Performance analysis of a finite-source retrial queueing system with two-way communication, catastrophic breakdown and impatient customers using simulation

Ádám Tóth, János Sztrik
An M/M/1//N retrial queueing system with two-way communication to the infinite source and impatient customers in the orbit is considered in the paper. There is a finite source in which the primary or regular customers are coming, while requests from the infinite source are the secondary customers. Because of not having waiting queues, the service of an arriving, primary customer begins immediately. Otherwise, in the case of a busy server, the primary customers are forwarded to the orbit waiting an exponentially distributed random time to try to reach the service unit. When the service unit is in an idle state, it may call a customer from the infinite source for service. All requests possess an impatience property resulting in an earlier departure from the system through the orbit if they wait too much for being served. Besides, the service unit is supposed to break down according to several distributions which have a specialty removing all the customers located in the system. In the case of a faulty state, blocking is applied not allowing the customers into the system until the service unit fully recovers. This work concentrates on examining the effect of those distributions on several performance measures like the distribution of the number of customers in the system, the probability of a primary customer departing because of catastrophe. The obtained results are graphically realized to show the differences and curiosities among the used parameter settings of the various distributions.