Average Rate Speed Scaling

Abstract

Speed scaling is a power management technique that involves dynamically changing the speed of a processor. This gives rise to dual-objective scheduling problems, where the operating system both wants to conserve energy and optimize some Quality of Service (QoS) measure of the resulting schedule. Yao, Demers, and Shenker [8] considered the problem where the QoS constraint is deadline feasibility and the objective is to minimize the energy used. They proposed an online speed scaling algorithm Average Rate () that runs each job at a constant speed between its release and its deadline. They showed that the competitive ratio of is at most (2α)^α/2 if a processor running at speed s uses power s ^α. We show the competitive ratio of is at least ((2 − δ) α)^α/2, where δ is a function of α that approaches zero as α approaches infinity. This shows that the competitive analysis of by Yao, Demers, and Shenker is essentially tight, at least for large α. We also give an alternative proof that the competitive ratio of is at most (2α)^α/2 using a potential function argument. We believe that this analysis is significantly simpler and more elementary than the original analysis of in [8].

D.P. Bunde was supported in part by Howard Hughes Medical Institute grant 52005130. Ho-Leung Chan and Kirk Pruhs were supported in part by NSF grants CNS-0325353, CCF-0514058 and IIS-0534531.