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

Abstract

Looking Beyond Mean Delay in Queue Scheduling A central aim of queueing theory is to design scheduling policies that reduce delays. Much of literature focuses on minimizing mean delay, but, in practice, it can be more important to reduce the delay tail—that is, the probability of especially large delays. There is a subtle interplay between these objectives. For instance, the SRPT policy (Shortest Remaining Processing Time) prioritizes short jobs over long jobs, which optimizes mean delay. Sometimes, SRPT also has optimal delay tail, but other times, its delay tail is pessimal. Thus, good mean delay need not imply good delay tail. The article When Does the Gittins Policy Have Asymptotically Optimal Response Time Tail in the M/G/1? explores the interplay between mean delay and delay tail for systems with unknown job durations. The article studies the Gittins policy, which optimizes mean delay in this setting. Curiously, its delay tail can be optimal, pessimal, or in between, depending on the job duration distribution. Fortunately, the worst case can be avoided: the article shows how to modify Gittins to avoid pessimal delay tail while maintaining near-optimal mean delay.