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In this paper, we propose a novel dynamic decision method by applying thesensitivity-based optimization theory to find the optimal energy-efficientpolicy of a data center with two groups of heterogeneous servers. Servers inGroup 1 always work at high energy consumption, while servers in Group 2 mayeither work at high energy consumption or sleep at low energy consumption. Anenergy-efficient control policy determines the switch between work and sleepstates of servers in Group 2 in a dynamic way. Since servers in Group 1 arealways working with high priority to jobs, a transfer rule is proposed tomigrate the jobs in Group 2 to idle servers in Group 1. To find the optimalenergy-efficient policy, we set up a policy-based Poisson equation, and provideexplicit expressions for its unique solution of performance potentials by meansof the RG-factorization. Based on this, we characterize monotonicity andoptimality of the long-run average profit with respect to the policies underdifferent service prices. We prove that the bang-bang control is always optimalfor this optimization problem, i.e., we should either keep all servers sleep orturn on the servers such that the number of working servers equals that ofwaiting jobs in Group 2. As an easy adoption of policy forms, we further studythe threshold-type policy and obtain a necessary condition of the optimalthreshold policy. We hope the methodology and results derived in this paper canshed light to the study of more general energy-efficient data centers.

Optimal Energy-Efficient Policies for Data Centers through Sensitivity-Based Optimization