A General Microscopic Traffic Model Yielding Dissipative Shocks

  • Yuri Borissovich GaidideiEmail author
  • Jean-Guy Caputo
  • Peter Leth Christiansen
  • Jens Juul Rasmussen
  • Mads Peter Sørensen
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


We consider a general microscopic traffic model with a delay. An algebraic traffic function reduces the equation to the Aw-Rascle microscopic model while a sigmoid function gives the standard “follow the leader”. For zero delay we prove that the homogeneous solution is globally stable. For a positive delay, it becomes unstable and develops dispersive and dissipative shocks. These are followed by a finite time singularity for the algebraic traffic function and by kinks for the sigmoid function.



Yu.G. acknowledges a Guest Professorship funded by Civilingeniør Frederik Christiansens Almennyttige Fond and partial financial support from the National Academy of Sciences of Ukraine. He thanks the Department of Physics, Technical University of Denmark for its hospitality. J.G. C. received support from the Region of Normandy through the program Xterm.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Yuri Borissovich Gaididei
    • 1
    Email author
  • Jean-Guy Caputo
    • 2
  • Peter Leth Christiansen
    • 3
  • Jens Juul Rasmussen
    • 3
  • Mads Peter Sørensen
    • 4
  1. 1.Bogolyubov Institute for Theoretical PhysicsKievUkraine
  2. 2.Laboratoire de MathématiquesINSA de RouenSaint-Etienne du RouvrayFrance
  3. 3.Department of PhysicsTechnical University of DenmarkKongens LyngbyDenmark
  4. 4.Department of Applied Mathematics and Computer ScienceTechnical University of DenmarkKongens LyngbyDenmark

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