Initially homogeneous traffic flow can become inhomogeneous even in the absence of obstructions of any kind, leading to the formation of ''phantom'' traffic jams. Phantom traffic jams can be explained as instabilities that occur in certain types of macroscopic traffic models. Under appropriate conditions, if the traffic density exceeds a critical threshold value, small perturbations amplify and grow into nonlinear traveling waves. These traffic waves, called jamitons, are observed in reality and have been reproduced experimentally. In this project, a mathematical analogy between jamitons and detonation waves in reacting gas dynamics is established and exploited: phantom traffic jams are the analogs of instabilities in the fluid's motion, and jamitons are the analogs of detonation waves. Using the Zel'dovich-von Neumann-Doering theory from combustion theory, the analogy allows the prediction of the exact shape and travel velocity of the jamitons. A key feature in the analysis is the presence of a sonic point, which acts as an event horizon (similar to the one that occurs in a black hole) across which information cannot propagate. Traffic waves are studied theoretically and by numerical simulations. A particular goal is to understand phantom traffic jams well enough to allow the development of effective countermeasures.
A ''phantom'' traffic jam is a small congestion in vehicular traffic that occurs spontaneously, in the absence of bottlenecks, obstacles, or any discernible causes on the road. Observations show that uniform traffic flow can develop inhomogeneities, which turn into traveling traffic jams. These traffic jam waves (''jamitons'') enforce unexpected braking maneuvers, and thus impose stress on drivers and materials, waste fuel and increase pollution, and are hot spots for potential vehicle collisions. In this project, the behavior of phantom traffic jams and jamitons is studied. Theoretical analogies between traffic modeling and gas dynamics, hydraulics, and astrophysics, are established and used to advance the understanding of traffic flow. These connections yield insight into the situations under which phantom traffic jams can occur, and allow the prediction of the shape and velocity of the resulting jamitons. A fundamental understanding of phantom traffic jams is a key step in devising appropriate countermeasures to avoid or ameliorate them. The development of effective ways to manage or prevent phantom traffic jams could have a considerable impact on the reduction of fuel consumption and pollution. Two possible strategies that will be incorporated into the models and investigated are: assisted driving devices in the individual vehicles, and adaptively controlled speed limits on highways. A crucial component of this study is the interplay between theoretical analysis and numerical experiments. The research in this project involves three international collaborations, as well as graduate and undergraduate research projects.
This project has contributed a deeper understanding of phantom traffic jams and of jamitons. The term "phantom traffic jam" denotes the phenomenon that initially uniform traffic flow can become inhomogeneous, in the absence of obstacles or bottlenecks on the road; and a "jamiton" is a traveling wave in traffic flow, in which vehicles are forced to brake suddenly, and then slowly accelerate again. In this project macroscopic traffic models are studied, that describe vehicular traffic flow via equations that resemble those of fluid dynamics. In these models, phantom jams appear as instabilities of uniform traffic flow, that occur when the traffic density is above a critical threshold density. Moreover, jamitons are mathematical analogs of self-sustained detonation waves, that are known to arise in equations describing reacting gases. The Intellectual Merit of this research stems from the exploitation of the analogy of traffic waves and detonation waves. Using the Zel'dovich-von Neumann-Doering theory from combustion theory, the exact shape and travel speeds of jamitons can be predicted and related to the collective driving behavior, as can the threshold density above which they occur. The understanding of phantom jams as instabilities and traffic waves as self-sustained waves gives rise to new insights into the nature of these dynamical features of traffic flow. For instance, traffic waves are not necessarily a single driver's fault; instead they are a result of the collective behavior of all drivers on the road. Moreover, the self-sustained nature of jamitons implies that individual drivers, once they have passed sufficiently far through the wave (beyond a special "sonic point" in the wave), cannot do anything against the wave through their driving behavior. Finally, in traffic engineering it is generally observed that for sufficiently dense traffic, a single density corresponds to multiple possible flow rates. The research in this project shows that such multi-valued fundamental diagrams can in fact be explained through the presence of jamitons. The Broader Impacts that stem from the deeper understanding of jamitons are as follows. First, since phantom jams arise without any discernable causes, the braking enforced on the drivers occurs suddenly and unexpectedly. Thus, jamitons are plausibly hot spots for accidents. Moreover, the unsteady driving caused by jamitons is likely to increase fuel consumption. The understanding of the mathematical connection between driving behavior and the occurrence and structure of the undesirable jamitons can serve as the first step in devising technologies to prevent them. Second, the analogy of traffic waves to detonation waves yields a better understanding of many other phenomena related to detonation theory, such as hydraulic jumps, roll waves, gravitational collapse in astrophysics, and sedimentation. Several undergraduate student researchers were involved in this project, as well as three international collaborators from mathematics and engineering. Products created in this project that go beyond journal publications are: 1) an article for the New York Times, "The Ripple Effect of Bad Driving", and an article for the popular science magazine Nautilus, "Traffic Ghost Hunting"; 2) a website that shows figures and animations of traffic waves and their simulation, and that explains the findings of this research in a language accessible to the broader public.
