Pfair scheduling of periodic tasks with allocation constraints on multiple processors

Pfair scheduling for periodic tasks on multiple processors in a time slotted environment can not only guarantee task deadlines to be respected, but also make tasks execute at steady progressive rates. In this paper we consider pfair schedulability of periodic tasks with allocation constraints in the sense that some tasks can only be assigned to one or more specified processors. The contributions of the paper lie in the following four aspects. Firstly, we prove that there exists pfair schedule in the case that fixed tasks are assigned to disjoined processor subsets. Secondly, we give a sufficient and necessary condition of the existence of pfair schedule for periodic tasks with arbitrary allocation constraints. Thirdly, we show that pfair schedulability test of periodic tasks with arbitrary allocation constraints can be done in polynomial time. Finally, an on-line approximate pfair scheduling algorithm called HPA (hierarchical pfair algorithm) is proposed for scheduling fixed and migrating tasks. With HPA although idea a fixed task is not guaranteed to respect its deadline completely, the amount of time by which it misses its deadline is bounded.