Cutting-plane algorithms for preemptive uniprocessor real-time scheduling problems

TL;DR

This paper reveals that popular fixed-point iteration algorithms for uniprocessor schedulability are suboptimal cutting-plane methods for integer programming formulations, and introduces optimal cutting-plane algorithms that outperform existing methods.

Contribution

The paper establishes a connection between RTA/QPA and cutting-plane algorithms, and proposes optimal cutting-plane algorithms for schedulability analysis.

Findings

Optimal cutting-plane algorithms converge faster than RTA and QPA.

New algorithms demonstrate improved running times on synthetic systems.

Theoretical link between schedulability algorithms and integer programming methods.

Abstract

Fixed-point iteration algorithms like RTA (response time analysis) and QPA (quick processor-demand analysis) are arguably the most popular ways of solving schedulability problems for preemptive uniprocessor FP (fixed-priority) and EDF (earliest-deadline-first) systems. Several IP (integer program) formulations have also been proposed for these problems, but it is unclear whether the algorithms for solving these formulations are related to RTA and QPA. By discovering connections between the problems and the algorithms, we show that RTA and QPA are, in fact, suboptimal cutting-plane algorithms for specific IP formulations of FP and EDF schedulability, where optimality is defined with respect to convergence rate. We propose optimal cutting-plane algorithms for these IP formulations. We compare the new algorithms with RTA and QPA on large collections of synthetic systems to gauge the improvement in convergence rates and running times.