Packing-Inspired Algorithms for Periodic Scheduling Problems with Harmonic Periods

TL;DR

This paper introduces packing-inspired algorithms for non-preemptive periodic scheduling with harmonic periods, demonstrating their effectiveness through Constraint Programming and heuristics on synthetic communication network instances.

Contribution

It establishes a bijection between scheduling and rectangle packing, and develops a packing-inspired heuristic outperforming existing methods.

Findings

CP formulation outperforms ILP on difficult instances

Heuristic provides competitive solutions efficiently

Methods are validated on synthetic message communication problems

Abstract

We tackle the problem of non-preemptive periodic scheduling with a harmonic set of periods. Problems of this kind arise within domains of periodic manufacturing and maintenance, and also during the design of industrial, automotive, and avionics communication protocols, where efficient scheduling of messages is crucial for the performance of a time-triggered network. We consider the decision variant of the periodic scheduling problem on a single highly-utilized machine. We first prove a bijection between periodic scheduling and a particular (so-called height-divisible) 2D packing of rectangles. We formulate the problem using Constraint Programming and compare it with equivalent state-of-the-art Integer Linear Programming formulation, showing the former's superiority on difficult instances. Furthermore, we develop a packing-inspired first fit heuristic, which we compare with methods described in the literature. We justify our proposed methods on synthetically generated problem instances inspired by the communication of messages on one channel.