Energy-Efficient Job-Assignment Policy with Asymptotically Guaranteed Performance Deviation

TL;DR

This paper introduces a scalable, near-optimal job-assignment policy for large server farms that maximizes energy efficiency, with proven asymptotic optimality and rapid convergence, supported by theoretical bounds and simulations.

Contribution

It proposes a novel, scalable job-assignment policy with proven asymptotic optimality and exponential convergence guarantees for energy efficiency in large, diverse server systems.

Findings

Policy approaches asymptotic optimality exponentially fast as system size grows.

The proposed policy is effective and robust across different job-size distributions.

Simulation results confirm theoretical guarantees and practical efficiency.

Abstract

We study a job-assignment problem in a large-scale server farm system with geographically deployed servers as abstracted computer components (e.g., storage, network links, and processors) that are potentially diverse. We aim to maximize the energy efficiency of the entire system by effectively controlling carried load on networked servers. A scalable, near-optimal job-assignment policy is proposed. The optimality is gauged as, roughly speaking, energy cost per job. Our key result is an upper bound on the deviation between the proposed policy and the asymptotically optimal energy efficiency, when job sizes are exponentially distributed and blocking probabilities are positive. Relying on Whittle relaxation and the asymptotic optimality theorem of Weber and Weiss, this bound is shown to decrease exponentially as the number of servers and the arrival rates of jobs increase arbitrarily and in proportion. In consequence, the proposed policy is asymptotically optimal and, more importantly, approaches asymptotic optimality quickly (exponentially). This suggests that the proposed policy is close to optimal even for relatively small systems (and indeed any larger systems), and this is consistent with the results of our simulations. Simulations indicate that the policy is effective, and robust to variations in job-size distributions.