Waiting time analysis of the multiple priority dual queue with a preemptive priority service discipline

The dual queue consists of two queues, called the primary queue and the secondary queue. There is a single server in the primary queue but the secondary queue has no service facility and only serves as a holding queue for the overloaded primary queue. The dual queue has the additional feature of a priority scheme to help reduce congestion. Two classes of customers, class 1 and 2, arrive to the dual queue as two independent Poisson processes and the single server in the primary queue dispenses an exponentially distributed service time at the rate which is dependent on the customer's class. The service discipline is preemptive priority with priority given to class 1 over class 2 customers. In this paper, we use matrix-analytic method to construct the infinitesimal generator of the system and also to provide a detailed analysis of the expected waiting time of each class of customers in both queues.