A preemptive priority queue with balking

This paper analyzes a 2-class, single-server preemptive priority queueing model with low priority balking customers. Arrivals to each class are assumed to follow a Poisson process with exponentially distributed service times. The decision to balk or not is made on the basis of queue length, and two specific forms of balking behaviour are considered. The system under consideration is a quasi-birth and death process, and the steady-state joint distribution of the number of high and low priority customers in the system is derived explicitly via the method of generalized eigenvalues.