Online Scheduling with a Stochastic Signal

Abstract

Nonclairvoyant scheduling is a fundamental online model in which processing times are initially unknown to the scheduler. Unfortunately, for important objectives such as total completion time and makespan, worst-case analysis yields pessimistic guarantees: every nonclairvoyant algorithm has a competitive ratio of at least $2$ for these objectives. Recent work introduced $\varepsilon$-clairvoyance, where a scheduler receives a signal once an $\varepsilon$-fraction of a job remains (FOCS'25, NeurIPS'25). This model avoids giving the algorithm a priori predictions as done in learning-augmented algorithms, a practice that is often hard to justify in practice. However, existing algorithms and analyses rely crucially on signal times being precise, an assumption hardly justifiable in applications such as task profiling. We introduce stochastic clairvoyance, a beyond-worst-case model in which each job emits a randomly timed signal during its execution, drawn from a distribution over its processing length. For this model, we design new online scheduling algorithms whose competitive ratios are strictly below $2$ for minimizing total completion time and makespan. On the technical side, we prove a new black-box theorem that converts bounds on expected pairwise job delays into competitive guarantees via a continuous amortized charging argument. Our results show that stochastic clairvoyance is not merely a curiosity: it yields robust improvements across different scheduling objectives and machine environments. More broadly, stochastic clairvoyance suggests a new direction in beyond-worst-case analysis for online algorithms, and builds a bridge between learning-augmented algorithms and stochastic information models.