Optimality of static control policies in some discrete event systems

We consider a class of discrete event systems (DES) that involves the control of resources allocated to tasks under real-time constraints. This is motivated by power-limited wireless environments such as sensor networks, where the objective is to minimize energy consumption while guaranteeing that task deadlines are always met. In obtaining optimal off-line controllers for such systems, we prove that simple static control gives the unique optimal solution. The result is of interest because it asserts the optimality of a simple controller that does not require any data collection or processing in environments where the cost of such actions is high.