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Slow Down and Sleep for Profit in Online Deadline Scheduling

  • Peter Kling
  • Andreas Cord-Landwehr
  • Frederik Mallmann-Trenn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7659)

Abstract

We present and study a new model for energy-aware and profit-oriented scheduling on a single processor. The processor features dynamic speed scaling as well as suspension to a sleep mode. Jobs arrive over time, are preemptable, and have different sizes, values, and deadlines. On the arrival of a new job, the scheduler may either accept or reject the job. Accepted jobs need a certain energy investment to be finished in time, while rejected jobs cause costs equal to their values. Here, power consumption at speed s is given by P(s) = s α  + β and the energy investment is power integrated over time. Additionally, the scheduler may decide to suspend the processor to a sleep mode in which no energy is consumed, though awaking entails fixed transition costs γ. The objective is to minimize the total value of rejected jobs plus the total energy.

Our model combines aspects from advanced energy conservation techniques (namely speed scaling and sleep states) and profit-oriented scheduling models. We show that rejection-oblivious schedulers (whose rejection decisions are not based on former decisions) have - in contrast to the model without sleep states - an unbounded competitive ratio w.r.t. the processor parameters α and β. It turns out that the worst-case performance of such schedulers depends linearly on the jobs’ value densities (the ratio between a job’s value and its work). We give an algorithm whose competitiveness nearly matches this lower bound. If the maximum value density is not too large, the competitiveness becomes α α  + 2. Also, we show that it suffices to restrict the value density of low-value jobs only. Using a technique from [13] we transfer our results to processors with a fixed maximum speed.

Keywords

Competitive Ratio Online Algorithm Sleep Mode Sleep State Energy Investment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Peter Kling
    • 1
  • Andreas Cord-Landwehr
    • 1
  • Frederik Mallmann-Trenn
    • 1
  1. 1.Heinz Nixdorf Institute and Computer Science DepartmentUniversity of PaderbornGermany

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