Asymptotic Analysis of Retrial Queueing System M/GI/1 with Collisions and Impatient Calls

Abstract

In the paper, the retrial queueing system of M/GI/1 type with input Poison flow of events, collisions and impatient calls is considered. The delay time of calls in the orbit and the impatience time of calls in the orbit have exponential distribution. Service time on server is with any distribution function. Asymptotic analysis method is proposed for the solving problem of finding distribution of the number of calls in the orbit under a long delay of calls in orbit and long time patience of calls in the orbit condition. The theorem about the Gauss form of the asymptotic probability distribution of the number of calls in the orbit is formulated and proved. Numerical illustrations, results are also given.