Optimal Quantization of Periodic Task Requests on Multiple Identical Processors
IEEE Transactions on Parallel and Distributed Systems
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We consider the problem of scheduling $m$ periodic tasks on $n,~nm,$ identical processors. Our main contribution is to show that the condition $\rho\leq n$, where $\rho$ is the total density of the task set, is a sufficient 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 flow problem. The structure of the network ensures that task and processor conflicts are both avoided. Using results from network flow theory, we show that the maximum flow in the network is integer, and that there exists a feasible flow assignment in which all arc flows are integers. We also show that such a flow 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.