Analysis of preemptive loss priority queues with preemption distance

In a queueing system with preemptive loss priority discipline, customers disappear from the system immediately when their service is preempted by the arrival of another customer with higher priority. Such a system can model a case in which old requests of low priority are not worthy of deferred service. This paper is concerned with preemptive loss priority queues in which customers of each priority class arrive in a Poisson process and have general service time distribution. The strict preemption in the existing model is extended by allowing the preemption distance parameter d such that arriving customers of only class 1 through p – d can preempt the service of a customer of class p. We obtain closed-form expressions for the mean waiting time, sojourn time, and queue size from their distributions for each class, together with numerical examples. We also consider similar systems with server vacations.