Space-efficient scheduling of stochastically generated tasks

TL;DR

This paper investigates the problem of scheduling tasks with stochastic task generation, providing probabilistic bounds on the maximum space needed by the processor under different scheduling strategies.

Contribution

It introduces a framework for analyzing space requirements in stochastic task scheduling and derives tail bounds and expected values for the maximum space used.

Findings

Derived tail bounds for space distribution under various schedulers

Analyzed expected maximum space needed for task execution

Applicable to both offline and online scheduling scenarios

Abstract

We study the problem of scheduling tasks for execution by a processor when the tasks can stochastically generate new tasks. Tasks can be of different types, and each type has a fixed, known probability of generating other tasks. We present results on the random variable S^sigma modeling the maximal space needed by the processor to store the currently active tasks when acting under the scheduler sigma. We obtain tail bounds for the distribution of S^sigma for both offline and online schedulers, and investigate the expected value of S^sigma.