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

V.V. Anisimov ()

Annals of Operations Research, 2002, vol. 112, issue 1, 63-82

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. Copyright Kluwer Academic Publishers 2002

Keywords: Markov process; queueing system; averaging principle; switching process; stationary distribution; random environment (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1020924920565

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