Sequencing Stochastic Jobs with a Single Sample

TL;DR

This paper studies a stochastic scheduling problem where only one sample per job's processing time is available, analyzing the performance of a simple scheduling algorithm across different input distribution classes.

Contribution

It introduces a framework for evaluating the algorithm's performance on reasonable inputs and identifies distribution classes where the algorithm outperforms random scheduling.

Findings

Algorithm performs better than random on certain distribution classes.

Identifies natural classes of input distributions with guaranteed performance.

Highlights limitations of single-sample scheduling under adversarial distributions.

Abstract

This paper revisits the well known single machine scheduling problem to minimize total weighted completion times. The twist is that job sizes are stochastic from unknown distributions, and the scheduler has access to only a single sample from each of the distributions. For this restricted information regime, we analyze the simplest and probably only reasonable scheduling algorithm, namely to schedule by ordering the jobs by weight over sampled processing times. In general, this algorithm can be tricked by adversarial input distributions, performing in expectation arbitrarily worse even in comparison to choosing a random schedule. The paper suggests notions to capture the idea that this algorithm, on reasonable inputs, should exhibit a provably good expected performance. Specifically, we identify three natural classes of input distributions, such that for these classes, the algorithm performs better than random on any input.