Schedulability Analysis for Real-Time P-FRP Tasks Under Fixed Priority Scheduling

This paper studies the schedulability of real-time tasks in the Priority-based Functional Reactive Programming (P-FRP) model under fixed priority scheduling, one of the influential scheduling policies. Since the abort-and-restart execution paradigm of the P-FRP model is different from that of the classic preemptive model, the schedulability analysis for P-FRP tasks under fixed priority scheduling differs widely. In P-FRP, for a synchronous n-task set under fixed priority scheduling, the least common multiple (LCM) of all n task periods is the typical length of a testing interval for a schedulability test. In this paper, we propose and prove a simulation-based tightly sufficient schedulability test in the P-FRP model under fixed priority scheduling for a given priority order, covering scenarios from synchronous task release to asynchronous task release with the initial busy condition, and from implicit deadlines to constrained deadlines. The length of a testing interval for the tightly sufficient test is the LCM of the first n-1 task periods. The tightness of the sufficient condition is shown by examples and the optimality of the search length is proved.