Total reward criteria for unconstrained/constrained continuous-time Markov decision processes |
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Authors: | Xianping Guo Lanlan Zhang |
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Institution: | 1.School of Mathematics and Computational Science,Sun Yat-sen University,Guangzhou,China;2.School of Public Health and Tropical Medicine,Southern Medical University,Guangzhou,China |
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Abstract: | This paper studies denumerable continuous-time Markov decision processes with expected total reward criteria. The authors
first study the unconstrained model with possible unbounded transition rates, and give suitable conditions on the controlled
system’s primitive data under which the authors show the existence of a solution to the total reward optimality equation and
also the existence of an optimal stationary policy. Then, the authors impose a constraint on an expected total cost, and consider
the associated constrained model. Basing on the results about the unconstrained model and using the Lagrange multipliers approach,
the authors prove the existence of constrained-optimal policies under some additional conditions. Finally, the authors apply
the results to controlled queueing systems. |
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Keywords: | |
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