An N-class structured priority queue with vacations

The authors consider a queue with batch arrivals, accepting N priority classes of customers. The arrival process is Poisson; the service times have a general distribution, common within each class. The server takes multiple vacations each time the system becomes empty. The Laplace transforms of the joint distributions of the system states and the elapsed or remaining service (or vacation) time are obtained for the transient regime and for steady state. They are used to study the amount of unfinished work in the system.