Abstract
Aiming at reduction of complexity, this work is concerned with two-time-scale Markov chains and applications to quasi-birth-death queues. Asymptotic expansions of probability vectors are constructed and justified. Lumping all states of the Markov chain in each subspace into a single state, an aggregated process is shown to converge to a continuous-time Markov chain whose generator is an average with respect to the stationary measures. Then a suitably scaled sequence is shown to converge to a switching diffusion process. Extensions of the results are presented together with examples of quasi-birth-death queues.
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