Poisson's equation for discrete-time quasi-birth-and-death processes

Sarah Dendievel; Guy Latouche; Yuanyuan Liu

doi:10.1016/j.peva.2013.05.008

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arXiv · 1308.2444

Poisson's equation for discrete-time quasi-birth-and-death processes

Sarah Dendievel·Guy Latouche·Yuanyuan Liu

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Abstract

We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and we exploit the special transition structure of QBDs to obtain its solutions in two different forms. One is based on a decomposition through first passage times to lower levels, the other is based on a recursive expression for the deviation matrix. We revisit the link between a solution of Poisson's equation and perturbation analysis and we show that it applies to QBDs. We conclude with the PH/M/1 queue as an illustrative example, and we measure the sensitivity of the expected queue size to the initial value.

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BibTeX RIS

Sarah Dendievel, Guy Latouche, Yuanyuan Liu. 2013-08-12. Poisson's equation for discrete-time quasi-birth-and-death processes. https://doi.org/10.1016/j.peva.2013.05.008

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