Some improvements for the computation of the steady-state distribution of a markov chain by monotone sequences of vectors

Authors:
Jean-Michel Fourneau;Franck Quessette
Affiliations:
PRiSM, Université de Versailles-Saint-Quentin, CNRS UMR 8144, UniverSud, Versailles, France;PRiSM, Université de Versailles-Saint-Quentin, CNRS UMR 8144, UniverSud, Versailles, France
Venue:
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
Year:
2012

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Abstract

We present several new improvements for a recently published algorithm [5] for computing the steady-state distribution of a finite ergodic Markov chain, which has a proved monotone convergence under some structural constraints on the matrix. We show how to accommodate infinite state space and that the structural constraints of the algorithm are consistent with Pagerank matrix. We present how to combine this algorithm with stochastic comparison theory to numerically obtain bounds and we prove a pre-processing of the matrix which allows to alleviate the structural constraints. The approaches are illustrated through several small examples.