On Preemption and Learning in Stochastic Scheduling

TL;DR

This paper investigates stochastic scheduling on a single machine, comparing preemptive and non-preemptive strategies under unknown job types, and demonstrates the advantages of preemption through algorithms, theory, and simulations.

Contribution

It introduces algorithms for learning in stochastic scheduling with unknown job types, providing sublinear excess cost guarantees and highlighting the benefits of preemption.

Findings

Preemptive algorithms outperform non-preemptive ones when job types have diverse durations.

Algorithms achieve sublinear excess cost in learning scenarios.

Preemption offers significant advantages when type durations are far apart.

Abstract

We study single-machine scheduling of jobs, each belonging to a job type that determines its duration distribution. We start by analyzing the scenario where the type characteristics are known and then move to two learning scenarios where the types are unknown: non-preemptive problems, where each started job must be completed before moving to another job; and preemptive problems, where job execution can be paused in the favor of moving to a different job. In both cases, we design algorithms that achieve sublinear excess cost, compared to the performance with known types, and prove lower bounds for the non-preemptive case. Notably, we demonstrate, both theoretically and through simulations, how preemptive algorithms can greatly outperform non-preemptive ones when the durations of different job types are far from one another, a phenomenon that does not occur when the type durations are known.