Cutting-plane algorithms for preemptive uniprocessor real-time scheduling problems
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.
Keywords
Cite
@article{arxiv.2210.11185,
title = {Cutting-plane algorithms for preemptive uniprocessor real-time scheduling problems},
author = {Abhishek Singh},
journal= {arXiv preprint arXiv:2210.11185},
year = {2023}
}
Comments
45 pages, 5 figures. Changes in v2: new terms like CP-KERN are added to explain ideas more clearly; models include release jitter. Changes in v3: typos are fixed; evaluation section is modified so that it is in sync with public code. Changes in v4: algorithm, theoretical and empirical analyses are improved. Changes in v5: minor structural changes, acknowledgements added