Energy-efficient heuristics for job assignment in processor-sharing server farms

Energy efficiency of server farms is an important design consideration of data centers. One effective approach is to optimize energy consumption by controlling carried load on the networked servers. In this paper, we propose a robust heuristic policy for job assignment in a server farm, aiming to improve the energy efficiency by maximizing the ratio of the long-run average throughput to the expected energy consumption. Our model of the server farm considers parallel processor-sharing queues with finite buffer sizes, heterogeneous server speeds, and an arbitrary energy consumption function. We devise the new energy-efficient (EE) policy in a way that the state distribution of the system depends on the service requirement distribution only through the mean. We show that the state-of-the-art slowest server first (SSF) policy can be obtained as a special case of EE and both policies have the same computational complexity. We provide a rigorous analysis of EE and derive conditions under which EE is guaranteed to outperform SSF in terms of energy efficiency. Extensive numerical results are presented and demonstrate that, in comparison with SSF, EE yields a consistently better system throughput and yet improves the energy efficiency by up to 70%.