Anisimov, V. V.2019-01-312019-01-3120020254-5330http://hdl.handle.net/11693/48596An 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 MM,Q/MM,Q/m/N with fast Markov switches is considered.EnglishMarkov processQueueing systemAveraging principleSwitching processStationary distributionRandom environmentArticle10.1023/A:1020924920565