Investigation of M/G/1//N system with collisions, unreliable primary and a backup server

This paper explores a finite-source retrial queueing system featuring collisions of the requests, unreliability of the primary server and a backup server. In the case of collisions, wherein a new job arriving when the service facility is occupied results in a collision, sending both jobs to a virtual waiting room, termed the orbit. In the orbit, customers initiate further attempts to access the server after a random time interval. In the event of a breakdown, the customer at the server is forwarded to the orbit. The novelty of this study lies in implementing a backup facility when the primary server is unreachable and carrying out a sensitivity analysis employing various service time distributions of the primary customers. We investigated a scenario where the most important performance measures are visually represented highlighting the observed disparities.