Rendiconti del Seminario Matematico della Università di Padova

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Volume 131, 2014, pp. 217–235
DOI: 10.4171/RSMUP/131-13

On the micro-macro limit in traffic flow

Rinaldo M. Colombo[1] and E. Rossi[2]

(1) Università degli Studi di Brescia, Italy
(2) Università di Milano-Bicocca, Italy

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 $+ \infty$ 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.

Keywords: Macroscopic traffic models, microscopic traffic models, conservation laws

Colombo Rinaldo, Rossi E.: On the micro-macro limit in traffic flow. Rend. Sem. Mat. Univ. Padova 131 (2014), 217-235. doi: 10.4171/RSMUP/131-13