Equilibrium distribution of block-structured Markov chains with repeating rows

Abstract

In this paper we consider two-dimensional Markov chains with the property that, except for some boundary conditions, when the transition matrix is written in block form, the rows are identical except for a shift to the right. We provide a general theory for finding the equilibrium distribution for this class of chains. We illustrate theory by showing how our results unify the analysis of the M/G/ 1 and GI/M/ 1 paradigms introduced by M. F. Neuts.