On Definitions of Congestion in Communication Networks

The concepts of time-congestion and call-congestion luive been in common use since the early days of telephone traffic theory. Both ideas are quite simple when applied to a single set of devices used in telephony, such as a full-access trunk-group. But applications of these ideas in the theory of networks of more general structure, composed of elements arranged both in series and in parallel, have not always been consistent, either internally or with each other. This paper describes an attempt to resolve some of the difficulties, which may have arisen because the simplicity of many "classical" models renders unnecessary some distinctions which are important in the general case. This section describes the nomenclature used below and the assumptions on which the remainder of the paper rests. The following section treats a useful model in the context of a full-access trunk-group. In the third section, similar ideas are applied to the theory of general communication networks. The fourth section contains a brief discussion of some of the switching literature, in the light of Section III. Some conclusions appear in the fifth section. In order to save space, I propose the abbreviations " C C " for call-congestion and " T C " for time-congestion. I use the following terminology. A single element of a system carrying traffic is busy or idle. This choice is binary and tells whether or not 2271