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Absorbing Continuous-Time Markov Decision Processes with Total Cost Criteria

Part of: Markov processes

Published online by Cambridge University Press:  22 February 2016

Xianping Guo ,
Mantas Vykertas  and
Yi Zhang
Xianping Guo*
Affiliation:
Sun Yat-Sen University
Mantas Vykertas*
Affiliation:
Open University
Yi Zhang*
Affiliation:
University of Liverpool
*
∗ Postal address: School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, P. R. China. Email address: mcsgxp@mail.sysu.edu.cn
∗∗ Postal address: Department of Mathematics and Statistics, Open University, Milton Keynes, MK7 6AA, UK. Email address: mantas.vykertas@gmail.com
∗∗∗ Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK. Email address: yi.zhang@liv.ac.uk
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Abstract

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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.

Keywords

CTMDPtotal costconstrained optimalitylinear program

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 60J25: Continuous-time Markov processes on general state spaces 60J75: Jump processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 2 , June 2013 , pp. 490 - 519
Copyright
© Applied Probability Trust 

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