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

2026-05-02

AI Summary

This study addresses a critical limitation in classical queueing analysis—its frequent neglect of preemption overhead—which hinders accurate assessment of stability and response time in preemptive scheduling systems. Focusing on the M/G/1 queue with preemption overhead, this work investigates class-based preemptive priority scheduling and presents the first exact analysis of response time distributions for such systems. By introducing a novel theoretical construct termed “task joint transform,” which integrates Laplace transforms with stochastic process techniques, the authors derive recursive formulas for the Laplace transforms of response times for tasks of arbitrary classes. This framework enables closed-form computation of all response time moments, clearly elucidates the performance impact of preemption overhead, and establishes a general analytical foundation extendable to broader scheduling overhead models.

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.

Problem

• preemption overhead
• M/G/1 queue
• priority scheduling
• response time distribution
• queueing theory

Innovation

• preemption overhead
• M/G/1 queue
• priority scheduling
• response time distribution
• job joint transform