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This paper presents a new condition for the existence of optimal stationarypolicies in average-cost continuous-time Markov decision processes withunbounded cost and transition rates, arising from controlled queueing systems.This condition is closely related to the stability of queueing systems. Itsuggests that the proof of the stability can be exploited to verify theexistence of an optimal stationary policy. This new condition is easier toverify than existing conditions. Moreover, several conditions are providedwhich suffice for the average-cost optimality equality to hold.

A New Condition for the Existence of Optimal Stationary Policies in  Denumerable State Average Cost Continuous Time Markov Decision Processes with  Unbounded Cost and Transition Rates