Matrix-analytic methods for solving Poisson's equation with applications to Markov chains of GI/G/1-type

Jinpeng Liu; Yuanyuan Liu; Yiqiang Q. Zhao

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arXiv · 2204.09972

Matrix-analytic methods for solving Poisson's equation with applications to Markov chains of GI/G/1-type

Jinpeng Liu·Yuanyuan Liu·Yiqiang Q. Zhao

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Abstract

In this paper, we are devoted to developing matrix-analytic methods for solving Poisson's equation for irreducible and positive recurrent discrete-time Markov chains (DTMCs). Two special solutions, including the deviation matrix D and the expected additive-type functional matrix K, will be considered. The results are applied to Markov chains of GI/G/1-type and MAP/G/1 queues with negative customers. Further extensions to continuous-time Markov chains (CTMCs) are also investigated.

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Jinpeng Liu, Yuanyuan Liu, Yiqiang Q. Zhao. 2022-04-21. Matrix-analytic methods for solving Poisson's equation with applications to Markov chains of GI/G/1-type. https://arxiv.org/abs/2204.09972

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