Abstract
Queues for service of one kind or another arise in many different fields of activity. In recent years a considerable amount of research has been conducted into the properties of simplified mathemtical models of such queuing systems. Initially, it was my aim to present a short but balanced survey of the literature; but I soon found myself unequal to the task. It is not so much the subject material as the inassessability of the literature which makes for the difficulty. Many of the the most important articles have appeared only in technical journals, and a university library is not the best place in which to look for them. Instead, therefore, the objects of this paper shall be threefold. First, I have tried to give an account of the general ideas that are useful in describing and thinking about queuing systems. Secondly, I have set forth the basic equations governing the queue and illustrated how the technique would work with a single-channel, single-phase queue. Finally, I have applied these equations to an actual production problem. | When confronted with a problem involving waiting lines, the decision maker must use his knowledge of the characteristics of the queue in attempting to reduce costs, maximize output, and so forth. Some of the changes he might recommend are1: changing the number of servicing stations, changing the service time in one or more stations, splitting a single queue or combining several queues. Such changes would be evaluated by first considering their effect on the characteristics of the waiting line, and then translating these changes in characteristics into changes in the chosen measure of effectiveness. | It is my intention that this paper will prove useful to those decision makers who want a short introduction to the problems of this special field. I fully appreciate that every practical problem has its own specific complexities but I believe that consideration of the general ideas which are discussed in this paper can aid in an understanding of such special systems. It is also possible that intelligent use of various equations which have been presented for particular simple systems can lead to useful approximations when analyzing more complex systems.