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When Does the Gittins Policy Have Asymptotically Optimal Response Time Tail in the M/G/1?

Author

Listed:
  • Ziv Scully

    (School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853)

  • Lucas van Kreveld

    (Stochastic Operations Research, Eindhoven University of Technology, 5612 AZ Eindhoven, Netherlands)

Abstract

We consider scheduling in the M/G/1 queue with unknown job sizes. It is known that the Gittins policy minimizes mean response time in this setting. However, the behavior of the tail of response time under Gittins is poorly understood, even in the large-response-time limit. Characterizing Gittins’s asymptotic tail behavior is important because if Gittins has optimal tail asymptotics, then it simultaneously provides optimal mean response time and good tail performance. In this work, we give the first comprehensive account of Gittins’s asymptotic tail behavior. For heavy-tailed job sizes, we find that Gittins always has asymptotically optimal tail. The story for light-tailed job sizes is less clear-cut: Gittins’s tail can be optimal, pessimal, or in between. To remedy this, we show that a modification of Gittins avoids pessimal tail behavior, while achieving near-optimal mean response time.

Suggested Citation

  • Ziv Scully & Lucas van Kreveld, 2025. "When Does the Gittins Policy Have Asymptotically Optimal Response Time Tail in the M/G/1?," Operations Research, INFORMS, vol. 73(3), pages 1412-1429, May.
    • Handle: RePEc:inm:oropre:v:73:y:2025:i:3:p:1412-1429
    DOI: 10.1287/opre.2022.0038
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    References listed on IDEAS

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    1. Adam Wierman & Bert Zwart, 2012. "Is Tail-Optimal Scheduling Possible?," Operations Research, INFORMS, vol. 60(5), pages 1249-1257, October.
    2. 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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