  In this paper we study the global scheduling of periodic task systems upon
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
feasible schedules of periodic task systems are periodic from some point with a
period equal to the least common multiple of task periods and (ii) for the
specific case of synchronous periodic task systems, we show that feasible
schedules repeat from the origin. We then present our main result: we
characterize, for task-level fixed-priority schedulers and for asynchronous
constrained or arbitrary deadline periodic task models, upper bounds of the
first time instant where the schedule repeats. We show that job-level
fixed-priority schedulers are predictable upon unrelated multiprocessor
platforms. For task-level fixed-priority schedulers, based on the upper bounds
and the predictability property, we provide for asynchronous constrained or
arbitrary deadline periodic task sets, exact feasibility tests. Finally, for
the job-level fixed-priority EDF scheduler, for which such an upper bound
remains unknown, we provide an exact feasibility test as well.
