Series Expansions for Continuous-Time Markov Processes

• 成果类型: Article
• 署名作者: Heidergott, Bernd; Hordijk, Arie; Leder, Nicole
• 署名单位: Vrije Universiteit Amsterdam; Tinbergen Institute; Leiden University - Excl LUMC; Leiden University; University of Hamburg
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1090.0738
• 发表日期: 2010
• 页码: 756-767
• 关键词: perturbation bounds; queuing models; chains; sensitivity; ergodicity; network; matrix

摘要

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.