From kinetic to macroscopic models and back

arXiv (Cornell University)

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.

Authors 3

1. M. Herty Aachen Institute für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institute für Geometrie und Praktische Mathematik - RWTH Aachen University -Templergraben 55 , 52062 Aachen , Germany -

2. G. Puppo

   Sapienza University of Rome

   Affiliation as printed

   Dipartimento di Matematica -"La Sapienza " Università di Roma - Piazza Aldo Moro 5 , 00185 Roma , Italy -

3. Giuseppe Visconti Aachen Institute für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institute für Geometrie und Praktische Mathematik - RWTH Aachen University -Templergraben 55 , 52062 Aachen , Germany -