A two-stage discretionary priority service system with Markovian arrival inputs

We study a two-stage priority service system in which the first stage can be interrupted but the second stage can not. There are two classes of customers, low priority and high priority. The server adopts the preemptive priority discipline if the service is at the first stage and adopts the non-preemptive priority discipline if it is at the second stage service. By treating the high priority queue as bounded, the steady-state probability vector for the system can be expressed in a matrix-geometric form. We also obtain the sojourn time of an arbitrary low priority customer. The numerical results demonstrate the effectiveness of our approach.