Euler and Lagrange Representation of Traffic Models

  • K. Nishinari
Conference paper


The relations among different traffic models are studied by using the ultra-discrete method and the Euler-Lagrange transformation. It is found that the Burgers CA(BCA) in the Euler form can be transformed into the Lagrange form by using the formulae of the max-algebra. It is also shown that the Lagrange model is related to the optimal velocity model, the slow-to-start model and the Nagel-Schreckenberg model. Moreover, a new hybrid Lagrange model is proposed by extending the BCA, which shows a complex phase transition from free to a jamming state.


Traffic Flow Lagrange Form Traffic Model Lagrange Model Euler Form 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • K. Nishinari
    • 1
  1. 1.Department of Applied Mathematics and InformaticsRyukoku UniversitySeta, OhtsuJapan

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