Sleep with guilt and work faster to minimize flow plus energy

Abstract

In this paper we extend the study of flow-energy scheduling to a model that allows both sleep management and speed scaling. Our main result is a sleep management algorithm called IdleLonger, which works online for a processor with one or multiple levels of sleep states. The design of IdleLonger is interesting; among others, it may force the processor to idle or even sleep even though new jobs have already arrived. IdleLonger works in both clairvoyant and non-clairvoyant settings. We show how to adapt two existing speed scaling algorithms AJC [15] (clairvoyant) and LAPS [9] (non-clairvoyant) to the new model. The adapted algorithms, when coupled with IdleLonger, are shown to be O(1)-competitive clairvoyant and non-clairvoyant algorithms for minimizing flow plus energy on a processor that allows sleep management and speed scaling. The above results are based on the traditional model with no limit on processor speed. If the processor has a maximum speed, the problem becomes more difficult as the processor, once overslept, cannot rely on unlimited extra speed to catch up the delay. Nevertheless, we are able to enhance IdleLonger and AJC so that they remain O(1)-competitive for flow plus energy under the bounded speed model. Non-clairvoyant scheduling in the bounded speed model is left as an open problem. © 2009 Springer Berlin Heidelberg.