An approximation approach for the deviation matrix of continuous-time Markov processes with application to Markov decision theory

An approximation approach for the deviation matrix of continuous-time Markov processes with application to Markov decision theory

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Article ID: iaor20105590
Volume: 58
Issue: 4-Part-1
Start Page Number: 918
End Page Number: 932
Publication Date: Jul 2010
Journal: Operations Research
Authors: , ,
Keywords: queues: theory
Abstract:

We present an update formula that allows the expression of the deviation matrix of a continuous-time Markov process with denumerable state space having generator matrix Q* through a continuous-time Markov process with generator matrix Q. We show that under suitable stability conditions the algorithm converges at a geometric rate. By applying the concept to three different examples, namely, the M/M/1 queue with vacations, the M/G/1 queue, and a tandem network, we illustrate the broad applicability of our approach. For a problem in admission control, we apply our approximation algorithm to Markov decision theory for computing the optimal control policy. Numerical examples are presented to highlight the efficiency of the proposed algorithm.

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