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We consider the problem of selecting threshold times to transition a device to lowpower 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 ratiodoi:10.1109/focs.2004.50 dblp:conf/focs/AugustineIS04 fatcat:jdltxkmajjhpblynbrlwi72hgy