Optimal energy-efficient policies for data centers through sensitivity-based optimization
Optimal energy-efficient policies for data centers through sensitivity-based optimization
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DOI：
10.1007/s10626-019-00293-x
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发表时间：
2018-08
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影响因子：
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通讯作者：
Jing-Yu Ma;L. Xia;Quanlin Li
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文献类型：
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作者：
Jing-Yu Ma;L. Xia;Quanlin Li
本文提出了一种新的动态决策方法，利用基于灵敏度的优化理论寻找具有两组异构服务器的数据中心的最优节能策略。组1中的服务器始终在高能耗状态下工作，组2中的服务器可能在高能耗状态下工作，也可能在低能耗状态下休眠。节能控制策略以动态的方式决定组2服务器的工作状态和睡眠状态的切换。由于组1中的服务器总是对作业具有高优先级，因此建议使用传输规则将组2中的作业迁移到组1中的空闲服务器。为了找到最优的节能策略，我们建立了一个基于策略的泊松方程，并通过rg分解给出了其性能潜力唯一解的显式表达式。在此基础上，刻画了不同服务价格下保单长期平均利润的单调性和最优性。我们证明，对于这个优化问题，bang-bang控制总是最优的，即我们要么让所有的服务器都处于睡眠状态，要么打开服务器，使工作服务器的数量等于组2中等待作业的数量。作为一种易于采用的策略形式，我们进一步研究了阈值型策略，得到了最优阈值策略的一个必要条件。我们希望本文的方法和结果可以为更普遍的节能数据中心的研究提供启示。
In this paper, we propose a novel dynamic decision method by applying the sensitivity-based optimization theory to find the optimal energy-efficient policy of a data center with two groups of heterogeneous servers. Servers in Group 1 always work at high energy consumption, while servers in Group 2 may either work at high energy consumption or sleep at low energy consumption. An energy-efficient control policy determines the switch between work and sleep states of servers in Group 2 in a dynamic way. Since servers in Group 1 are always working with high priority to jobs, a transfer rule is proposed to migrate the jobs in Group 2 to idle servers in Group 1. To find the optimal energy-efficient policy, we set up a policy-based Poisson equation, and provide explicit expressions for its unique solution of performance potentials by means of the RG-factorization. Based on this, we characterize monotonicity and optimality of the long-run average profit with respect to the policies under different service prices. We prove that the bang-bang control is always optimal for this optimization problem, i.e., we should either keep all servers sleep or turn on the servers such that the number of working servers equals that of waiting jobs in Group 2. As an easy adoption of policy forms, we further study the threshold-type policy and obtain a necessary condition of the optimal threshold policy. We hope the methodology and results derived in this paper can shed light to the study of more general energy-efficient data centers.