Optimal admission control of discrete event systems with real-time constraints

The problem of optimally controlling the processing rate of tasks in discrete event systems (DES) with hard real-time constraints has been solved in (J. Mao, C.G. Cassandras, and Q.C. Zhao. Optimal dynamic voltage scaling in power-limited systems with real-time constraints. IEEE Trans, on Mobile Computing, 6(6):678-688, June 2007.) under the assumption that a feasible solution exists. Since this may not always be the case, we introduce in this paper an admission control scheme in which some tasks are removed with the objective of maximizing the number of remaining tasks which are all guaranteed feasibility. In the off-line case where task information is known, we derive several optimality properties and develop a computationally efficient algorithm for solving the admission control problem under certain conditions. In the on-line case, we derive necessary and sufficient conditions under which idling is optimal and define a metric for evaluating when and how long it is optimal to idle. Numerical examples are included to illustrate our results.