Asymptotic Analysis of RQ-System with Feedback and Batch Poisson Arrival Under the Condition of Increasing Average Waiting Time in Orbit

Abstract

The paper studies the retrial queueing system M\(^{[n]}\)/M/1 with feedback and batch Poisson arrival. Customers for the system come in groups. Not more than one customer is served at once, others wait in the orbit. Having been served, the customer leaves the system or goes to re-service or into the orbit. An asymptotic analysis method is used to find the stationary distribution of the number of customers in the orbit. A long delay between customers from the orbit is proposed as an asymptotic condition. It is proved that the asymptotic probability distribution of the number of customers in the orbit is Gaussian. As a result the parameters of this distribution are obtained. The calculations to determine the range of the method applicability are carried out. The accuracy of the approximation is compared to numerical results obtained by matrix method.