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

Abstract

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.

Sensitivity-Based Optimization for Blockchain Selfish Mining

“…A similar computation to that in Ma et al [14,15] is omitted here, we can provide an expression for the vector g (p)…”

“…The following lemma provides the performance difference equation for the difference η p ′ − η p of the long-run average performances for any two blockchainpegged policies p, p ′ ∈ P. Here, we only restate it without proof, while readers may refer to Cao [1] and Ma et al [14] for more details.…”

“…Thus, the sensitivity-based optimization theory has been applied to performance optimization in many practical areas. For example, the energy-efficient data centers by Xia et al [21] and Ma et al [14,15]; the inventory rationing by Li et al [12]; the multi-hop wireless networks by Xia and Shihada [22] and the finance by Xia [23].…”

An Overview for Markov Decision Processes in Queues and Networks

“…So far some work has applied the sensitivity-based optimization to deal with MDPs of queues and networks, e.g., see Xia and Cao [326], Xia and Shihada [331], Xia [324], Xia and Jia [329], Xia et al [328] and Xia and Chen [327]; Ma et al [233,234] for data centers; and…”

“…It is worthwhile to note that the sensitivitybased optimization of queues and networks can be effectively supported and developed by means of the matrix-analytic method by Neuts [245,246] and the RG-factorizations by Li [218]. Also see Ma et al [233,234] and Li et al [222] for more details.…”