SEE PROFILE

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 (xn(t), ζn(t)) is proved in the following form: if a component xn(·) has fast switches, then under some asymp-totic mixing conditions the component ζn(·) weakly converges in Skorokhod space to a Markov process with transition rates averaged by some stationary measures constructed by xn(·). The convergence of a stationary distribution of (xn(·), ζn(·)) 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