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Theory of Computing Systems

, Volume 39, Issue 1, pp 121–136 | Cite as

The Expected Competitive Ratio for Weighted Completion Time Scheduling

  • Alexander Souza
  • Angelika Steger
Article

Abstract

A set of n independent jobs is to be scheduled without preemption on m identical parallel machines. For each job j, a diffuse adversary chooses the distribution Fj of the random processing time Pj from a certain class of distributions F j. The scheduler is given the expectation μj = E[Pj], but the actual duration is not known in advance. A positive weight wj is associated with each job j and all jobs are ready for execution at time zero. The scheduler determines a list of the jobs, which is then scheduled in a non-preemptive manner. The objective is to minimise the total weighted completion time ∑j wj Cj. The performance of an algorithm is measured with respect to the expected competitive ratio maxF ∈ F E[∑j wj Cj/OPT], where Cj denotes the completion time of job j and OPT the offline optimum value. We show a general bound on the expected competitive ratio for list scheduling algorithms, which holds for a class of so-called new-better-than-used processing time distributions. This class includes, among others, the exponential distribution. As a special case, we consider the popular rule weighted shortest expected processing time first (WSEPT) in which jobs are processed according to the non-decreasing μj/wj ratio. We show that it achieves E[WSEPT/OPT] ≤ 3 – 1/m for exponential distributed processing times.

Keywords

Processing Time Completion Time Schedule Algorithm Parallel Machine Competitive Ratio 
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 2005

Authors and Affiliations

  1. 1.Institute of Theoretical Computer Science, ETH Zurich, Universitatstr. 6, CH-8092 ZurichSwitzerland

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