Packing-Inspired Algorithms for Periodic Scheduling Problems with Harmonic Periods

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 an efficient static schedule 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 2D packing of rectangles (we name it height-divisible 2D packing). 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 problem instances ins pired by the communication of messages on one channel.