Fault-tolerant parallel scheduling of arbitrary length jobs on a shared channel

TL;DR

This paper investigates fault-tolerant parallel job scheduling on shared channels, analyzing how preemption and adversarial failures affect performance, and establishing bounds and algorithms for different failure and preemption scenarios.

Contribution

It introduces a comprehensive analysis of scheduling arbitrary length jobs with machine failures and preemption, identifying features that influence problem complexity and providing bounds and algorithms.

Findings

Preemption significantly impacts scheduling difficulty.

Randomization benefits are limited to non-adaptive adversaries.

The problem's complexity varies with adversary severity and preemption ability.

Abstract

We study the problem of scheduling jobs on fault-prone machines communicating via a shared channel, also known as multiple-access channel. We have $n$ arbitrary length jobs to be scheduled on $m$ identical machines, $f$ of which are prone to crashes by an adversary. A machine can inform other machines when a job is completed via the channel without collision detection. Performance is measured by the total number of available machine steps during the whole execution. Our goal is to study the impact of preemption (i.e., interrupting the execution of a job and resuming later in the same or different machine) and failures on the work performance of job processing. The novelty is the ability to identify the features that determine the complexity (difficulty) of the problem. We show that the problem becomes difficult when preemption is not allowed, by showing corresponding lower and upper bounds, the latter with algorithms reaching them. We also prove that randomization helps even more, but only against a non-adaptive adversary; in the presence of more severe adaptive adversary, randomization does not help in any setting. Our work has extended from previous work that focused on settings including: scheduling on multiple-access channel without machine failures, complete information about failures, or incomplete information about failures (like in this work) but with unit length jobs and, hence, without considering preemption.