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12 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 25, NO. 1, JANUARY 2014 A Novel Economic Sharing Model in a Federation of Selfish Cloud Providers Nancy Samaan, Member, IEEE Abstract—This paper presents a novel economic model to regulate capacity sharing in a federation of hybrid cloud providers (CPs). The proposed work models the interactions among the CPs as a repeated game among selfish players that aim at maximizing their profit by selling their unused capacity in the spot market but are uncertain of future workload fluctuations. The proposed work first establishes that the uncertainty in future revenue can act as a participation incentive to sharing in the repeated game. We, then, demonstrate how an efficient sharing strategy can be obtained via solving a simple dynamic programming problem. The obtained strategy is a simple update rule that depends only on the current workloads and a single variable summarizing past interactions. In contrast to existing approaches, the model incorporates historical and expected future revenue as part of the virtual machine (VM) sharing decision. Moreover, these decisions are not enforced neither by a centralized broker nor by predefined agreements. Rather, the proposed model employs a simple grim trigger strategy where a CP is threatened by the elimination of future VM hosting by other CPs. Simulation results demonstrate the performance of the proposed model in terms of the increased profit and the reduction in the variance in the spot market VM availability and prices. Index Terms—Cloud federation, cloud provider, capacity outsourcing, repeated game, subgame perfect equilibrium Ç 1 INTRODUCTION C LOUD computing is an emerging paradigm that substantiates the vision of commodifying computational power, storage, and software services [1], [2]. In such a vision, software applications of different clients are executed over the shared cloud which offers its infrastructure as-a service (IaaS). Yet, all applications run in complete isolation through virtual execution environments or virtual machine (VM) instances which are seamlessly launched and terminated on the cloud data centers to host applications of cloud clients on a per-needed basis. Clients of an IaaS cloud are mostly service providers ranging from small-scale companies to world-wide enterprises and webservice providers but can also represent single users. Unfortunately, one of the major problems that face the cloud providers (CPs) is the uncertainty in their workloads; a spike in the requested VMs may result in higher service rejection rates and experienced delays by clients due to congested resources. A straightforward solution to overcome this problem is to over-provision the available resources to be able to meet their peak demands. Yet, this solution may lead to highly underutilized capacity during other periods of low demands. A more efficient solution, followed by hybrid clouds, is to only guarantee the availability of VMs to a limited number of clients and plan the cloud capacity to meet their peak workloads [3]. The CP would then offer the spare capacity during low . The author is with the School of Electrical Engineering and Computer Science, University of Ottawa, 800 King Edward, Ottawa, Ontario K1N 6N5, Canada. E-mail: Manuscript received 17 Oct. 2012; revised 3 Jan. 2013; accepted 3 Jan. 2013; published online 22 Jan. 2013. Recommended for acceptance by V. Misic. For information on obtaining reprints of this article, please send e-mail to:, and reference IEEECS Log Number TPDS-2012-10-1077. Digital Object Identifier no. 10.1109/TPDS.2013.23. 1045-9219/14/$31.00 ß 2014 IEEE utilization periods to second-class clients in a spot market [4]. These clients would take advantage of reduced prices but with no service availability guarantees. This model has been successfully adopted by a number of existing CPs such as Amazon EC2 [5]. Nonetheless, demand fluctuations of guaranteed-service clients reflect similar variations in spot VM availability and, in turn, results in nonpredictable request delays, rejections, and termination as well as price fluctuations [6]. Federated clouds [7], depicted in Fig. 1, approach the CP problem by allowing peer CPs to share their unused capacities during low-demand periods and borrow spare capacity during peaks to maximize their profits and enhance their clients’ experience [8], [9], with several strategies for capacity sharing in the federation proposed in [4], [8], [10]. These efficient schemes help the federated CPs to decide on outsourcing capacity from other CPs by launching or migrating VMs on their servers or insourcing capacity by hosting VMs of clients of other CPs. A number of these sharing mechanisms employ either predefined or dynamic pricing rules (e.g., [7]) to regulate the VM hosting exchange among CPs, mostly, with the objective of maximizing their instantaneous revenues. To the best of the author’s knowledge, the work presented in this paper is the first to address the general problem of maximizing the CP’s long-term revenue where current capacity sharing decisions in the federation depend on the revenue obtained from previous sharing decisions as well as on the expected revenue in the future. To this end, the contributions of the proposed work can be summarized as follows: . We derive the capacity sharing strategies that maximize the long-run revenue of the federation, dubbed as socially optimal spot market allocations, and demonstrate their enforcement limitation. Published by the IEEE Computer Society SAMAAN: A NOVEL ECONOMIC SHARING MODEL IN A FEDERATION OF SELFISH CLOUD PROVIDERS Fig. 1. The adopted model of the federated clouds. Using a formulation based on multistage games, we introduce a set of self-enforceable CPs capacity sharing strategies that maximize the federation’s long-term revenue yet can achieve more revenue than what the individual CP can achieve outside the federation. We prove that the profit obtained from the aforementioned repeated game can derive a higher revenue using a simple grim trigger punishment strategy. . We derive a simple update rule to find the subgame perfect Nash Equilibrium (SPNE) values for the spot market allocations. This rule is only dependent on the observed current state and a single variable that summarizes the history of previous interactions. We also develop a simple dynamic program that can be employed to obtain the exact values for these allocations in practice. The remainder of the paper is organized as follows: Section 2 discuses related approaches in the literature. The capacity sharing problem of the cloud federation is formulated in Section 3. Section 4 is dedicated to analyzing the federation’s socially optimal revenue and the individual CPs revenues. The proposed repeated game model is analyzed in Section 5. A recursive formulation of the optimal strategies is then introduced in Section 6, while Section 7 discusses how to numerically obtain these strategies. Finally, the performance of the proposed mechanism is demonstrated in Section 8, and Section 9 concludes the paper. . 2 RELATED WORK Early approaches to a model of a cloud federation can be found in [7], [8], [11]. Buyya et al. [1] introduced a marketoriented VM exchange model among clouds. The proposed work complements these approaches by deriving closedform formulations for the sharing strategies among the CPs that, if followed, leads to optimal revenues. Federations of hybrid clouds were also discussed in [10], [12]. Goiri et al. [10] proposed a novel federation management architecture and focused on building an accurate revenue function of CPs when taking one of the following decisions: participate in the federation by outsourcing or insourcing capacity or turning off spare capacity. Similarly, Toosi et al. [12] provided a comprehensive analysis of the related costs and revenue associated with the various decisions of the CP in the federation. 13 A mechanism to dynamically allocate resources of distributed data centers among different spot markets with the objective of maximizing the total revenue is introduced in [13]. Similar to the proposed approach, the authors necessitate the need to model or forecast the CP’s demand. It can be seen that their developed mechanism is similar to the fully federated model discussed in Section 4. A marketclearing pricing mechanism is developed in [14], where a centralized broker dynamically adjusts a single VM price for the federation. The proposed model does not assume any specific pricing scheme for the spot markets, and can employ that of [14] following resource allocation. Mihailescu et al. [15] relied on a centralized market broker in the federation, to which sellers publish resources and buyers send requests. Le et al. [9] addressed the cooperation problem among CPs but from the perspective of load balancing and electricity consumption. On the other hand, Lee et al. [16] focused on achieving a better quality of service by the CPs. The problem of allocating the appropriate cloud provider when considering tasks with deadline constraints is presented in [17]. Finally, the work in [18] addresses the consumer’s problem of selecting a VM reservation plan or request resources on demand with the objective of reducing the service cost. In general, existing approaches in the literature are concerned only with the instantaneous CP gains. To the best of the author’s knowledge, the presented work is the first to take into consideration the outcome of historical and future interactions among the CPs in making sharing decisions in the federation. This new generalization leads, as will be shown by the simulation results, to a higher accumulated profit by the CPs. The model can also be extended to incorporate additional constraints for each CP to account for different issues (e.g., energy consumption). Economic theories have also been adapted to the context of resource allocation in the literature (e.g., [19], [20]). However, most of the attention of these approaches has been focused on finding efficient pricing strategies or techniques for solving the centralized optimization problem of utility maximization in a decentralized manner. For example, Streitberger and Eymann [21] describe a model of resource seller and buyer agents which learn from previous resource trades to decide the exchanged prices for the current resource request. To the best of the author’s knowledge, the presented work is the first to address the problem of the federated CPs long-term revenue maximization given future workloads uncertainty. 3 PROBLEM FORMULATION As shown in Fig. 1, we consider a federation N of jN j ¼ N hybrid cloud providers, CP1 , . . . , CPN . Each CP, CPi , owns a fixed amount of computational resources (e.g., CPU and storage) which are sold to clients as instances of virtual machines that are hosted on the CP’s data centers. For simplicity, we will focus on a single VM type, with Ci denoting the number of VM instances that can be hosted by CPi . This assumption can be easily relaxed by either assuming a different market for each VM configuration or by adopting a more elementary resource measure such as 14 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, the Amazon EC2 compute units [3], [5], which are used as the building units for different types of VMs. Each CP services two classes of clients [22], namely, guaranteedservice and spot market clients. Those in the first class pay up-front fees and have predefined contracts with the CP so that they are always guaranteed the allocation of their requested VMs. On the other hand, spot market clients are public users who are allowed access to the unused computing resources over the Internet through remote interfaces (e.g., web-services) to create and manage VM instances. This model is similar to Amazon’s guaranteed and spot market service classes [5]. These public users can utilize the spare capacity after assigning sufficient VM instances to satisfy the guaranteed-service requests. We assume a discrete time horizon, t ¼ 1; 2; . . . , where at the beginning of each time period t (e.g., t can represent a 1-hour period [5]), CPi observes the total demand of the guaranteed-service clients di ðtÞ and, in turn, determines the remaining capacity, ei ðtÞ ¼ Ci  di ðtÞ. CPi is then faced with the problem of determining the number of VMs to offer on the spot market, wi ðtÞ, and that to offer for sharing in the federation, ei ðtÞ  wi ðtÞ, with the difference ei ðtÞ  wi ðtÞ being negative whenever CPi is outsourcing VMs from the federation. As shown in Fig. 1, the VM exchange is coordinated through the federation broker which performs the actual VM allocation after the CPs have agreed on sharing them. The broker relies on the existence of a virtual infrastructure management architecture (e.g., the OpenNebula manager and its external-resource lease manager Haizea [23]) that manages the VM’s life cycles and encompasses the necessary means for the configuration of the resources. Offering VMs to host the federation tasks is free of charge; hence, no profit is obtained from ei ðtÞ  wi ðtÞ. On the other hand, the revenue obtained from offering wi ðtÞ on the spot market is ri ðwi ðtÞÞ ¼ wi ðtÞP ðwi ðtÞÞ, where Pi ðwi ðtÞÞ is the inverse of the spot market demand function, i.e., the expected price of a VM when there are wi ðtÞ VMs offered in the spot market of CPi . No specific pricing model is imposed; however, similar to other approaches (e.g., [22]), it is assumed that ri ðwi ðtÞÞ is increasing, concave, and twice continuously differentiable with ri ð0Þ ¼ 0. Next, we use ri ðwi ðtÞÞ to formally define the CP’s marginal revenue. Definition 1. The marginal revenue of CPi , r0i ðwi ðtÞÞ, is the additional revenue generated by an additional VM instance in i ðwi ðtÞÞ . its spot market, i.e., r0i ðwi ðtÞÞ ¼ @r@w i ðtÞ We note that the spot market client is allowed to retain the requested VM as long as the consumed resources are not needed by the CP. Hence, at the beginning of each epoch t, CPi may terminate a spot VM instance and possibly direct its resources to serve its guaranteed-service clients or the spot market clients of other CPs in the federation, without incurring any additional cost. The CP makes this decision only if it is more profitable to contribute in the federation. The advantage to this approach is that it alleviates the CPs’ need to migrate these shared spot market VMs. Nonetheless, this simple model can be easily modified to allow a CP to maintain spot market VM instances whenever VOL. 25, NO. 1, JANUARY 2014 it has enough resources borrowed from other CPs by migrating them to the other CPs’ clouds. In this case, the revenue function must be modified to account for the incurred migration cost, denoted by ci ðwi ðtÞ  ei ðtÞÞ, of the borrowed wi ðtÞ  ei ðtÞ VMs. The cost function is defined such that ci ðwi ðtÞ  ei ðtÞÞ ¼ 0 for wi ðtÞ  ei ðtÞ and is convex otherwise. In this case, we have ri ðwi ðtÞÞ ¼ wi ðtÞP ðwi ðtÞÞ  cðwi ðtÞ  ei ðtÞÞ, which remains concave due to the convexity of ci ð:Þ. 3.1 A Markovian Model of Spot Market Resources Since the majority of guaranteed-service clients operate business applications that exhibit strong temporal and spatial correlations, the CPs can easily characterize their expected VM demands by monitoring their behavior over a period of time [18], [24], [25], [26], [27]. By predicting the guaranteed-service clients demands, the CP can also estimate the unused capacity facilitating the decision of selecting wi ðtÞ and the shared portion ei ðtÞ  wi ðtÞ. Motivated by recent advances in Markovian modeling of the expected workloads (for example, see [24], [25], [28]), we model the transition of the CPs’ spare capacities as follows: At each period t ¼ 1; 2; . . . , the observed unused capacity of the N CPs is described by a state vector st ¼ ðe1 ðst Þ;    ; eN ðst ÞÞ. st is drawn from a, possibly large, finite set S ¼ fs1 ; . . . ; sjSj g and its evolution follows a Markov process with a probability of transition from state s 2 S at t  1 to a state s0 2 S at t given by ðs0 jsÞ ¼ P rðst ¼ s0 jst1 ¼ sÞ. The cloud federation undergoes a change in the workloads and, in turn, the spare capacity in discrete time epochs, according to a first-order Markov chain described by the state transition matrix  ¼ ½ðsi jsj Þ, i; j ¼ 1; . . . ; jSj, with the state transition coefficients having the properties: PjSj ðsi jsi Þ  0 and ðs j jsi Þ ¼ 1. With a slight abuse of j¼1 notation, st will be used to denote the actual state observed at t and we will use ht ¼ ðs1 ; s2 ; . . . ; st Þ to denote a history of state observation up to time t. Moreover, if we know the state st or history ht at t, we will refer to the spot market allocation as wi ðst Þ and wi ðht Þ, respectively. We also note that unused capacities at st are history independent, i.e., ei ðht Þ ¼ ei ðst Þ, 8i. Moreover, because of the Markov property, we can see that the conditional probability ðh jht Þ for  > t is only dependent on the last observed state st in ht and does not depend on the history before t, i.e., ðh jht Þ ¼ ðs js1 Þðs1 js2 Þ . . . ðstþ1 jst Þ. Finally, we note that the presented work can easily be adapted to include other Markovian workload models (e.g., Markovian Arrival Processes [24]). 4 FULLY FEDERATED AND NON-FEDERATED MODELS 4.1 Limitation of the Fully Federated Model Here, a centralized broker (see Fig. 1) is tasked with redistributing the unused capacities among CPs’ spot markets with the objective of maximizing the federation’s total revenues. Termed as socially optimal spot market allocation, this problem is formulated as follows. Definition 2. The socially optimal spot market allocation, w1 ðht Þ; . . . ; wN ðht Þ, after each history ht , is the one that SAMAAN: A NOVEL ECONOMIC SHARING MODEL IN A FEDERATION OF SELFISH CLOUD PROVIDERS maximizes the net federation revenue without regard to the individual CPs gains, i.e., it solves P 1 : max wi ðht Þ N X i¼1 i 1 X t t¼1 s:t: ‘‘capacity constraint : ’’ X ðht Þri ðwi ðht ÞÞ ð1Þ ht N X i¼1 wi ðht Þ  N X ei ðst Þ; ð2Þ i¼1 8ht ; 8t, where  2 ð0; 1Þ1 is the future discount factor and i is the normalized exogenous constant weight of CPi in the P  federation such that N i¼1 i ¼ 1. We note that the weights i can be used to express some service characteristics such as reliability or offered service quality. The following proposition fully characterizes the solution of P1. Proposition 1.2 A VM allocation, w1 ðht Þ; . . . ; wN ðht Þ, in the CPs spot markets is the socially optimal allocation for the federation if allPVMs are allocated in the spot markets, i.e., PN w ðs Þ¼ N i t i¼1 i¼1 ei ðst Þ, and for any state st 2 S, the ratios of the marginal revenues remain constant for any CPi , CPj i; j ¼ 1; . . . ; N, i 6¼ j, after any history of workload states ht1 ¼ ðs1 ; . . . ; st1 Þ, such that r0i ðwi ðht ÞÞ r0i ðwi ðst ÞÞ j ¼ ¼ ; 8ht ; 8t: r0j ðwj ðht ÞÞ r0j ðwj ðst ÞÞ i ¼tþ1 In Section 5, a new dynamic sharing rule will be derived to overcome the limited enforcement problem of the above model. 4.2 Limitation of the Nonfederated Model In this section, we regard the sharing problem from the perspective of the individual CPs and characterize the maximum revenue they can achieve outside the federation. Each CP, CPi , aims at maximizing its long-term revenue by solving the following problem: P 2 : max wi ðht Þ 1 X t X t¼1 ðht Þri ðwi ðht ÞÞ ð5Þ ht subject to the same capacity constraint of (2). Given the u ...
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