CSCDR seminar: On the Mathematical Properties of Some Multi-Scale Traffic Models
On the Mathematical Properties of Some Multi-Scale Traffic Models
by Xiaoqian Gong (Amherst College)
Abstract: In this talk, we examine the mathematical properties of traffic flow models across microscopic, mesoscopic, and macroscopic scales. At the microscopic level, we analyze the well-posedness of the classical Bando Follow-the-Leader (Bando-FtL) model, as well as its time-delayed and nonlocal extensions. As an application of the microscopic car-following models, we also discuss optimal cruise control strategies for traffic smoothing. From a mesoscopic viewpoint, we rigorously derive the mean-field limit of a finite-dimensional hybrid system that captures multi-lane, multi-class traffic dynamics involving both human-driven and autonomous vehicles. At the macroscopic scale, we briefly address the well-posedness of a nonlocal GARZ model. Numerical simulations and field experiment results will also be presented.