Analysis of a multi-server queue with two priority classes and (M, N)-threshold service schedule I: Non-preemptive priority

In this paper, we propose an (M, N)-threshold non-preemptive priority service schedule for a queueing system consisting of two-parallel queues and a multi-server. The arrival process for each queue is Poisson, and the service times are exponentially distributed with different means. We derive the generating functions of the stationary joint queue-length distribution, and then obtain the mean queue length and the mean waiting time for each queue.