Simulating Retrial Queues with Finite Source, Two-Way Communication to the Orbit, Backup Server, and Impatient Customers

This paper explores a retrial queuing system with two-way communication and an unreliable server that may encounter random breakdowns. The system is of the finite-source M/M/1//N type, where the idle server can initiate calls to customers in the orbit, termed as secondary customers. Both primary and secondary customer service times are characterized by exponential distributions, with rates denoted as \(\mu _1\) and \(\mu _2\) , respectively. The novelty of this study lies in its investigation of various failure time distributions and their impact on critical performance metrics, such as the mean response time of a random customer, while utilizing a backup server with impatient customers. The backup server can be likened to a primary server operating at a reduced rate during maintenance intervals. To ensure a valid comparison, a fitting process equalizes the mean and variance across all distributions. The outcomes are visually depicted through the utilization of our self-made simulation program.