(N,n)(N,n)-preemptive priority queues

In this paper, we propose a new priority discipline, called the (N,n)(N,n)-preemptive priority discipline. Under this discipline, the preemption of the service of a low-class customer is determined by two thresholds NN and nn 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)(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)(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.