Discrete Event Dynamic Systems

, Volume 29, Issue 4, pp 567–606 | Cite as

Optimal energy-efficient policies for data centers through sensitivity-based optimization

  • Jing-Yu Ma
  • Li XiaEmail author
  • Quan-Lin Li


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.


Queueing Data center Energy-efficient policies Sensitivity-based optimization Markov decision process 



Li Xia was supported by the National Key Research and Development Program of China (2016YFB0901900, 2017YFC0704100), the National Natural Science Foundation of China under grant No. 61573206 and No. 11931018, the National 111 International Collaboration Project (B06002), and Tsinghua-Tencent Cooperation Research Project.

Quan-Lin Li was supported by the National Natural Science Foundation of China under grant No. 71932002, No. 71671158 and No. 71471160, and by the Natural Science Foundation of Hebei province under grant No. G2017203277.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Economics and ManagementYanshan UniversityQinhuangdaoChina
  2. 2.Business SchoolSun Yat-Sen UniversityGuangzhouChina
  3. 3.School of Economics and ManagementBeijing University of TechnologyBeijingChina

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