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.

On the micro-macro limit in traffic flow / Colombo, R; Rossi, Elena. - In: RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA. - ISSN 0041-8994. - 131:(2014), pp. 217-235. [10.4171/RSMUP/131-13]

On the micro-macro limit in traffic flow

ROSSI, ELENA
2014

Abstract

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.
2014
131
217
235
On the micro-macro limit in traffic flow / Colombo, R; Rossi, Elena. - In: RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA. - ISSN 0041-8994. - 131:(2014), pp. 217-235. [10.4171/RSMUP/131-13]
Colombo, R; Rossi, Elena
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1226943
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