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

2022/04/21 by Liu, Jinpeng, Liu, Yuanyuan, Zhao, Yiqiang Q.
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2204.09972

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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