The Simulation of Finite-Source Retrial Queues with Two-Way Communication to the Orbit, Incorporating a Backup Server

This paper investigates a two-way communication retrial queuing system with a server that may experience random breakdowns. The system is a finite-source M/M/1//N type, and the idle server can make calls to the customers in the orbit, also known as secondary customers. The service time of the primary and secondary customers follow independent exponential distributions with rates of \(\mu _1\) and \(\mu _2\) , respectively. The novelty of this study is to analyze the impact of various distributions of failure time on the key performance measures using a backup server, such as the mean response time of an arbitrary customer. One could think of a backup server as a primary server that operates at a reduced rate during periods of repair. To ensure a valid comparison, a fitting process is conducted so that the mean and variance of every distribution are equal. The self-developed simulation program provides graphical illustrations of the results.