A 'Thermodynamic' Theory of Traffic in Connecting Networks

Like the physicist, the traffic engineer is faced with the study of an extremely complex system which is best described in statistical terms. The great success of the theoretical methods of statistical physics has given rise to a fervent hope, sometimes voiced among traffic theorists, that similar methods exist and can be found for the study of congestion. Indeed, the problems are much the same: one desires a small amount of "macroscopic" information about averages, based in a rational way on vast complexities of detail. A. K. Frlang was probably influenced by statistical mechanics when he introduced his method of "statistical equilibrium" into traffic theory. This method has had great success in dealing with problems of the birth-and-death type, like trunking and queueing, but as applied to more complex cases it has led mostly to algebraic and combinatory difficulties. Nothing as elegant or powerful as statistical mechanics has resulted so far. We shall present two traffic models in this paper. The first is the outcome of a deliberate attempt to ape the methods of physicists in statistical mechanics, and thus to realize, at least in part, the hope mentioned above. It is called the "thermodynamic" model, and it is treated in detail. The second model is introduced later in the paper in an attempt to avoid certain drawbacks that appear in the interpretation of the "thermodynamic" model. Since it has independent interest and leads to involved, more realistic results, it is studied in detail in a later paper.