We investigate the relations between a macroscopic Lighthill-Whitham and Richards model and a microscopic follow-the-leader model for traffic flow. Solutions to the microscopic model are proved to tend to those to the macroscopic one in a sort of kinetic limit, i.e. as the number of individuals tends to while their total mass is constant. Based on this convergence result, we approximately compute the solutions to a conservation law by means of the integration of an ordinary differential system.
Cite this article
Rinaldo M. Colombo, E. Rossi, On the micro-macro limit in traffic flow. Rend. Sem. Mat. Univ. Padova 131 (2014), pp. 217–235DOI 10.4171/RSMUP/131-13