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Tordeux, Antoine

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Schadschneider, Andreas - 76 publications, 11 shared
Chraibi, Mohcine - 44 publications, 12 shared
Seyfried, Armin - 250 publications, 19 shared
Herty, Michael - 4 publications, 1 shared
Costeseque, Guillaume - 1 publications, 1 shared
Zhang, Jinfen - 131 publications, 4 shared
Boltes, Maik - 51 publications, 3 shared
Jun, Zhang - 2 publications, 1 shared
Wang, Jiayue - 2 publications, 1 shared
Ziemer, Verena - 3 publications, 1 shared
Weng, Wenguo - 2 publications, 1 shared
Zhao, Ying - 9 publications, 2 shared
Drzycimski, Kevin - 1 publications, 1 shared
Liao, Weichen - 6 publications, 3 shared
Zheng, Xiaoping - 7 publications, 3 shared
Holl, Stefan - 17 publications, 1 shared
Lang, Ulrich - 1 publications, 1 shared
Steffen, Bernhard - 39 publications, 1 shared
Zhao, Yin - 1 publications, 1 shared
Ezaki, Takahiro - 4 publications, 1 shared
Nishinari, Katsuhiro - 4 publications, 1 shared
Roussignol, Michel - 5 publications, 5 shared
Monneau, Regis - 3 publications, 3 shared
Lassarre, Sylvain - 13 publications, 2 shared
Period of publication
2019
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2010

article

From Traffic and Pedestrian Follow-the-Leader Models with Reaction Time to First Order Convection-Diffusion Flow Models

  • Tordeux, Antoine
  • Seyfried, Armin
  • Herty, Michael
  • Costeseque, Guillaume
Abstract

In this work, we derive first order continuum traffic flow models from a microscopic delayed follow-the-leader model. These are applicable in the context of vehicular traffic flow as well as pedestrian traffic flow. The microscopic model is based on an optimal velocity function and a reaction time parameter. The corresponding macroscopic formulations in Eulerian or Lagrangian coordinates result in first order convection-diffusion equations. More precisely, the convection is described by the optimal velocity while the diffusion term depends on the reaction time. A linear stability analysis for homogeneous solutions of both continuous and discrete models is provided. The conditions match those of the car-following model for specific values of the space discretization. The behavior of the novel model is illustrated thanks to numerical simulations. Transitions to collision-free self-sustained stop-and-go dynamics are obtained if the reaction time is sufficiently large. The results show that the dynamics of the microscopic model can be well captured by the macroscopic equations. For nonzero reaction times we observe a scattered fundamental diagram. The scattering width is compared to real pedestrian and road traffic data.

Topics
  • crash
  • automobile
  • data
  • road
  • behavior
  • highway traffic
  • highway transportation
  • simulation
  • velocity
  • stability analysis
  • pedestrian
  • traffic flow
  • pedestrian traffic
  • reaction time
  • traffic data
  • scattering