Multiscale Properties of Traffic Flow: The Macroscopic Impact of Traffic Waves

Vehicular traffic flow is a fascinating real-world system in which interactions at the vehicle scale, occurring on the scale of seconds, shape urban-scale flow patterns that develop over the scale of hours. A fundamental goal of traffic modeling is the development of mathematical equations that reproduce the fundamental laws that govern the flow behavior, without requiring detailed information about the human drivers or their vehicles. Starting from such models, it is shown how an additional scale can arise that lies between the microscopic vehicle scale and the macroscopic urban scale, namely: the mesoscopic scale of traffic waves. In certain flow regimes, uniform traffic flow is dynamically unstable, and small perturbations grow into traveling waves. Suitable models can quantify how this “phantom traffic jam” phenomenon lead to significant energy waste and reduction in flow efficiency. Moreover, via models and simulations, it is demonstrated how the introduction of a small number of automated vehicles can serve to recover the efficient uniform flow state.