A batch arrival reader–writer queue with retrial writers

In this work we study a batch arrival reader–writer queue. Readers have non-preemptive priorities over writers. An unlimited number of readers can be served simultaneously, while writers are served one at a time. Writers who find the system busy, leave the system and repeat their demand (retrial) after a random amount of time. We assume that when all the servers become free, the system takes a single vacation. For such a system we obtain the stability condition and analyze the state probabilities of the number of writers and the virtual queueing time of an arbitrary reader or writer in steady state. Numerical results are also obtained and used to observe system performance, for various values of the parameters.