Packing-Inspired Algorithms for Periodic Scheduling Problems with Harmonic Periods

2024-10-18

International Conference on Operations Research and Enterprise Systems

AI Summary

This paper addresses the non-preemptive periodic task scheduling problem on a uniprocessor, targeting high-utilization scenarios such as time-triggered networks and industrial communication protocols. We establish, for the first time, a bijective mapping between feasible periodic schedules and solutions to the highly divisible two-dimensional bin packing problem, thereby reformulating schedulability analysis as a geometric packing problem. Leveraging this insight, we propose an efficient first-fit–based heuristic and formulate a constraint programming (CP) model. Experimental evaluation demonstrates that CP solvers significantly outperform state-of-the-art integer linear programming (ILP) approaches on hard instances, while our new heuristic achieves superior performance over established benchmarks on synthetic communication workload instances. The core contributions are: (i) a novel theoretical modeling framework grounded in the bijective correspondence; (ii) the design of computationally efficient algorithms; and (iii) empirical validation confirming substantial improvements in both exact and heuristic solution quality.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Constraint Satisfaction and Optimization: Constraint Programming
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements

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.

Problem

• Non-preemptive periodic scheduling with harmonic periods
• Efficient scheduling for time-triggered networks
• Comparison of Constraint Programming and Integer Linear Programming

Innovation

• Bijection between scheduling and 2D packing
• Constraint Programming outperforms Integer Linear Programming
• Packing-inspired first fit heuristic developed