Waiting times of a finite-capacity multi-server model with non-preemptive priorities

We consider a non-preemptive head of the line multi-server priority model with finite capacity. The arrival processes of the different priority classes are independent Poisson processes. The service times are exponentially distributed and identical for the different priority classes. The model is described by a homogeneous continuous-time Markov chain. For the two-class model we derive an explicit representation of its steady-state distribution. Applying matrix-analytic methods we calculate the Laplace–Stieltjes Transform of the actual waiting time of each priority class of a p-class system.