In this paper we study absorbing continuous-time Markov decision processes in Polish state spaces with unbounded transition and cost rates, and history-dependent policies. The performance measure is the expected total undiscounted costs. For the unconstrained problem, we show the existence of a deterministic stationary optimal policy, whereas, for the constrained problems with N constraints, we show the existence of a mixed stationary optimal policy, where the mixture is over no more than N+1 deterministic stationary policies. Furthermore, the strong duality result is obtained for the associated linear programs.
"Absorbing continuous-time Markov decision processes with total cost criteria." Adv. in Appl. Probab. 45 (2) 490 - 519, June 2013. https://doi.org/10.1239/aap/1370870127