Waiting Time Asymptotic Analysis of a M/M/1 Retrial Queueing System Under Two Types of Limiting Condition

Abstract

In our paper, the waiting time analysis of a M/M/1 retrial queueing system is presented and the asymptotic distribution of the number of returns of the tagged request to the orbit is driven since they are connected to each other. The research was conducted by the use of asymptotic analysis method. Two different cases are considered. First we conduct analysis under a heavy load condition and then under a low rate of retrials condition. Two different characteristic functions of the waiting time were obtained. The analysis was carried out using asymptotic distributions of the number of requests in the orbit under a heavy load condition and a low rate of retrials condition, which were also obtained. To show the effectiveness of asymptotic results for the considered retrial queuing system, the approximation of the distribution of the number of returns of the tagged request to the orbit in prelimit situation, numerical illustrations and results are given. Keywords: Retrial queue • Asymptotic analysis • Waiting time • Number of returns • Number of retrials