Batch Arrival Preventive Loss Priority Queues with Preventive Distance

Abstract

This paper is concerned with preemptive loss priority queues in which a batch of failed machines of each priority class arrive in a Poisson process and have general service time distribution. In this queuing system, failed machines are not considered for repair again when their services are preempted by the arrival of another batch of failed machines with higher priority They disappear immediately. A case can be modeled by such a system in which deferred service is worthless for old demands of low priority. This model is based on the situation of strict preemption with preemption distance parameter d such that failures of only class l to p - d can preempt the service of failures of class p. The closed form expressions are obtained in the mean waiting time and source time from their distributions for each class. Several numerical examples illustrate the approach.