Parametric convergence analysis of an aggregated Markov chain

Markov chains are commonly used in system identification, modelling and statistical signal processing. In particular they provide powerful analysis tools for digital communications, computer networks and flexible manufacturing systems. For most practical systems the underlying Markov chain possesses a prohibitively large number of states. This necessitates state aggregation in an effort to maintain the computational complexity at manageable levels. In this paper we consider the aggregation of an underlying Markov chain for a parallel synchronized structure in a closed network. Such Markov chains are encountered in the modelling of computer networks and manufacturing systems, and do not have closed-form solutions, requiring numerical computation. Based on an asymptotic convergence result we provide a parametric convergence analysis of the transition rates of the aggregated Markov chain and develop reduced complexity solutions.