Finite capacity priority queues with potential health applications (Q1081980)

The queueing processes of interest in this paper are that of waiting lines with two priorities and multiple service channels. The arrival process is assumed Poisson and the service time distribution is negative exponential. Arriving units enter service if there is at least one idle channel, otherwise they join a finite queue and are served according to a non-preemptive priority discipline. If a low priority arriving unit finds the queue full, it is not allowed to enter the system and is considered ''blocked'' or lost. In the first model a high priority arrival may displace a low priority unit from the full queue and may be ''blocked'' if the queue consists of high priority units only. In the second model the high priority unit may still displace a low priority unit from the full queue but it will never be ''blocked'' and may wait ''outside'' the system if the system is full. Thus far there has been no discussion of such models in queueing theory literature. In this paper analytical expressions for average waiting times have been obtained for the two models. Two potential applications of the models are described and the usefulness of the models is illustrated by numerical examples.