An Approximation Approach for the Deviation Matrix of Continuous-Time Markov Processes with Application to Markov Decision Theory

作者：Leder Nicole^*; Heidergott Bernd; Hordijk Arie

来源：Operations Research, 2010, 58(4): 918-932.

DOI：10.1287/opre.1090.0786

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.

• 出版日期2010-8