Averaging in Markov Models with Fast Semi-Markov Switches and Applications

Abstract

An averaging principle for a two component Markov process with fast semi-Markov switches (x n (⋅), ζ n (⋅)) is studied. Here x n (⋅) is a switching semi-Markov process and ζ n (⋅) is a Markov process switched by x n (⋅). If x n (⋅) satisfies an asymptotic mixing property as n → ∞, then under some regular assumptions ζ n (⋅) weakly converges in Skorokhod space to a Markov process with transition rates averaged by the stationary measure of x n (⋅). Applications to the analysis of state-dependent queueing systems and multicentre clinical trials in a fast semi-Markov environment are considered.