Analysis of mixed priority retrial queueing system with two way communication and working breakdown

Incoming calls are arrive at the service system according to compound Poisson process. During the idle time, the server making an outgoing call with an exponentially distributed time. If the incoming call that finds the server busy will join an orbit. Here we use mixed priority services i.e., an arriving call may interrupt the service of an outgoing call or join the retrial queue (orbit). The server takes Bernoulli vacation. The server may become inactive due to normal as well as abnormal breakdown. After the completion of service, vacation and repair the server is in idle state. We consider reneging to occur at the orbit. Using supplementary variable technique, the stability condition is derived.