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

Ziv Scully () and Lucas van Kreveld ()
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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

Operations Research, 2025, vol. 73, issue 3, 1412-1429

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.

Keywords: Stochastic Models; queueing theory; scheduling; M/G/1 queue; Gittins index; response time tail; heavy-tailed distributions; light-tailed distributions (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:73:y:2025:i:3:p:1412-1429

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