The Gittins Policy in the M/G/1 Queue
Ziv Scully, Mor Harchol-Balter

TL;DR
This paper provides the first fully general proof that the Gittins policy optimally minimizes various mean holding cost metrics in the M/G/1 queue, including mean response time and slowdown, even with batch arrivals or partial service time knowledge.
Contribution
It offers a novel, direct proof of Gittins's optimality in the M/G/1 queue, extending previous results to more general settings and metrics.
Findings
Gittins minimizes mean response time in the M/G/1.
Gittins minimizes mean slowdown with unknown or partial service times.
Gittins's optimality holds under batch arrivals.
Abstract
The Gittins policy is a highly general scheduling policy that minimizes a wide variety of mean holding cost metrics in the M/G/1 queue. Perhaps most famously, Gittins minimizes mean response time in the M/G/1 when jobs' service times are unknown to the scheduler. Gittins also minimizes weighted versions of mean response time. For example, the well-known " rule", which minimizes class-weighted mean response time in the multiclass M/M/1, is a special case of Gittins. However, despite the extensive literature on Gittins in the M/G/1, it contains no fully general proof of Gittins's optimality. This is because Gittins was originally developed for the multi-armed bandit problem. Translating arguments from the multi-armed bandit to the M/G/1 is technically demanding, so it has only been done rigorously in some special cases. The extent of Gittins's optimality in the M/G/1 is thus not…
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Optimization and Search Problems · Advanced Wireless Network Optimization
