel is introuce to obtain the optimal strategies of service proviers on capacity expansion such that their profits are maximize. Inex Terms Mobile clou Computing, cooperative game, an the core. I. INTRODUCTION Mobile clou computing combines wireless access service an clou computing to improve the performance of mobile applications. With clou computing, mobile applications can offloa some computing moules to be execute on a powerful server in a clou. As a result, mobile clou computing introuces a variety of benefits over traitional mobile services [1]. First, the power consumption of the mobile evice can be reuce since the complicate computations can be performe on a server. Secon, computing moules can communicate with an access other entities an services on Internet easily. Thir, reliability an security of mobile application are enhance since the full protection (e.g., antivirus software) can be eploye in a clou. Due to these benefits, many mobile applications are evelope uner mobile clou computing concept incluing e-commerce [2], healthcare [3], an computer games [4]. For mobile clou computing, the issue of offloaing has been stuie extensively in the literature [1]-[6]. In [5], an architecture to ynamically partition an application at a runtime was introuce. The coe portability is use to create two versions of a mobile application, one for the local execution on mobile evices an the other for the remote execution in a clou. In [6], an offloaing metho was propose in which the online statistics of the computation time are use to compute optimal timeout. If the computation on the mobile evice is not complete before the timeout, this computation will be offloae to the server. Apart from offloaing, resource management has emerge to be an important issue. Resource management for mobile clou computing must take into account not only the raio resource for wireless access, but also the computing resource for ata processing. In [7], an architecture to provie an intelligent network access strategy for mobile users to meet the application requirements was propose. A context management architecture (CMA) to acquire, manage, an istribute a context information was also introuce. In [8], a security service amission moel was evelope base on semi- Markov ecision process to support critical security (CS) an normal security (NS) services for clou users. The objective of this moel is to maximize the system rewar (i.e., clou income minus cost of the resource occupation) with resource consumption of the applications given the state (i.e., ongoing users). In this paper, we consier a scenario where multiple service proviers cooperatively offer mobile services (e.g., online gaming in mobile environments) to the users. The mobile service proviers can form a coalition to create a resource pool to improve the efficiency an utilization of long-term reserve wireless access banwith an servers in ata centers (which are presumably owne by clou service proviers). Three issues are aresse in this scenario: amission control of the mobile applications to the resource pool owne by the coalition of mobile service proviers, revenue sharing among the mobile service proviers, an optimal short-term capacity expansion by the mobile service proviers. An amission control scheme is evelope base on a linear programming optimization formulation to etermine the number of instances for the mobile applications (i.e., the number of supporte users) such that the maximum revenue can be obtaine from a resource pool. Given the amission control policy, a coalitional game moel is introuce for sharing the revenue among proviers. The solution in terms of ual payoff ensures that none of the proviers receives a revenue that is less than that achieve without joining a coalition. Then, proviers may have /12/$ IEEE 3160

2 a choice to expan their capacity to contribute more resources to a pool. This can be moele as a game an the Nash equilibrium solution ensures that the profit (i.e., revenue minus cost of expansion) of a provier cannot be improve if other proviers o not change their strategies of capacity expansion. The rest of this paper is organize as follows: Section II presents the system moel. The amission control an revenue sharing schemes are presente in Section III. Section IV escribes the game moel to obtain an optimal capacity expansion strategy of the service proviers. The numerical results are presente in Section V. Section VI raws the conclusions. II. SYSTEM MODEL In this section, we first introuce a mobile clou computing environment uner consieration. The efinition of the resources to support mobile applications in such an environment is then given. The escription of the cooperation among mobile clou service proviers to create a resource pool is presente. A. Mobile Clou Computing To provie seamless mobile service, it is assume that a mobile service provier reserves in avance the raio resources in its access network an computing resources from ata center (owne by clou service provier) in a long term basis, respectively. Note that reserving resource in a long term (e.g., 1 year) is cheaper compare with on-eman basis (e.g., 1 ay). Given the reserve resources, the number of application instances (i.e., the number of users running an application) to be able to support is etermine an use for amission control. Multiple mobile service proviers (or network operators) can cooperate by creating a pool to share their reserve raio an computing resources, an amission control is performe accoringly. In aition, each service provier can ecie to expan the capacity by reserving more resources in a short-term an on-eman basis. However, there will be a cost incurre to the provier. B. Wireless Network an Data Center Fig. 2. System moel of mobile clou computing. Fig. 1. Mobile clou computing moel. We consier a mobile clou computing environment in which a mobile application is ivie into two parts, i.e., local an remote computing moules running on a mobile unit an on a server, respectively (Fig. 1). The communications between these moules are through a wireless access. 1 Therefore, both raio an computing resources are require to run mobile applications. Wireless access points provie raio resource (i.e., banwith), while ata centers provie computing resources (e.g., CPU, memory, an storage) to support ifferent mobile applications. As shown in Fig. 1, a user requests to run a mobile application from an application server belonging to a mobile clou service provier (i.e., provier in short). An application server performs an amission control by checking the availability of the raio an computing resources at the associate wireless access point an ata center. If there are enough resources, the application server initializes the remote computing moules on a server in the ata center. Then, a mobile application is run. 1 Wire network is require for communications between mobile unit an server as well. However, in this paper, we assume that the banwith of wire network is much larger than that of wireless access. In a mobile clou computing environment, there is a set of areas (i.e., coverage areas of wireless access points) enote by A = {1,...,A} where A is the total number of areas. A set of access points is enote by B = {1,...,B} where B is the total number of access points. The availability of an access point b Bto the user in area a Ais enote by α a,b where α a,b =1if user in area a can connect an use banwith from access point b, an α a,b =0otherwise. There are P mobile applications offere in this mobile clou computing environment, an the set of mobile applications is enote by P = {1,...,P}. A set of ata centers is enote by D = {1,...,D} where D is the total number of ata centers. The accessibility of a ata center by a user using a mobile application is enote by β a,,p where β a,,p =1if user in area a Ausing application p Pcan run remote computing moule on a server in ata center D, an β a,,p =0otherwise. An example of mobile clou computing environment is shown in Fig. 2. There are three areas an five access points. Access points 1 an 2, 3 an 4, an 5 provie wireless access for areas 1, 2, an 3, respectively. Data center 1 provies computing resource for users in areas 1 an 2, while ata center 2 provies computing resource for users in areas 2 an

3 There are S mobile clou service proviers whose set is enote by N. The reserve banwith of provier s N at access point b is enote by Kb,s bw. The number of servers reserve by provier s at ata center is enote by K cp,s. The banwith require per instance of application p is enote by Rp bw. For computing resource, we assume that one server can accommoate 1/Rp cp instances of application p. In other wors, Rp cp can be consiere as the server utilization require per application instance. Supporting one instance of mobile application p generates revenue of V p for the service provier. C. Service Provier Cooperation an Resource Pool To increase the available resource for mobile applications, multiple proviers can cooperate an create a resource pool. A resource pool is logically compose of the reserve banwith from access points an servers in ata centers to support mobile applications. Let S N enote a set of proviers (i.e., coalition) cooperating to create a resource pool. Kb bw (S) an K cp (S) are the total reserve banwith an the total number of reserve servers at access point b an at ata center given coalition S, respectively. They can be obtaine from Kb bw (S) = Kb,s bw, an s S K cp (S) = K cp,s. (1) s S The revenue obtaine from a resource pool is aggregate for all cooperative proviers in a coalition. With the cooperation among proviers to create a resource pool, a couple of issues arise. First, the revenue obtaine from a resource pool must be share among cooperative proviers. Secon, the proviers have to ecie the strategy of contribution to a resource pool (i.e., to expan their capacity to gain higher profit or not). To aress these issues, in the following, a coalitional game moel will be evelope. III. ADMISSION CONTROL OF MOBILE CLOUD USERS In this section, an amission control mechanism to support mobile applications in mobile clou computing environments is presente. First, an optimization problem is formulate to obtain the optimal number of instances for running mobile applications. Then, a linear programming game moel is evelope to obtain the revenue sharing among proviers. A. Linear Programming Formulation The objective of amission control is to etermine the number of application instances (i.e., the number of active users) that maximizes the revenue. Let x a,b,,p enote the number of instances from users in area a running application p using banwith from access point b an server from ata center. Given the reserve banwith from access points an reserve servers in a resource pool for coalition S, the optimal number of application instances can be obtaine by solving the linear programming (LP) formulation efine as in (2)-(8). The objective function efine in (2) is to maximize the revenue obtaine from users in all areas with all access points an ata centers. The constraints in (3) an (4) are base on the reserve banwith an number of reserve servers in a resource pool. The constraint in (5) efines the maximum eman of applications D a,p. The constraints in (6) an (7) efine the feasibility of supporting mobile applications from access point an ata center, respectively. In this case, M is the maximum number of application instances that can be supporte. max x a,b,,p s.t. x a,b,,p V p (2) a A b B D p P a A D p P a A b B p P x a,b,,p R bw p x a,b,,p R cp p K bw b (S), b B(3) K cp (S), D (4) x a,b,,p D a,p, a A,p P (5) b B D x a,b,,p Mα a,b, a A, b B (6) D p P x a,b,,p Mβ a,,p, b B a A, D,p P(7) x a,b,,p 0 a A,b B, D,p P (8) B. Linear Programming Game of Revenue Sharing While the LP formulation efine in (2)-(8) etermines the optimal number of instances of mobile applications, revenue sharing is also an important issue. Therefore, a linear programming game which is a coalitional game with transferable utility (TU) is formulate an solve. A general coalitional game is efine as (M,v( )) where M is a set of players an v( ) is a value function. A value function v(s) is a mapping from nonempty coalition S to a real number. A value function v(s) is the maximum aggregate payoff available for ivision among players who are members of coalition S. A linear programming game of revenue sharing among all mobile clou service proviers is efine by M = N (i.e., gran coalition). The value function is obtaine as follows: v(s) = max x v T x (9) s.t. Ax g(s), (10) x 0, (11) where x is a vector of ecision variables x a,b,,p (i.e., number of application instances) an v is a vector of revenue per application instance V p. Specifically, each element of x is x a,b,,p an each element of v is V p as efine in (2). Matrix A is compose of coefficients Rp bw, R cp in (3)-(8). g(s) is a vector of constants K bw Mα a,b, an Mβ a,,p efine in (3)-(8). p, an constant 1 efine b (S), K cp (S), D a,p, 3162

4 z bw b min,zcp,zm a,p,zα a,b,zβ a,,p s.t. z bw b Kb bw (S)+ z cp Kcp D z m a,pd a,p (S)+ b B a A p P + za,bmα α a,b + z β a,,p Mβ a,,p (12) a A b B a A D p P zb bw Rp bw + z cp Rcp p + za,p m + za,b α + z β a,,p V p, a A,b B, D,p P, (13) zb bw,z cp,zm a,p,za,b,z α β a,,p 0, a A,b B, D,p P. (14) μ s (v(n)) = b B zb bw Kb,s bw + z cp K cp,s + D a A p P z m a,p D a,p + a A b B z α a,bmα a,b + a A D p P z β a,,p Mβ a,,p (15) The ual payoff is consiere to be a solution of the linear programming game efine in (9)-(11). To obtain the ual payoff, the ual problem of (2)-(8) is require, which can be expresse as in (12)-(14). zb bw, z cp, zm a,p, za,b α, an zβ a,,p are the ual variables corresponing to the constraints in (3)-(8). Their optimal solutions are enote as zb bw, z cp, za,p m, za,b α, an z β a,,p. With a gran coalition, the revenue of cooperative provier s N enote as μ s (v(n)) can be obtaine from (15). IV. OPTIMAL CAPACITY EXPANSION STRATEGY OF MOBILE CLOUD SERVICE PROVIDERS The proviers can ecie on an aitional capacity to be contribute into a resource pool through the short-term capacity expansion. Given the amission control ecision an ual payoff obtaine from Section III, optimal capacity expansion strategies of service proviers can be etermine base on game moel. Also, the istribute algorithm to reach the equilibrium strategy is presente. A. Game Formulation Although capacity expansion can increase the revenue obtaine from a resource pool, it incurs a certain cost to a provier. Therefore, the strategies of proviers to expan their capacities in a resource pool have to be optimize. The capacity expansion game efine as < N, {T s, }, {u s ( )} > can be evelope to moel an obtain the equilibrium strategies. N is a set of players (i.e., proviers). The strategy is the capacity (i.e., reserve banwith an servers) to be expane. Let the strategy space of provier s be a iscrete set efine as T s = {t s =(Kb,s bw(i),kcp,s (i)); i {1,...,I s} where I s is the total number of options for capacity expansion of provier s. Note that Kb,s bw (i =1)=Kbw b,s an Kcp,s (i =1)=Kcp,s are the original reserve banwith an servers, respectively. The payoff of provier s is a profit efine as u s (t s, t s )= μ s [v(n), (t s, t s )] C s (i), where t s is a strategy of provier s an t s are the strategies of all proviers except provier s. In this case, the ual payoff μ s ( ) from (15) of provier s is efine as a function of capacity expansion strategies of all proviers (i.e., t s an t s ). C s (i) is the fixe cost incurre to provier s associate with strategy expansion inex i. Note that the amission control an revenue sharing utilizes the results of resource capacity from the capacity expansion game as an input. Also, the capacity expansion game uses the ual payoff from the amission control an revenue sharing to etermine the solution. The Nash equilibrium is consiere to be a solution of this game < N, {T s, }, {u s ( )} >. The Nash equilibrium strategies are efine as t s an t s which satisfy the following conition: u s (t s, t s) u s (t s, t s), t s T s, s N. (16) B. Distribute Algorithm To reach a Nash equilibrium of the capacity expansion game of mobile clou service proviers efine in (16), the istribute algorithm can be evelope (Algorithm 1). In each iteration, one player is ranomly selecte to evaluate its current strategy (line 3). In this case, for most of the time (i.e., with probability 1 ɛ where ɛ is a small probability, e.g., ɛ = 10 4 ), the player optimally chooses the current best strategy (line 5). However, with small probability ɛ, the player chooses a ranom strategy to explore possible choices (line 7). Note that ran() is a ranom number generator. V. PERFORMANCE EVALUATION A. Parameter Setting We consier 3 mobile clou service proviers an 15 service areas. There are 30 access points in these service areas in which access points 1 an 2 are in area 1, access points 3 an 4 in area 2, an so on. There are two ata centers. Data centers 1 an 2 can support mobile applications from users in areas 1-10 an 6-15, respectively. Proviers 1, 2, an 3 reserve banwith of 1, 2, an 1 Mbps at each access point, respectively. Proviers 1, 2, an 3 reserve 20, 10, an 10 servers at each ata center, respectively. Two game applications are consiere, i.e., Worl of Warcraft game [9] an Plane-Shift game [10]. Worl of Warcraft game requires 500kbps of banwith an 40% of server utilization. The 3163

5 Algorithm 1 Distribute algorithm for capacity expansion game of mobile clou service proviers 1: Each player s initializes strategy t s [n] at iteration n 0 2: loop 3: Player s is ranomly selecte to perform strategy switching 4: if ran() < 1 ɛ then 5: Player s optimally chooses the new strategy t s [n + 1] arg max ts u s (t s [n], t s [n]) 6: else 7: Player s chooses the new strategy ranomly 8: en if 9: n n +1 10: en loop Fig. 4. Barycentric coorinates of the core an ual payoff. revenue of running this game is 5 money units (MUs) per instance. Plane-Shift game requires 400kbps of banwith an 80% of server utilization, an generates revenue of 6 MUs. B. Numerical Results Revenue Provier 1 (without cooperation) Provier 2 (without cooperation) Provier 1 (with cooperation) Provier 2 (with cooperation) Reserve banwith of provier 2 (Mbps) Fig. 3. Revenue of service proviers 1 an 2 with an without cooperation uner ifferent amount of reserve banwith of provier 2. We first consier two proviers (i.e., 1 an 2) with an without cooperation. Fig. 3 shows the revenue of both proviers when the reserve banwith of provier 2 is varie. Without cooperation, revenue of provier 1 remains constant, while that of provier 2 increases at the beginning. However, when reaching a certain point (i.e., about 0.8 Mbps) where the servers reserve by provier 2 are not enough to support mobile applications, the revenue of provier 2 remains constant since no more application instances (i.e., users) can be supporte. However, with a cooperation, provier 2 can utilize the servers reserve by provier 1, an consequently, the revenue of provier 2 increases. Note that a similar result can be observe when the number of reserve servers in a ata center is varie. This numerical result is omitte for brevity of the paper. In aition to ual payoff solution, the core of a gran coalition is consiere. Let r s enote a revenue of provier s. The core can be efine as follows: { C = r r s = v(n), } r s v(s), S N (17) s N s S where r is a vector of r s. In short, at the core of gran coalition, the sum of payoffs of proviers in any subcoalition S is always equal to or larger than the value of that coalition. Fig. 4 shows the barycentric coorinates of the core an ual payoff of the coalitional game of mobile clou service proviers. Without cooperation, the payoff of proviers 1, 2, an 3 are ( ,250,250), respectively. A set of efficient payoff shares is efine as a set of payoff shares of all proviers such that the sum of shares equals to the maximum payoff of all proviers. This set can be shown as a plane with coorinates ( , 250, ), (500, 250, 250), an ( , , 250). The coorinate inicates the payoffs of proviers 1, 2, an 3, respectively. The ual payoff is locate at (500, 250, 250). To etermine the core, there are three cooperation structures which efine the constraints of a set of efficient payoff shares. First, when proviers 1 an 2 cooperate, the value of this cooperation is v({1, 2}) = 750, an the corresponing constraint is shown to be a line at the bottom of a plane. When proviers 1 an 3 cooperate, the value is v({1, 3}) = 650, an that of proviers 2 an 3 is v({2, 3}) = 500. We observe that the core in this case is on the line along the constraint when proviers 1 an 2 cooperate. Dual payoff is part of the core. Then, we consier the case that the proviers can expan their capacities by 10% (i.e., by reserving more banwith an servers). With the cost of 40 MUs, again a set of efficient payoff shares can be shown as a plane (Fig. 5) with coorinates (580,250,250), ( , ,250), an ( ,250, ). In this case, the cost of capacity expansion is small. As a result, a plane of efficient payoff shares is above that without capacity expansion. Also, the core exists as a plane. Note however that if the cost of capacity expansion is high, a set of efficient payoff shares will ecrease an the core may not exist. In this case, the strategies of capacity expansion must be optimize. 3164

6 (2,2) (2,1)(2,0) (1,2) (1,1)(1,0) Strategies of proviers 1 an 2 (0,2) (0,1)(0,0) Stationary probability Strategy of provier 3 Fig. 5. Barycentric coorinates with capacity expansion. TABLE I GAME IN A MATRIX FORM Provier 3 P1 P (620,270,270)* (620,270,260) (620,270,270)* 2 1 (620,260,270) (620,260,260) (620,260,250) 2 0 ( ,270, ) ( ,270,300) (420,270,270) 1 2 (560,270,270) (560,270,260) (560,270,270) 1 1 (560,260,270) (560,260,260) (560,260,270) 1 0 (400,270, ) (400,270,300) (460,270,270) 0 2 (500,270,270) (500,270,260) (500,190,270) 0 1 (500,260,270) (500,260,260) (500,230,270) 0 0 (500,270,190) (500,270,230) (500,270,270)* Table I shows the game in a matrix form when proviers 1, 2, an 3 can choose to expan their resource capacity (i.e., reserve banwith at the access points an reserve servers at the ata centers). In this case, strategies 0, 1, an 2 mean no expansion, 10% expansion, an 20% expansion, respectively. The costs per 10% an 20% expansion are 40 an 80 MUs, respectively. Note that P1 an P2 stan for proviers 1 an 2, respectively. From this matrix form of a capacity expansion game, the Nash equilibria can be etermine (i.e., with * in Table I). Given the propose istribute algorithm, the probability of choosing strategies for capacity expansion by proviers 1, 2, an 3 is shown in Fig. 6. It is clear that the strategies with non-zero probability correspon to the Nash equilibria of the game. VI. CONCLUSION We have consiere a mobile clou computing environment in which some computing moules of mobile applications can be run remotely on a powerful server in a clou. Mobile applications are supporte by the mobile clou service proviers in which the raio an computing resources in terms of banwith an servers are reserve for the users, respectively. To improve the resource utilization an revenue, mobile service proviers can cooperate to form a coalition an create a resource pool for users running mobile applications. The amission control of this cooperative environment has been evelope base on optimization formulation. Also, the Fig. 6. Probability of using strategies by service proviers 1, 2, an 3. revenue sharing among cooperative proviers has been introuce base on a coalitional game (i.e,. linear programming game). With a coalition, proviers can optimize the capacity expansion, which etermines the reserve banwith an servers to be contribute to a resource pool. The objective of provier is to maximize the profit from supporting mobile applications through a resource pool. REFERENCES [1] K. Kumar an Y. Lu, Clou computing for mobile users: Can offloaing computation save energy?, Computer, vol. 43, no. 4, pp , April [2] X. Yang, T. Pan, an J. Shen, On 3G mobile e-commerce platform base on clou computing, in Proceeings of the 3r IEEE International Conference on Ubi-Meia Computing (U-Meia), pp , August [3] U. Varshney, Pervasive healthcare an wireless health monitoring, Journal on Mobile Networks an Applications, vol. 12, no. 2-3, pp , March [4] Z. Li, C. Wang, an R. Xu, Computation offloaing to save energy on hanhel evices: A partition scheme, in Proceeings of the 2001 international conference on Compilers, architecture, an synthesis for embee systems (CASES), pp , [5] E. Cuervo, A. Balasubramanian, D. Cho, A. Wolman, S. Saroiu, R. Chanra, an P. Bahl, MAUI: Making smartphones last longer with coe offloa, in Proceeings of the International Conference on Mobile Systems, Applications, an Services (MobiSys), pp , ACM, [6] C. Xian, Y. Lu, an Z. Li, Aaptive computation offloaing for energy conservation on battery-powere systems, in IEEE International Conference on Parallel an Distribute Systems (ICPAD), vol. 2, pp. 1 8, [7] A. Klein, C. Mannweiler, J. Schneier, an D. Hans, Access schemes for mobile clou computing, in Proceeings of the 11th International Conference on Mobile Data Management (MDM), pp. 387, June 2010 [8] H. Liang, D. Huang, L. X. Cai, X. Shen, an D. Peng, Resource allocation for security services in mobile clou computing, in Proceeings of Computer Communications Workshops (IEEE Conference on INFOCOM WKSHPS), pp , April [9] S. Wang an S. Dey, Moeling an characterizing user experience in a clou server base mobile gaming approach, in Proceeings of IEEE Global Telecommunications Conference (GLOBECOM), November- December [10] S. Wang an S. Dey, Renering aaptation to aress communication an computation constraints in clou mobile gaming, in Proceeings of IEEE Global Telecommunications Conference (GLOBECOM), December