Denumerable continuous-time Markov decision processes with multiconstraints on average costs

Qiuli Liu, Hangsheng Tan and Xianping Guo

International Journal of Systems Science, 2011, vol. 43, issue 3, 576-585

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.

Date: 2011
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DOI: 10.1080/00207721.2010.517868

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