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In this paper we study the global scheduling of periodic task systems uponmultiprocessor platforms. We first show two very general properties which arewell-known for uniprocessor platforms and which remain for multiprocessorplatforms: (i) under few and not so restrictive assumptions, we show thatfeasible schedules of periodic task systems are periodic from some point with aperiod equal to the least common multiple of task periods and (ii) for thespecific case of synchronous periodic task systems, we show that feasibleschedules repeat from the origin. We then present our main result: wecharacterize, for task-level fixed-priority schedulers and for asynchronousconstrained or arbitrary deadline periodic task models, upper bounds of thefirst time instant where the schedule repeats. We show that job-levelfixed-priority schedulers are predictable upon unrelated multiprocessorplatforms. For task-level fixed-priority schedulers, based on the upper boundsand the predictability property, we provide for asynchronous constrained orarbitrary deadline periodic task sets, exact feasibility tests. Finally, forthe job-level fixed-priority EDF scheduler, for which such an upper boundremains unknown, we provide an exact feasibility test as well.

Exact Feasibility Tests for Real-Time Scheduling of Periodic Tasks upon Multiprocessor Platforms