  This work focuses on time-inhomogeneous Markov chains with two time scales.
Our motivations stem from applications in reliability and dependability,
queueing networks, financial engineering and manufacturing systems, where
two-time-scale scenarios naturally arise. One of the important questions is: As
the rate of fluctuation of the Markov chain goes to infinity, if the limit
distributions of suitably centered and scaled sequences of occupation measures
exist, what can be said about the convergence rate? By combining singular
perturbation techniques and probabilistic methods, this paper addresses the
issue by concentrating on sequences of centered and scaled functional
occupation processes. The results obtained are then applied to treat a queueing
system example.
