Two asymptotic conditions in queue with MMPP arrivals and feedback

Abstract

We consider infinite-server queue with Markov modulated Poisson arrivals and feedback. Asymptotic analysis of the aggregate arrival process is made under conditions of frequent changing of the underlying chain states of the arrival process and increasing service time. It is proved that the aggregate arrival process is Poisson asymptotically. Parameter of the Poisson approximation is obtained. Applicability area of the asymptotic results is derived by means of numerical experiments.