Optimality of Periodic Static Priority Policies in Real-time Communications

We consider the problem of real-time communication with delay constraints. In earlier work it has been shown that a certain weighted-debt policy is feasibility-optimal in the sense that if any scheduling policy can satisfy the throughput-with-deadline requirements of all the clients, then the weighted-debt policy can do so. This raises the interesting question: Why is it that a periodic static priority policy can satisfy any set of requirements that the more general class of history dependent policies can? We answer this by showing that the set of feasible timely-throughput vectors is a polymatroid. We do so by establishing a submodularity property of the complement of the unavoidable idle time function. This shows that the periodic static priority policy, where the period is evictedrevised each period, can attain any feasible timely-throughput vector.