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Is Tail-Optimal Scheduling Possible?

Author

Listed:
  • Adam Wierman

    (Department of Computer Science, California Institute of Technology, Pasadena, California 91125)

  • Bert Zwart

    (VU University Amsterdam, Eurandom, Georgia Institute of Technology, and CWI Amsterdam, 1098 XG Amsterdam, The Netherlands)

Abstract

This paper focuses on the competitive analysis of scheduling disciplines in a large deviations setting. Although there are policies that are known to optimize the sojourn time tail under a large class of heavy-tailed job sizes (e.g., processor sharing and shortest remaining processing time) and there are policies known to optimize the sojourn time tail in the case of light-tailed job sizes (e.g., first come first served), no policies are known that can optimize the sojourn time tail across both light- and heavy-tailed job size distributions. We prove that no such work-conserving, nonanticipatory, nonlearning policy exists, and thus that a policy must learn (or know) the job size distribution in order to optimize the sojourn time tail.

Suggested Citation

  • Adam Wierman & Bert Zwart, 2012. "Is Tail-Optimal Scheduling Possible?," Operations Research, INFORMS, vol. 60(5), pages 1249-1257, October.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:5:p:1249-1257
    DOI: 10.1287/opre.1120.1086
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    References listed on IDEAS

    as
    1. Misja Nuyens & Adam Wierman & Bert Zwart, 2008. "Preventing Large Sojourn Times Using SMART Scheduling," Operations Research, INFORMS, vol. 56(1), pages 88-101, February.
    2. A. P. Zwart, 2001. "Tail Asymptotics for the Busy Period in the GI/G/1 Queue," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 485-493, August.
    3. Linus Schrage, 1968. "Letter to the Editor—A Proof of the Optimality of the Shortest Remaining Processing Time Discipline," Operations Research, INFORMS, vol. 16(3), pages 687-690, June.
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    Cited by:

    1. Bo Zhang & Bert Zwart, 2013. "Steady-State Analysis for Multiserver Queues Under Size Interval Task Assignment in the Quality-Driven Regime," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 504-525, August.
    2. Nikhil Bansal & Bart Kamphorst & Bert Zwart, 2018. "Achievable Performance of Blind Policies in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 949-964, August.

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