Priority Scheduling in the M/G/1 with Preemption Overhead

TL;DR

This paper presents the first response time distribution analysis for an M/G/1 queue with class-based preemptive priority considering stochastic preemption overheads, providing a recursive Laplace transform formula.

Contribution

It introduces a novel analytical framework and recursive formula for response time distribution in queues with preemption overheads, advancing queueing theory analysis methods.

Findings

Derived a recursive Laplace transform formula for response times

Introduced the job joint transform as a new analytical tool

Provided insights into the impact of preemption overheads on response times

Abstract

Virtually all practical settings where preemptive scheduling is employed are susceptible to preemption overhead, and accounting for these overheads is necessary to make informed scheduling design decisions. However, preemption overhead is almost never accounted for in queueing-theoretic analyses of preemptive scheduling policies. This is true even for simple preemptive policies in simple queueing models: even the stability region, let alone the response time distribution, is difficult to analyze under overhead. In this work, we give the first response time distribution analysis of an M/G/1 under a preemptive scheduling policy with preemption overhead. Specifically, we consider class-based preemptive priority, where a stochastic overhead is incurred when pausing or resuming a job. We derive a recursive formula for the Laplace transform of response time for jobs of any given class, from which all response time moments can be extracted. Beyond the specific policy and model we analyze, our broader aim is to provide a first step towards a general framework for analyzing queues with preemption overhead. To that end, we perform much of our analysis in a way that applies to a wide variety of overhead models by introducing a new theoretical tool called the job joint transform.