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From heterogeneous microscopic traffic flow models to macroscopic models

Cardaliaguet, Pierre; Forcadel, Nicolas (2021), From heterogeneous microscopic traffic flow models to macroscopic models, SIAM Journal on Mathematical Analysis, 53, 1, p. 309-322. 10.1137/20M1314410

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Type
Article accepté pour publication ou publié
Date
2021
Journal name
SIAM Journal on Mathematical Analysis
Volume
53
Number
1
Publisher
SIAM - Society for Industrial and Applied Mathematics
Pages
309-322
Publication identifier
Metadata
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Author(s)
Cardaliaguet, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Forcadel, Nicolas cc
Laboratoire de Mathématiques de l'INSA de Rouen Normandie [LMI]
Abstract (EN)
The goal of this paper is to derive rigorously macroscopic traffic flow models from microscopic models. More precisely, for the microscopic models, we consider follow-the-leader type models with different types of drivers and vehicles which are distributed randomly on the road. After a rescaling, we show that the cumulative distribution function converge to the solution of a macroscopic model. We also make the link between this macroscopic model and the so-called LWR model.
Subjects / Keywords
traffic flow; heterogeneous microscopic models; macroscopic models; stochastic homogenisation