Optimality of Mixed Policies for Average Continuous-Time Markov Decision Processes with Constraints

This article concerns the average criteria for continuous‐time Markov decision processes with N constraints. We show the following; (a) every extreme point of the space of performance vectors corresponding to the set of stable measures is generated by a deterministic stationary policy; and (b) there exists a mixed optimal policy, where the mixture is over no more than N + 1 deterministic stationary policies.