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.
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