Convergence of controlled models and finite-state approximation for discounted continuous-time Markov decision processes with constraints

Xianping Guo and Wenzhao Zhang

European Journal of Operational Research, 2014, vol. 238, issue 2, 486-496

Abstract: In this paper we consider the convergence of a sequence {Mn} of the models of discounted continuous-time constrained Markov decision processes (MDP) to the “limit” one, denoted by M∞. For the models with denumerable states and unbounded transition rates, under reasonably mild conditions we prove that the (constrained) optimal policies and the optimal values of {Mn} converge to those of M∞, respectively, using a technique of occupation measures. As an application of the convergence result developed here, we show that an optimal policy and the optimal value for countable-state continuous-time MDP can be approximated by those of finite-state continuous-time MDP. Finally, we further illustrate such finite-state approximation by solving numerically a controlled birth-and-death system and also give the corresponding error bound of the approximation.

Keywords: Constrained continuous-time Markov decision processes; Unbounded transition rate; Convergence; Finite approximation (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:238:y:2014:i:2:p:486-496

DOI: 10.1016/j.ejor.2014.03.037

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