Optimal Power-Down Strategies

Abstract

We consider the problem of selecting threshold times to transition a device to low-power sleep states during an idle period. The two-state case, in which there is a single active and a single sleep state, is a continuous version of the ski-rental problem. We consider a generalized version in which there is more than one sleep state, each with its own power-consumption rate and transition costs. We give an algorithm that, given a system, produces a deterministic strategy whose competitive ratio is arbitrarily close to optimal. We also give an algorithm to produce the optimal online strategy given a system and a probability distribution that generates the length of the idle period. We also give a simple algorithm that achieves a competitive ratio of $3 + 2\sqrt{2} \approx 5.828$ for any system.