Feasibility Intervals for Multiprocessor Fixed-Priority Scheduling of Arbitrary Deadline Periodic Systems

In this paper we study the global scheduling of periodic task systems with arbitrary deadlines upon identical multiprocessor platforms. We first show two very general properties which are well-known for uniprocessor platforms and which remain for multiprocessor platforms: (i) under few and not so restrictive assumptions, we show that any feasible schedule of arbitrary deadline periodic task systems is periodic from some point and (ii) for the specific case of synchronous periodic task systems, we show that the schedule repeats from the origin. We then present our main result: any feasible schedule of asynchronous periodic task sets using a fixed-priority scheduler is periodic from a specific point. Moreover, we characterize that point and we provide a feasibility interval for those systems.