Collaborative Research: Phantom traffic jams, continuum modeling, and connections with detonation wave theory

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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.