Some Special Features of Finite-Source Retrial Queues with Collisions, an Unreliable Server and Impatient Customers in the Orbit

The goal of the paper is to study a finite-source retrial queuing system with collisions and customers’ impatience behavior in the orbit. The situation when an incoming customer from the orbit or from the source finds the server busy causes a collision and both requests are directed toward the orbit. It is assumed that every request in the source is eligible to generate customers whenever the server is failed but these requests immediately go into orbit. A customer after some waiting in the orbit can depart without fulfilling its service requirement these are the so-called impatient/reneging/abandoned customers. In that case it returns to the source. A customer who is under service when the server fails is also sent to the orbit. The source, service, retrial, impatience, operation and repair times are supposed to be independent of each other. The novelty of the investigation is to carry out a sensitivity analysis comparing various distributions of impatience time of customers on the performance measures such as mean number of customers in the orbit, mean waiting time of an arbitrary, successfully served and reneging customers, probability of abandonment, server utilization, etc.