Abstract

Autonomous vehicles are likely to decide their driving strategy on the basis of more information than that available to human drivers. This technological shift motivates the study of traffic through a dual-population model: a “farsighted” population (AVs) and a “myopic” one (human drivers). Analytically, this mutual interaction is captured by a mixed system of nonlocal-local conservation laws.

Various qualitative properties of the solutions, as well as control problems, such as the potential for farsighted vehicles to stabilize traffic flow, are better studied in a periodic setting. To this setting, hardly considered in the current nonlocal literature, we establish a well-posedness result for the system (global in time existence, uniqueness and continuous dependence on the initial datum) through the interplay of nonlocal and local techniques.

Requiring the kernel to be merely smooth and compactly supported, a variety of non trivial travelling wave solutions to the mixed nonlocal-local problem above are shown to exist provided that the local component of the solution is positive almost everywhere. Moreover, we provide a characterization of the travelling wave profiles and of their stability properties. These theoretical findings are supported by numerical simulations that illustrate the qualitative behavior of the system and highlight new open questions in the field.

The work is a joint collaboration with Rinaldo M. Colombo (University of Brescia) and Mauro Garavello (University of Milano-Bicocca).