Computing entry-wise bounds of the steady-state distribution of a set of markov chains

Abstract

We present two algorithms to find the component-wise upper and lower bounds of the steady-state distribution of an ergodic Markov chain. whose transition matrix is entry-wise larger than matrix. The algorithms are faster than Muntz's approach. They are based on the polyhedral theory developed by Courtois and Semal and on a new iterative algorithm which gives bounds of the steady-state distribution at each iteration. © 2013 Springer-Verlag London.