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.

Colombo, R., Rossi, E. (2014). On the micro-macro limit in traffic flow. RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA, 131, 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.
Articolo in rivista - Articolo scientifico
Conservation laws; Macroscopic traffic models; Microscopic traffic models
English
2014
131
217
235
none
Colombo, R., Rossi, E. (2014). On the micro-macro limit in traffic flow. RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA, 131, 217-235 [10.4171/RSMUP/131-13].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/77526
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