Analysis of the Finite-source Multi-class Priority Queue with an Unreliable Server and Setup Time

In this paper, we study a queueing system serving multiple classes of customers. Each class has a finite-calling population. The customers are served according to the preemptive-resume priority policy. We assume general distributions for the service times. For each priority class, we derive the steady-state system size distributions at departure/arrival, and arbitrary time epochs. We introduce the residual augmented process completion times conditioned on the number of customers in the system to obtain the system time distribution. We then extend the model by assuming that the server is subject to operation-independent failures upon which a repair process with random duration starts immediately. We also demonstrate how setup times, which may be required before resuming interrupted service or picking up a new customer, can be incorporated in the model.