Multiple constrained continuous-time Markov Decision Processes with expected discounted reward criteria

Since the theory of discrete-time Markov decision processes is quite mature, in allusion to multiple constrained continuous-time Markov decision processes with expected discounted reward criteria, the criterion to be minimized is the expected discounted reward, and a given constraint vector is imposed on the expected discounted cost. Using the uniformization technique of transforming the continuous-time MDP to equivalent discrete-time MDP for the case of bounded transition rate, and the existence of a constrained optimal policy is shown.