Memoirs on Highway Traffic Flow Theory in the 1950s

T has been a revival of interest in traffic flow theory in the late 1990s, mostly because vehicle detectors have been installed at many highway locations throughout the world to record the passing of vehicles. The purpose of these detectors is to monitor congestion and provide information for possible control or to advise motorists of possible alternative routing. To understand the consequences of some strategy, however, one must have some theories or models of how traffic will respond to various actions. Students who review the literature on traffic flow theory in an attempt to develop such models observe that most of the references on this subject are dated in the 1950s and 1960s. There is very little useful literature in the 1970s, 1980s, or early 1990s. Students wonder how this started, who were these people who wrote the early papers, and why did the subject die in the 1970s? There are not many people left who were involved in the early developments of traffic flow theory, so it is difficult to research the history of it. Many of these people were involved for only a short time and then moved on to other things. Most of them had grown up during the Depression era and had lived through World War II. Any one of them could have told stories about what the world was like then and what motivated them, but perhaps the stories would be rather similar. The 1950s was a time to try to put civilization back together and to create a society people could live with. I can tell the story only from my own perspective and from my encounters with others. It is appropriate that traffic flow theory be included as part of the anniversary celebration of Operations Research, because many of the early papers on traffic flow theory were published in this publication, and the national meetings of ORSA were one of the main forums for exchange of ideas. A special issue of Operations Research devoted to transportation was published in 1964, and the journal Transportation Science (sponsored by ORSA) was created in 1966. My first exposure to problems in transportation occurred in 1954. Professor William Prager, the distinguished professor of applied mathematics at Brown University, gave a lecture on a “fluid theory” of highway traffic. The theory he described was essentially what was later published in the famous papers by Lighthill and Whitham (1955). I will never know if Prager arrived at this himself or if he had learned about it from Lighthill. Prager never published a paper on this topic. I thought this was intriguing. After the lecture, I suggested to Prager (whose office was very close to mine) that one should model vehicles like a gas, as in the kinetic theory of gases, rather than as a fluid as in fluid dynamics—after all, cars are discrete objects like molecules that run around and occasionally interact. This is a “onedimensional gas.” Prager’s primary field of interest was continuum mechanics; mine (at that time) was physics, particularly statistical mechanics. Prager said he had assembled a bibliography on traffic flow theory. He showed me his folder, but the only paper in it that dealt with any real theory was a survey paper by Wardrop (1952). He also had a copy of the Highway Capacity Manual by Norman and Walker (1950), which describes most of what was known then from measurements of traffic behavior. Actually, it turns out that this was not a complete bibliography at the time. There were some earlier papers in various journals, but not many. Most of what Prager had was British literature, which leads me to suspect that he had learned about this from Lighthill, who knew the British literature. My first reaction to this literature was shock or disbelief. In nearly every branch of physics or any other welldeveloped science, researchers stumble over each other looking for new things to do and then race to see who can do them first. The paper by Wardrop (1951) involved only rather obvious things, rather crudely developed. I thought it was quite naïve at first, but later I could appreciate that this was a monumental work because, before Wardrop, there was essentially nothing. He was starting “from scratch.” How was it that the traffic engineering profession knew almost nothing about how to model things they could see with their own eyes? This Wardrop paper is best known for its description of the distinction between the “user optimal” and “system optimal” route choice and the formulation of what is now called “Wardrop’s principles.” This is, in essence,