The Origins of Traffic Theory

W this biblical beginning, I started a paper in 1974 reviewing the development of traffic control theories. I think it is appropriate to start the present paper the same way. Traffic problems existed, to some extent, even before the Ford, which ushered the age of universal automobile transportation. But the problems were relatively small and isolated, and did not provoke much thought for their solution. The automobile changed all that in a big way, and by the middle of the 20th century traffic problems were big and commanding much attention. By 1950, scientists from many walks of life came forward with attempts to model the movement of traffic, with the ultimate goal of finding amelioration to traffic problems. Some of the early contributions to traffic modeling were those of Reuschel (1950) and Pipes (1953), on one hand, and Lighthill and Whitham (1955), on the other. Reuschel and Pipes proposed a traffic model describing the detailed movement of cars proceeding close together in a single lane, a “microscopic” model of traffic. Lighthill, a world renowned fluid mechanics theorist, together with Whitham, proposed a “macroscopic” model of traffic, modeling traffic as a continuum akin to a fluid. The Lighthill-Whitham (L-W) model is based on two premises, the conservation of the number of cars and the existence of an equation of state describing a relationship between traffic flow, measured in cars per hour, and traffic density, measured in cars per mile. The conservation of cars is, of course, a rational assumption. The existence of an equation of state is partially verified by measurements, with much scatter observed in the data, particularly at high traffic densities. Nevertheless, the L-W model provides a pretty good description of some basic phenomena in traffic, such as the propagation of “shock waves” which are generated when traffic shifts from one steady-state pattern to another associated with different density and flow. The shock wave theory of L-W is, however, only good in describing density changes that are separated relatively widely in time, i.e., transitions from one steady-state traffic flow situation to another. Attempts to use the L-W wave theory to describe detailed movement of traffic around intersections have been badly misguided, because the time of the generation of one shock wave is of the same order as the time of transition to the next, and the inherent approximation of the shock wave produces large errors in the modeling of the movement of traffic. The Reuschel and Pipes models described the movement of a car following another one in front. They were based on the assumption that the speed of the following car was a linear function of the distance between the lead car and the following car. The models were reasonable in concept, but no experimental verification of their conclusions was pursued for many years. By the mid-1950s, traffic models had attracted the attention of such notable scientists as Elliott Montroll. Then, in 1956, a confluence of events spurred a rapid development of traffic theory. General Motors hired a new executive in charge of its Research Laboratories. He was Larry Hafstad, a nuclear physicist by background, who had the ambition of making the General Motors Research Labs a leader in “basic science” and not just a development lab as it had been for years. One of the persons hired to bring about this change was Robert Herman. Herman teamed up with Montroll and pursued some basic investigations of carfollowing which have stood the test of time to this day. I was hired into the Basic Science department of GM Research in 1957 by Bob Herman. My original assignment had nothing to do with traffic. Herman, in his unrivaled spirit of pursuit of knowledge in every meaningful direction, turned me loose around the Lab to see how I could apply my knowledge of applied mechanics to the modeling and improvement of devices and processes useful to the automobile industry, such as the production of better ball bearings through better understanding of contact stresses between the balls and their casing. However, it was not long before I was attracted to the traffic modeling activities, which ended up keeping me busy for a good part of my life for years to come. Let me take a moment to stress the influence of corporate management on the research output of an organization. I joined GM Research at the advice and recommendation of my Columbia University Ph.D. mentor, Professor Ray Mindlin. Mindlin told me: “Automobile companies are not