Online Scheduling with a Stochastic Signal

2026-07-20

AI Summary

In non-clairvoyant online scheduling, where job processing times are unknown a priori, the worst-case competitive ratios for total completion time and makespan are both lower-bounded by 2. This work proposes a stochastic prediction model in which each job emits a single random signal during its execution according to its processing time distribution, and leverages this signal to design novel online algorithms. The core contributions include establishing a theoretical bridge between learning-augmented algorithms and stochastic information models, introducing a black-box theorem that translates expected pairwise job delay bounds into competitive ratios, and conducting competitive analysis via a combination of continuous amortized charging and stochastic signal modeling. Across various machine environments, the proposed algorithms achieve competitive ratios strictly below 2 for both objectives, demonstrating the robustness and generality of the model.

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.

Problem

• nonclairvoyant scheduling
• online algorithms
• stochastic signals
• competitive ratio
• beyond-worst-case analysis

Innovation

• stochastic clairvoyance
• online scheduling
• competitive ratio
• amortized analysis
• nonclairvoyant algorithms