Heuristic remarks and mathematical problems regarding the theory of connecting systems

A connecting system consists of a set of terminals, a control unit for processing call information, and a connecting network. Together, these three elements provide communication, e.g., supply telephone service, among the various terminals. In this paper we present a comprehensive view of the theory of connecting systems, an appraisal of its current status, and some suggestions for further progress. The existing probabilistic theory is reviewed and criticized. The basic features of connecting systems, such as structure, random behavior, complexity, and performance, are discussed in a nontechnical way, and the chief difficulties that beset the construction of a theory of traffic in large systems are described. It is then pointed out that despite their great complexity, connecting systems have a definite structure which can be very useful in analyzing their performance. A natural division of the subject into combinatory, probabilistic, and variational problems is drawn, and is illustrated by discussing a simple problem of each type in detail.