A Priority-Based Admission Scheme for a Multiclass Queueing System

We consider a queueing problem involving multiple priority classes where the station is divided into waiting and service areas. The service area has a finite number of positions where a customer of a particular class has access to only a subset of these positions. The admission into the service area is controlled by a mechanism that allows customers within a priority class to enter the service area on a first-come first-served basis. The customers of different classes are assumed to be indistinguishable once they have entered the service area. We consider service under three different disciplines: last-come first-served preemptive resume, multiple server, and processor sharing. We show that the waiting time of a customer is related to that of a customer in an equivalent M/G/1 queue. We characterize the Laplace-Stieltjes transform of the time spent in the service area. We also discuss three potential applications in the area of computer and communication systems.