Approximately Optimal Scheduling of an M/G/1 Queue with Heavy Tails

TL;DR

This paper demonstrates that for M/G/1 queues with heavy-tailed service times, an approximately optimal scheduling policy can be effectively derived by truncating the heavy tail distributions, simplifying the complex estimation process.

Contribution

It introduces a method to obtain near-optimal scheduling policies for heavy-tailed M/G/1 queues through distribution truncation, overcoming estimation challenges.

Findings

Optimal scheduling can be approximated by truncating heavy tail distributions.

Truncation simplifies the estimation of scheduling policies.

The approach provides near-optimal solutions despite heavy tails.

Abstract

Distributions with a heavy tail are difficult to estimate. If the design of a scheduling policy is sensitive to the details of heavy tail distributions of the service times, an approximately optimal solution is difficult to obtain. This paper shows that the optimal scheduling of an M/G/1 queue with heavy tailed service times does not present this difficulty and that an approximately optimal strategy can be derived by truncating the distributions.