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Zbl 1228.90145
Heidergott, Bernd; Hordijk, Arie; Leder, Nicole
Series expansions for continuous-time Markov processes. (English)
[J] Oper. Res. 58, No. 3, 756-767 (2010). ISSN 0030-364X

Summary: We present update formulas that allow us to express the stationary distribution of a continuous-time Markov process with denumerable state space having generator matrix $Q^{*}$ through a continuous-time Markov process with generator matrix $Q$. Under suitable stability conditions, numerical approximations can be derived from the update formulas, and we show that the algorithms converge at a geometric rate. Applications to sensitivity analysis and bounds on perturbations are discussed as well. Numerical examples are presented to illustrate the efficiency of the proposed algorithm.

MSC 2000:: *90C40 Markov decision processes, etc.

Keywords: Markov processes; queues; numerical methods; retrial queue; deviation matrix; sensitivity analysis

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