A Cooperative Incentive Structure for Mobile Cloud Computing

Parallel and Cloud Computing Research, Volume 3 2015 www.seipub.org/pccr doi: 10.14355/pccr.2015.03.003

A Cooperative Incentive Structure for Mobile Cloud Computing Jianhua Fan1, Xianglin Wei*2, Ran Li3, Qin Sun4 PLA University of Science and Technology, Houbiaoying88#, Nanjing 210007, China ricy1213@126.com; *2wei_xianglin@163.com; ryanlee730@163.com

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Abstract Encouraging the mobile devices to contribute their idle resources is critical to promote the quality of service of Mobile Cloud Computing (MCC), especially when the remote cloud service is absent or the access bandwidth is limited.In order to achieve this goal, a carefully devised MCC architecture with appreciate incentive mechanismis needed. In this paper, inthe view point of cooperative game, an incentive structure based on Shapley Value is brought forward for Hybrid Local Mobile Cloud Model‐ with stabilityanalysis. Moreover, the implementation issues of the incentive structure and its experimental evaluation are pre‐ sented.

Keywords Mobile Cloud Computing; Architecture; Incentive; Shapley Value

Introduction Recent years we have witnessed the rapid development of mobile devices, such as PDAs, smartphones, etc.However, limited battery energy, CPU speed, store space and sensing capabilities of the mobile devices serious‐ ly restrict their quality of service, especially in the computing and sense intensive environments. Under this cir‐ cumstance, the concept of Mobile Cloud Computing (MCC) is suggested based on combining of cloud computing and mobile computing.

MCC brings rich resources ofcloud computing for mobile devices and applications, as well as inherits the cloud’s advantages, such as low cost, high scalability and robustness. Therefore, it greatly enlarges the potential of mobile computing. In MCC environment, mobile devices can offload full or part of their mobile applications to the data centers of the cloud so as to relievetheir own burden in CPU loads and energy consumption. This enables mobile devices to support more sophisticated and rich applications and services. In order to support these applications, researchers have proposed various architectures for MCC, such as MobiCloud[1], MAUI[2], CloneCloud[3], Cloud‐ let[4],Hyrax[5] and Hybrid Local Mobile Cloud Model (HLMCM)[6]. From these proposals, we can see that the resources resided on the mobile devices are very important for promoting the QoS of MCC.Therefore, how to stimulate the mobile devices to contribute their idle service capabilities is important as well as a chanllengingtask.

In this paper, from the perspective of cooperative game, an incentive structure based on Shapley Value is brought forward to stimulate the mobile devices to contribute their idle resources to the system. Morevoer, a mechanism which applies the proposed incentive structure to HLMCM is briefly presented.

This rest of the paper is organized as follows. Section 2 summarizes the related work. The background knowledge of Shapley Value is presented in Section 3. Section 4 puts forward the incentive structure with its stability analysis with simple experimental evaluation. Finally, weconclude our main work in Section 5.

Background and Related Work To provide high quality of service, MCC needs the contribution of computing and sensing capabilities from mobile devices. Therefore, ithas becomea hot topic in recent years. Under the framework of MCC, Yang et al. have pre‐ sented two different incentive mechanisms for two types of task sharing models [7]. In the platform‐centric model, their incentive mechanism is based on a Stackelberggame [8], which treats the platform and the users as the leader and the followers of the game respectively. They showed the unique Stackelberg Equilibrium, at which the utility of the platform is maximized, and noneof the users can improve its utility by unilaterally deviatingfrom its current

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strategy. For the user‐centric model, they design an auction‐based incentive mechanism, which is proved to be computationallyefficient, individually rational, profitable, andtruthful.Duanetet al.analyzedand compareddifferent incentivemechanisms for a client to motivate the collaborationof smartphone users on both data acquisition and distributedcomputing applications in MCC [9].For the data acquisition applications, they proposed a reward‐based collaboration mechanism,where the client announces a total reward to be shared amongcollaborators, and the col‐ laboration is successful if there areenough users willing to collaborate. Then they analyzed the distributed compu‐ ting applications with Contract theory [10]. Fernando et al. adopted a simple cost model and micro‐pay mechanism in their opportunistic job sharing framework [11]. Yang and Niyatoet al.modeled theresource allocation process of a MCC systemas an auction mechanism with premium and discount factors[12].The premium and discount factors indicate complementary andsubstitutable relations among cloud resources provided by theservice provider. Then they analyzed the individual rationality andincentive compatibility (truthfulness) properties of the users intheir proposed auction mechanism.

Shapley Value Let N be a set of players. Any nonempty subset S⊆N will be referred to as a coalition of the players. For each coali‐ tion S, itsworth function is denoted by V(S), which represents the total revenue produced by the service when all players of S provide resources. Let S be the profit of the i‐th player of S, we have V(S)=∑ ∈S S . The contribu‐ tion of each player to a coalition can be defined as marginal contribution.

The marginal contribution of player i to the coalition S⊆N\{i} is defined as Δ ,S S∪{ } S . Therefore, the contribution of a player only depends on the worth function. In cooperative game, there are two properties of the worth function need to be known, i.e. super‐additive and super‐modular.

A worth function V is super‐additive if S∪T S)+ T), for all S, T ⊆ N s.t. S∩T=∅. This means the worth of any two disjoint coalitions is notgreater than the worth of their union.

A worth function V is super‐modular if S∪ S T∪ T , ∀ S,T ⊆ N\{ },∀ ∈ N. This property means a player entering a larger coalition brings “more value” than that of a player entering a smaller coalition.

As an important solution of cooperative game, Shapley Value gives a method about how to divide the worth of the coalition among its players. For some particular coalition S and worth function V, the player i’s Shapley Value ∑ ∆ V,S π,i , ∀i ∈ S. Π refers to the set of all |S|! orderings of S, and S π,i is S, is defined as φi S, |S|! π∈Π the set of players preceding i in the ordering π. The Shapley value of player i can thus be interpreted as the ex‐ pectedmarginal contribution ∆i ,Sʹ), where Sʹ is the set of players in S preceding i in a uniformly distributed ran‐ dom ordering.

Shapley Value has been proved to have many attractive properties like anonymity, efficiency, additivity, symmetry and dummy. Therefore, in recent years, it has been widely applied to many areas. Moreover, there are two conclu‐ sions about the Shapley Value. , ∀ ∈ If V is super‐additive, then the Shapley value is individual rational, i.e. for all S⊂N, we have S, S. Individual rationality implies that no user has an incentive to abandon a coalition since the return it accrues through the Shapley value exceeds the individual profit that it would gain by abandoning S. In this sense, individ‐ ual rationality guarantees the stability of a coalition.

N, S , ∀ S ⊆ N. In other words, If V is super‐modular, then the Shapley value lies at the core of V, i.e. ∑ ∈S if V is super‐modular, no given subset of players has an incentive to leave the “grand coalition” N and form a smaller coalition. This implies that the “most stable” coalition is, in fact, the grand coalition. This is also called the condition to form the grand coalition.

Model and Incentive Structure Hybrid Local Mobile Cloud Model Hybrid Local Mobile Cloud Model (HLMCM)was put forward in [6], which extends the Cloudlet architectureto make the mobile devices contribute their computing and sensing capabilities. The general working process of

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HLMCM is shown in Fig. 1, and it mainly contains four steps:

FIG. 1THE GENERAL WORKING PROCESS OF HLMCM

(1) The Client offloads part or full of its applications to the Cloudlet. Note that the Client is also a mobile device, and it can also provide service for other devices’ mobile applications.

(2) The Cloudlet partitions the application into several tasks, and it sends some of the tasks to a few mobile de‐ vices that are willing to provide resources.Moreover, the Cloudlet also handles part of the tasks itself.

(3) The mobile devices handle received tasks and send their results to the Cloudlet.

(4) The Cloudlet aggregates the results from the mobile devices and its own processing result, and then sends the final result to the Client.

Model and Incentive Structure 1)

Players

From Section 4.1, we know that there are one Client who requests for service, one Cloudlet and a few mobile devices thatprovide service. From cooperative view, the Cloudlet and these mobile devices form a coalition.

2)

Revenue,operational cost

The Client needs to pay for the service received from the HLMCM. Here, we adopt a simple method, i.e. the cli‐ ent pays a flat rate R to the Cloudlet for each offloaded application. The payment happens outside HLMCM and is out of the scope of this paper. In order to provide the service, the coalition will incur an operational cost C, whichdepends on the number of devices who decide to join the coalition. Without loss of generality we assume that R is always larger than C, otherwise, HLMCM will reject to provide service to the Client.

3)

Coalition, worth function and Shapley value based incentive structure.

If Cloudlet itself handles all the offloaded applications, it can receive all the revenue R. However, as mentioned above, its resources are much less than those of the data center and cannot support a large amount of clients with acceptable QoS. Moreover, some applications need the sensing capabilities of the mobile devices rather than the computing capacity of the Cloudlet. Therefore, with the involvement of the mobile devices, the Cloud‐ let can provide high QoS for the clients, which will in turn bring more clients to the Cloudlet and more revenue.

At the same time, the cost C for each offloaded application can be reduced when it is separated among a few devices since putting it on the single device will lead to high CPU load and incur high cost while separated sub‐ task can be easily handled with less CPU load and energy consumption, i.e. less cost. In summary, the Cloudlet is willing to join the coalition. The mobile devices also want to join the coalition since providing service can bring extra profit to them. This profit can be implemented in many methods, such as a price reduction for the service it receives or electronic token and so on.

Let and P be the mobile devices that provide service and the Cloudlet respectively. Then, the coalition can be represented as N ∪ . Assume there are devices joining the coalition, i.e. | | .

Learningfrom theassumptions about the cost function in economics and game theory, this paper assumes that the cost function Cis a differentiable function of M, i.e. C=C(M), and C’<0, i.e. C is a monotony decreasing func‐ tion of M. Under this assumption, the worth of the coalition is . Since the Cloudlet (i.e. P) ∪ provides the mobile devices and the client with wireless infrastructure and application partition, the utility of any coalition without P equals to 0. In other words, N\ 0.This also means P is the veto player in the co‐

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alition.

When there is no mobile device in the coalition, i.e. N , P will receive all the revenue 0 . If there are M devices want to join the coalition, the cost will decreaseto C(M). This will bring extra utility for the coalition. For the coalition N ∪ , let N and N be the Shapley value of P and the i‐th mobile de‐ vices in N. We adopt a simple Shapley value based incentive mechanism that each player i will receive its corre‐ sponding Shapley value as its profit for providing service.

Analysis of the Incentive Structure This section mainly analyzes the stability of the incentive structure in the above section. We have two theorems about the structure.

Theorem 1.If the cost function C() is monotonicallydecreasing in M, then the incentivestructure is individually ra‐ tional.

Proof.From Section 3, we know that if the worth function V is super‐additive, then the incentive structure is indi‐ vidually rational. In other words, we have to prove that S∪T

S)+

T), for all S, T ⊆ N =

∪

s.t. S∩T=∅ (1)

When neither S nor T contains P, then ∪ 0, (1) holds. If S contains P, then we know ⊄ since ∩ ∅, thus 0. From the monotonicity of C(), we have ∪ , i.e. (1) holds. Thus when ⊆ , (1) still holds since S and T are symmetrical in (1). In summary, the worth function V() is super‐additive, and the proposed incentive structure is individually rational.

Theorem 2.If the cost function C() is monotonically decreasing, twice differentiable, andC’’<0, i.e. the second deriv‐ ative is lower than 0, then the incentive structure lies in the core of the game.

Proof.From Section 3, we know that we have to prove that V() is super‐modular, i.e. ∪

T∪

T , ∀ ⊆ T ⊆ N\

, ∀ ∈ N (2)

According to the monotonicity of C(), (2) is trivially true if j is P or ∈ T ⋀ ∉ . When ∈ , let ∪ and ∪ , we have ⊆ . Let M1, M2 be the number of mobile devices in and , then M1<M2. According to the definition of the worth function: V

∪

V

1

C

V T∪

V T

′

0 and

′′

′

C ′

= Since

C 1

C

d

d

0, we have d

′

1 d (3)

C′

Transform the bottom of logarithm of (3) with s=t+1, we have T∪

T ′

1

′

′

.

Therefore, (2) is true, i.e. V() is super‐modular. In other words, the proposed incentive structure lies in the core of the game.

Combining Theorem 1 and Theorem 2, we know that the proposed incentive structure is stable.

Mechanism Application and Evaluation In order to evaluate the effectiveness of the proposed incentive mechanism, this section conducts a few experi‐

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Parallel and Cloud Computing Research, Volume 3 2015 www.seipub.org/pccr

5500

5500

5000

5000

4500

4500

Profit

Profit

ments on the simulation platform adopted in [6].Moreover, we implement the application scheduling algorithms in [6] to reflect the profit of the system when various parts of the mobile devices adopt the proposed incentive mech‐ anism.The total number of the mobile devices is 100 while the number of applications to be scheduled is 200. Fig. 2 and Fig. 3 present the profit of HLMCM with Basic Scheduling (BS) algorithm[6] and Energy‐Efficient Application Scheduling (EEAS) algorithm[6] when various parts of the mobile devices adopt the proposed incentive mecha‐ nism. In Fig. 2 and Fig. 3, Mi represents for the ratio between the mobile devices adopted the incentive mechanism and the total number of mobile devices in the system.

4000

4000

3500

3500

3000

3000

2500 0.1

0.15

0.2

0.25

0.3 M

0.35

i

0.4

0.45

2500 0.1

0.5

FIG. 2THE PROFIT OF HLMCM WITH BS ALGORITHM WHEN VARIOUS PARTS OF THE MOBILE DEVICES ADOPTS THE INCENTIVE MECHANISM

0.15

0.2

0.25

0.3 M

0.35

0.4

i

0.45

0.5

FIG. 3THE PROFIT OF HLMCM WITH EEASALGORITHM WHEN VARIOUS PARTS OF THE MOBILE DEVICES ADOPTS THE INCENTIVE MECHANISM

From Fig. 2 and Fig. 3, we can see that the more mobile devices adopt the incentive mechanism, the more profits obtained by HLMCM. Moreover, this observation is independent of the scheduling algorithms adopted in the HLMCM.Therefore, it can greatly improve the profit as well as the QoS of HLMCM through adopting the incentive mechanism.

Conclusion and Future Work From the point view of cooperative game, an incentive structure based on Shapley Value is brought forward for HLMCM to stimulate the mobile devices to contribute their resources, its stability and the key problem on how to implement it is discussed also. Moreover, a simple experimental evalution on the incentive structure’s influence on the profit of HLMCM is provided.

ACKNOWLEDGMENT

This research was supported in part by National Natural Science Foundation of China under Grant No. 61402521, National Natural Science Foundation of China under Grant No. 61201216,Jiangsu Province Natural Science Foun‐ dation of China under Grant No. BK20140068.

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Jianhua Fanreceived the Ph. D. degree from Institute of Communication Engineering, Nanjing, China in 1999. Now he is work‐ ing as a senior researcher at the Nanjing Telecommunication Technology Institute, Nanjing, China. His research interests in‐ clude wireless ad hoc network, cognitive network and delay/disruption tolerant network.

Xianglin Weireceived a Bachelor’s degree from the Nanjing University of Aeronautics and Astronautics, Nanjing, China in 2007, and his Ph. D. degree in PLA University of Science and Technology, Nanjing, China. He is now working as a researcher at the Nanjing Telecommunication Technology Institute, Nanjing, China. His research interests include Cloud Computing, Peer‐ to‐Peer network, network anomaly detection, network measurement, and distributed system design and optimization.

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