Drift and monotonicity conditions for continuous-time controlled Markov chains with an average criterion

We give conditions for the existence of average optimal policies for continuous-time controlled Markov chains with a denumerable state-space and Borel action sets. The transition rates are allowed to be unbounded, and the reward/cost rates may have neither upper nor lower bounds. In the spirit of the "drift and monotonicity" conditions for continuous-time Markov processes, we propose a new set of conditions on the controlled process\´ primitive data under which the existence of optimal (deterministic) stationary policies in the class of randomized Markov policies is proved using the extended generator approach instead of Kolmogorov\´s forward equation used in the previous literature, and under which the convergence of a policy iteration method is also shown. Moreover, we use a controlled queueing system to show that all of our conditions are satisfied, whereas those in the previous literature fail to hold.