On a Problem of Preemptive Priority Queuing

A priority queuing system is considered possessing the following properties. There exist two populations of potential customers. One population of regular customers is infinitely large and its arrival characteristics are well-represented by a Poisson stream of constant intensity. The other population consists of a relatively small number of extraordinary customers. The arrival of each of these extraordinary customers is governed by an individual constant Poisson intensity. Service is given at a single station and regular customers on service are preempted by any arriving extraordinary customer. The expected value, the variance, etc., of the queue of ordinary customers is derived. Various relations given by previous authors are shown to represent special cases of the model discussed in this paper.