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A Compressible Fluid Model for Traffic Flow and Nonlinear Saturation of Perturbation Growth

  • Akiyasu Tomoeda
  • Daisuke Shamoto
  • Ryosuke Nishi
  • Kazumichi Ohtsuka
  • Katsuhiro Nishinari
Part of the Proceedings in Information and Communications Technology book series (PICT, volume 2)

Abstract

In this paper, we have proposed a new compressible fluid model for the one-dimensional traffic flow taking into account the reaction time of drivers, which is based on the actual measurements. This model is a generalization of Payne model by introducing a density-dependent function of reaction time. The linear stability analysis of this new model shows the instability of homogeneous flow around a critical density of vehicles. Moreover, the condition of the nonlinear saturation of density against small perturbation is derived from the analysis by using reduction perturbation method.

Keywords

Linear Stability Analysis Burger Equation Macroscopic Model Cellular Automaton Model Optimal Velocity 
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Copyright information

© Springer Tokyo 2010

Authors and Affiliations

  • Akiyasu Tomoeda
    • 1
    • 2
  • Daisuke Shamoto
    • 2
  • Ryosuke Nishi
    • 2
  • Kazumichi Ohtsuka
    • 2
  • Katsuhiro Nishinari
    • 2
    • 3
  1. 1.Meiji Institute for Advanced Study of Mathematical SciencesMeiji UniveristyJapan
  2. 2.Research Center for Advanced Science and TechnologyThe University of TokyoJapan
  3. 3.School of EngineeringUniversity of TokyoJapan

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