Total reward criteria for unconstrained/constrained continuous-time Markov decision processes

This paper studies denumerable continuous-time Markov decision processes with expected total reward criteria. The authors first study the unconstrained model with possible unbounded transition rates, and give suitable conditions on the controlled system’s primitive data under which the authors show the existence of a solution to the total reward optimality equation and also the existence of an optimal stationary policy. Then, the authors impose a constraint on an expected total cost, and consider the associated constrained model. Basing on the results about the unconstrained model and using the Lagrange multipliers approach, the authors prove the existence of constrained-optimal policies under some additional conditions. Finally, the authors apply the results to controlled queueing systems.