The energy management schemes in multi-server data centers with setup time mostly consider thresholds on the number of idle servers or waiting jobs to switch servers $\textit{on}$ or $\textit{off}$. An optimal energy management policy can be characterized as a $\textit{Markov decision process}$ (MDP) at large, given that the system parameters evolve Markovian. The resulting optimal reward can be defined as the weighted sum of mean power usage and mean delay of requested jobs. For large-scale data centers however, these models become intractable due to the colossal state-action space, thus making conventional algorithms inefficient in finding the optimal policy. In this paper, we propose an approximate $\textit{semi-MDP}$ (SMDP) approach, known as `$\textit{multi-level SMDP}$', based on state aggregation and Markovian analysis of the system behavior. Rather than averaging the transition probabilities of aggregated states as in typical methods, we introduce an approximate Markovian framework for calculating the transition probabilities of the proposed multi-level SMDP accurately. Moreover, near-optimal performance can be attained at the expense of increased state-space dimensionality by tuning the number of levels in the multi-level approach. Simulation results show that the proposed approach reduces the SMDP size while yielding better rewards as against existing fixed threshold-based policies and aggregation methods.

翻译：设置时间的多服务器数据中心的能源管理计划大多考虑闲置服务器或等待岗位的数量的阈值,以转换服务器 $\ textit{on} $ 或 $\ textit{ $ 美元 或 textit{ off}$ 美元。鉴于系统参数的演变,总体能源管理政策可以称为$ textit{ Markov 决策过程$ (MDP) (MDP) 。由此产生的最佳奖励可以定义为平均电力使用量的加权和平均延迟要求的工作。但是,对于大型数据中心来说,由于国家行动空间的庞大,这些模型变得难以解决,从而使常规算法在寻找最佳政策方面效率低下。在本文件中,我们提议采用一种近乎 $\ textit{sem-MDP} (SMDP) 的方法,即“$ textitle{ Multial MP}$ ” (SMDP) 方法,根据对系统行为进行的州统和Markovian分析,可以将所拟议的总合国的过渡概率与典型方法相比,我们引入了近似的Markovian 框架框架框架框架,用以计算出拟议的多空间标准的过渡性稳定度,而近为Smal- mal-al-ma 方法则可以准确显示Smal-al-mainal lemental asal lemental asal asal asal asal asal asal levelital asal asal asal asal lemental asal asal asal asal asal maxalital lemental lemental lemental lemental asal max maxal max max maxal maxal maxal asal maxal asal asal maxal laxal lamental ma ma asalal lactionalalalalalalalalalalalalalalal ma ma ma ma lavel ma lamental ma ma ma ma lamentalmentalalalalalalalalalalalalalalalalalal masalalalalalalalal