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

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. We propose optimal cutting-plane algorithms for these IP formulations; clearly, these new schedulability tests have better convergence rates than RTA and QPA. We compare the new tests with RTA and QPA on large collections of synthetic task sets to gauge the improvement in convergence rates.