A retrial queue with structured batch arrivals, priorities and server vacations

A retrial queue accepting two types of customers with correlated batch arrivals and preemptive resume priorities is studied. The service times are arbitrarily distributed with a different distribution for each type of cusomer and the server takes a single vacation each time he becomes free. For such a model the state probabilities are obtained both in a transient and in a steady state. Finally, the virtual waiting time of an arbitrary ordinary customer in a steady state is analysed.