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

Autor:	Liu, Jinpeng, Liu, Yuanyuan, Zhao, Yiqiang Q.
Rok vydání:	2022
Předmět:	Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	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. Comment: 26 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2204.09972 Zobrazit plný text záznamu View this record from Arxiv