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arXiv · 1308.4227

A Computational Framework for the Mixing Times in the QBD Processes with Infinitely-Many Levels

Quan-Lin Li·Jing Cao
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Abstract

In this paper, we develop some matrix Poisson's equations satisfied by the mean and variance of the mixing time in an irreducible positive-recurrent discrete-time Markov chain with infinitely-many levels, and provide a computational framework for the solution to the matrix Poisson's equations by means of the UL-type of $RG$-factorization as well as the generalized inverses. In an important special case: the level-dependent QBD processes, we provide a detailed computation for the mean and variance of the mixing time. Based on this, we give new highlight on computation of the mixing time in the block-structured Markov chains with infinitely-many levels through the matrix-analytic method.

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BibTeXRIS

Quan-Lin Li, Jing Cao. 2013-08-20. A Computational Framework for the Mixing Times in the QBD Processes with Infinitely-Many Levels. https://arxiv.org/abs/1308.4227

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