Decomposition and aggregation of large-dimensional Markov chains in discrete time

Motivated by a wide range of applications arising from stochastic networks (such as communication networks and/or manufacturing systems), this work focuses on a class of large-scale Markov chains in discrete time. In accordance with the rates of change of different states, we formulate the problem as a singularly perturbed Markov chain by introducing a small parameter ε>0. Under simple conditions, we show that aggregated process converges weakly to a Markov chain. In addition, we examine scaled and unscaled occupation measures and obtain their asymptotic properties