Stationary delays for a two-class priority queue with impatient customers

We consider a Markovian multiserver queue with two types of impatient customers, high and low priority ones. The first type of customers has a non-preemptive strict priority over the other type. After entering the queue, a customer will wait a random length of time for service to begin. If service has not begun by this time he will renege and be lost. We focus on deriving performance measures in terms of the sojourn times of customers in queue, either before starting service, or before reneging. We provide an exact analysis for systems where customers within each type are served under the FCFS discipline of service.

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