Optimal Scheduling of Periodic Tasks on Multiple Identical Processors

We consider the problem of scheduling m periodic tasks on n; n < m; identical processors. Our main contribution is to show that the condition n, where is the total density of the task set, is a suucient condition for scheduling the m tasks such that no deadlines are ever missed. We start with a novel representation of the periodic task scheduling problem as a maximum network ow problem. The structure of the network ensures that task and processor connicts are both avoided. Using results from network ow theory, we show that the maximum ow in the network is integer, and that there exists a feasible ow assignment in which all arc ows are integers. We also show that such a ow assignment corresponds to a feasible schedule for the original scheduling problem. Consequently, our work provides a positive answer to a question that has thus far remained open.