Denumerable continuous-time Markov decision processes with multiconstraints on average costs |
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Authors: | Qiuli Liu Hangsheng Tan |
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Affiliation: | 1. School of Mathematical Sciences , South China Normal University , Guangzhou 510631, P.R. China;2. School of Mathematics , Central South University , Changsha 410075, P.R. China |
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Abstract: | This article deals with multiconstrained continuous-time Markov decision processes in a denumerable state space, with unbounded cost and transition rates. The criterion to be optimised is the long-run expected average cost, and several kinds of constraints are imposed on some associated costs. The existence of a constrained optimal policy is ensured under suitable conditions by using a martingale technique and introducing an occupation measure. Furthermore, for the unichain model, we transform this multiconstrained problem into an equivalent linear programming problem, then construct a constrained optimal policy from an optimal solution to the linear programming. Finally, we use an example of a controlled queueing system to illustrate an application of our results. |
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Keywords: | Markov decision processes average cost constrained optimal policy occupation measure |
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