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

TL;DR

This paper introduces a sensitivity-based optimization approach to determine energy-efficient server management policies in heterogeneous data centers, proving bang-bang control is optimal and providing explicit solutions for long-term profit maximization.

Contribution

It develops a novel sensitivity-based optimization framework for data center energy management, deriving explicit solutions and optimal policies including bang-bang and threshold-type controls.

Findings

Bang-bang control is proven to be optimal for energy efficiency.

Explicit solutions for performance potentials are derived using RG-factorization.

Optimal policies depend on service prices and can be threshold-based.

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.