Asymptotic Diffusion Analysis of an Retrial Queueing System M/M/1 with Impatient Calls

Abstract

AbstractIn the paper, the retrial queueing system of M/M/1 type with input Poison flow of events and impatient calls is considered. The service time, delay time of calls in the orbit and the impatience time of calls in the orbit have exponential distribution. Asymptotic diffusion 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. Numerical results confirm that the probability distribution of the number of calls in the orbit is Gaussian. The range of applicability of the obtained results is given for different values of system parameters. The RQ-system under consideration is also investigated by the asymptotic analysis method. The results of the comparison of the two methods are presented.KeywordsRetrial queueing systemImpatient callsAsymptotic diffusion analysis