arXiv:1308.4227 Abstract | arXiv Analytics

arXiv:1308.4227 [math.PR]Abstract References Reviews Resources

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

Published 2013-08-20Version 1

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.

Categories: math.PR, cs.PF, cs.SY, math.OC

Subjects: 60J10, 60J22, 60J45, 90B15, 90B18, 90B22, G.3, C.4

Keywords: mixing time, infinitely-many levels, qbd processes, computational framework, matrix poissons equations

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