, Volume 60, Issue 4, pp 877–889 | Cite as

Average Rate Speed Scaling

  • Nikhil Bansal
  • David P. Bunde
  • Ho-Leung Chan
  • Kirk Pruhs


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 (Proc. IEEE Symp. Foundations of Computer Science, pp. 374–382, 1995) 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 (AVR) that runs each job at a constant speed between its release and its deadline. They showed that the competitive ratio of AVR is at most (2α) α /2 if a processor running at speed s uses power s α . We show the competitive ratio of AVR 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 AVR by Yao, Demers, and Shenker is essentially tight, at least for large α. We also give an alternative proof that the competitive ratio of AVR 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 AVR in Yao et al. (Proc. IEEE Symp. Foundations of Computer Science, pp. 374–382, 1995).

Speed scaling Voltage scaling Scheduling Online algorithms Power management 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Nikhil Bansal
    • 1
  • David P. Bunde
    • 2
  • Ho-Leung Chan
    • 3
  • Kirk Pruhs
    • 4
  1. 1.IBM T.J. Watson Research CenterYorktown HeightsUSA
  2. 2.Computer Science DepartmentKnox CollegeGalesburgUSA
  3. 3.Department of Computer ScienceThe University of Hong KongHong KongChina
  4. 4.Computer Science DepartmentUniversity of PittsburghPittsburghUSA

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