Two-class priority queueing system with restricted number of priority customers

In this paper, we analyze a two-class single-server preemptive priority queueing system with arrivals to each class are assumed to follow a Poisson process with exponentially distributed service times. Customers are served on a first-come, first-served basis within their own queue. Explicit expressions for the mean queue length and the steady-state joint distribution of the number of high and low priority customers in the system are derived. The analysis is based on the generating function technique. The obtained expressions are free from Bessel functions or any integral functions. Moreover, numerical values testing the quality of our analytical results are also presented.