Heuristic Remarks and Mathematical Problems Regarding the Theory of Connecting Systems

» Mass communication long ago spread beyond the manual central office and assumed a nationwide character; it is presently becoming world-wide in extent. Many of the world's telephones already form the terminals of one enormous switching system. The scale, cost, and importance of the system make imperative a comprehensive theoretical understanding of such global systems. Nevertheless, a lack of knowledge about the combinatory and probabilistic properties of large switching systems is still a major lacuna in the art of mass communication. Tt is a fact of experience that each time a new switching system is planned, its designers ask once again some of 1201 1202 T H E B E L L SYSTEM T E C H N I C A L J O U R N A L , J U L Y l ! ) f > 2 the perennial unanswered questions about connecting network design and system operation: How does one compute the probabilities of loss and of delay? What method of routing is best? What features make some networks more efficient than others? Etc. The present paper is an informal discussion of problems in the theory of traffic flow and congestion in connecting systems (called traffic theory, or congestion theory, for short). The comments to be made are prefatory, tutorial, and illustrative. They are intended as background for several papers of a more technical nature; one of these papers 1 appears in this issue, and the remaining three 2,8,4 are to appear later. In these papers, topics touched on in the present work arc considered in greater depth and detail.