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

• 成果类型: Article
• 署名作者: Scully, Ziv; van Kreveld, Lucas
• 署名单位: Cornell University; Eindhoven University of Technology
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.0038
• 发表日期: 2025
• 关键词: exponential decay; index

摘要

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 largeresponse -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.