(N, n)-preemptive priority queues

In this paper, we propose a new priority discipline, called the ( N , n ) -preemptive priority discipline. Under this discipline, the preemption of the service of a low-class customer is determined by two thresholds N and n of the queue length of high-class customers. We consider M/G/1 priority queueing models with two customer classes under two different ( N , n ) -preemptive priority disciplines and derive the Probability Generating Functions (PGFs) of queue lengths of each class. We also show that, under the ( N , n ) -preemptive priority discipline, the QoS for high-class customers can be controlled within a certain bound, regardless of the restarting mode of a preempted service.