Analysis of non-pre-emptive priority retrial queueing system with two-way communication, Bernoulli vacation, collisions, working breakdown, immediate feedback and reneging (Q2214212)

Summary: In this study, we investigate a single server priority retrial queueing system including two-way communication, collision, working breakdown, repair, immediate feedback, Bernoulli vacation and reneging. Incoming requests (calls) appear at the service station according to a compound Poisson process. During the idle time, the server can make an outgoing call with an exponentially distributed time. The incoming call that identifies the server occupied will join an orbit or collide with the call currently in service. The server renders the service following a non-pre-emptive priority service rule. The server takes a Bernoulli vacation. The server may become inactive due to normal breakdown and the call currently in service will get the remaining service at a moderate service rate. The repair process starts instantly. After the completion of service, vacation and repair the server is in an idle state. We allow reneging to happen at the orbit. Using the supplementary variable technique, the stability condition is derived.