Optimal Scheduling and Exact Response Time Analysis for Multistage Jobs

TL;DR

This paper introduces an optimal scheduling algorithm for multistage jobs in an M/G/1 queue, addressing partial information scenarios and providing exact response time analysis, extending classic scheduling theories.

Contribution

It proposes a new multistage job model and develops an optimal scheduling algorithm with precise response time analysis for partial-information settings.

Findings

Optimal scheduling algorithm for multistage jobs in M/G/1 queues.

Exact response time analysis for the proposed scheduling policy.

Addresses partial-information scenarios beyond classic models.

Abstract

Scheduling to minimize mean response time in an M/G/1 queue is a classic problem. The problem is usually addressed in one of two scenarios. In the perfect-information scenario, the scheduler knows each job's exact size, or service requirement. In the zero-information scenario, the scheduler knows only each job's size distribution. The well-known shortest remaining processing time (SRPT) policy is optimal in the perfect-information scenario, and the more complex Gittins policy is optimal in the zero-information scenario. In real systems the scheduler often has partial but incomplete information about each job's size. We introduce a new job model, that of multistage jobs, to capture this partial-information scenario. A multistage job consists of a sequence of stages, where both the sequence of stages and stage sizes are unknown, but the scheduler always knows which stage of a job is in progress. We give an optimal algorithm for scheduling multistage jobs in an M/G/1 queue and an exact response time analysis of our algorithm.