Class C Markov Chains and Transient Analysis.

It has been shown that a particular class of time-homogeneous Markov chains, called class C, possesses a closed form steady state solution. In this paper, we are interested in the transient analysis of this class of Markov chains. Unlike steady state analysis, transient analysis for continuous time (CTMC) and discrete time (DTMC) Markov chains have to be treated differently. First we show that transient distributions of class C Markov chains can be also computed through closed form solutions both for the cases of DTMC and CTMC. By means of the stochastic comparison approach, we construct bounding chains belonging to this class thus bounding transient distributions of the underlying Markov chain can be easily computed through the closed form solution. In this work we propose bounds both in the sense of the strong stochastic order, and the increasing convex stochastic order. [ABSTRACT FROM AUTHOR]