Dynamic Reallocation Problems in Scheduling

TL;DR

This paper introduces an efficient scheduling allocator for dynamic task systems that minimizes rescheduling, maintaining valid schedules with constant window sizes and proving optimality of the approach.

Contribution

It presents a novel allocator for dynamic scheduling with constant window sizes, achieving near-optimal rescheduling performance and exploring variants with different task window sizes.

Findings

Allocator maintains valid schedules with constant window sizes.

Reschedules O(1/ε * log(1/ε)) tasks per insertion as ε approaches 0.

Proved optimality of the allocator for arbitrary instances.

Abstract

In this paper we look at the problem of scheduling tasks on a single-processor system, where each task requires unit time and must be scheduled within a certain time window, and each task can be added to or removed from the system at any time. On each operation, the system is allowed to reschedule any tasks, but the goal is to minimize the number of rescheduled tasks. Our main result is an allocator that maintains a valid schedule for all tasks in the system if their time windows have constant size and reschedules O(1/{\epsilon}*log(1/{\epsilon})) tasks on each insertion as {\epsilon}->0, where {\epsilon} is a certain measure of the schedule flexibility of the system. We also show that it is optimal for any allocator that works on arbitrary instances. We also briefly mention a few variants of the problem, such as if the tasks have time windows of difference sizes, for which we have an allocator that we conjecture reschedules only 1 task on each insertion if the schedule flexibility remains above a certain threshold.