Network Equilibrium and Pricing

Traffic equilibrium models are commonly in use for the prediction of traffic patterns on transportation networks that are subject to congestion phenomena. Even though their application in various transportation planning contexts has increased dramatically over the past twenty five years, due to the development of efficient solution algorithms and the increasing power of various computing platforms, they are based on concepts that have been stated more than seventy years ago. The idea of traffic equilibrium originated as early as 1924, when Knight gave a simple and an intuitive description of a postulate of traffic behavior under congested conditions, as follows: Suppose that between two points there are two highways, one of which is broad enough to accommodate without crowding all the traffic which may care to use it, but is poorly graded and surfaced, while the other is a much better road, but narrow and quite limited in capacity. If a large number of trucks operate between the two termini and are free to choose either of the two routes, they will tend to distribute themselves between the roads in such proportions that the cost per unit of transportation, or effective returns per unit of investment, will be the same for every truck on both routes. As more trucks use the narrower and better road, congestion develops, until a certain point it becomes equally profitable to use the broader but poorer highway.