Analysis of a finite buffer with non-preemptive priority scheduling

A single-server queue with finite capacity, two distinct service classes and a non-preemptive priority scheduling discipline is analyzed. The arrival streams of the different classes are independent Poisson processes. The service times follow exponential distributions depending on the service classes. To calculate the steady-state distribution of the number of customers of each class in the system, we develop a new recursive approach. Applying matrix-analytic methods, we state the waiting-time distributions of both classes and calculate the Laplace–Stieltjes transform as well as the moments of the actual waiting-time distribution of each class.