Towards best-case response times of real-time tasks under fixed-priority scheduling with preemption thresholds

Fixed-priority scheduling with preemption thresholds (FPTS) is supported by the AUTOSAR and OSEK standards as a scheduling policy. Since FPTS is a generalization of fixed-priority preemptive scheduling (FPPS) and fixed-priority nonpreemptive scheduling (FPNS), it aims to improve schedulability. In this paper, we prove, as an intermediate step towards the exact best-case response time analysis for FPTS, that the best-case computation time of a non-preemptive task scheduled under FPTS or FPNS is a tight lower bound for its response time. In addition, we illustrate by means of an example that the best-case response time analysis for FPTS is most likely not a straight forward extension of the current best-case analysis for FPPS.