Abstract
We study kinetic models for traffic flow characterized by the property of producing backward propagating waves. These waves may be identified with the phenomenon of stop-and-go waves typically observed on highways. In particular, a refined modeling of the space of the microscopic speeds and of the interaction rate in the kinetic model allows to obtain weakly unstable backward propagating waves in dense traffic, without relying on non-local terms or multi–valued fundamental diagrams. A stability analysis of these waves is carried out using the Chapman-Enskog expansion. This leads to a BGK-type model derived as the mesoscopic limit of a Follow-The-Leader or Bando model, and its macroscopic limit belongs to the class of second-order Aw-Rascle and Zhang models.
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Acknowledgements
The research of M. Herty and G. Visconti is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2023 Internet of Production—390621612 as well as by DFG HE5386/13.
G. Puppo and G. Visconti acknowledge also support from GNCS (Gruppo Nazionale per il Calcolo Scientifico) of INdAM (Istituto Nazionale di Alta Matematica), Italy.
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Herty, M., Puppo, G., Visconti, G. (2021). From Kinetic to Macroscopic Models and Back. In: Puppo, G., Tosin, A. (eds) Mathematical Descriptions of Traffic Flow: Micro, Macro and Kinetic Models. SEMA SIMAI Springer Series(), vol 12. Springer, Cham. https://doi.org/10.1007/978-3-030-66560-9_2
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DOI: https://doi.org/10.1007/978-3-030-66560-9_2
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