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Averaging in Markov Models with Fast Markov Switches and Applications to Queueing Models

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Abstract

An approximation of Markov type queueing models with fast Markov switches by Markov models with averaged transition rates is studied. First, an averaging principle for two-component Markov process (x n (t),ζ n (t)) is proved in the following form: if a component x n (⋅) has fast switches, then under some asymptotic mixing conditions the component ζ n (⋅) weakly converges in Skorokhod space to a Markov process with transition rates averaged by some stationary measures constructed by x n (⋅). The convergence of a stationary distribution of (x n (⋅),ζ n (⋅)) is studied as well. The approximation of state-dependent queueing systems of the type M M,Q /M M,Q /m/N with fast Markov switches is considered.

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  1. Research Statistics Unit, GlaxoSmithKline, NFSP (South), Third Avenue, Harlow, CM19 5AW, UK

    V.V. Anisimov

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  1. V.V. Anisimov
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Anisimov, V. Averaging in Markov Models with Fast Markov Switches and Applications to Queueing Models. Annals of Operations Research 112, 63–82 (2002). https://doi.org/10.1023/A:1020924920565

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