Euler and Lagrange Representation of Traffic Models

  • K. Nishinari
Conference paper

Abstract

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.

Keywords

Transportation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K. Nishinari and D. Takahashi, J. Phys. A 31, 5439 (1998).MATHCrossRefGoogle Scholar
  2. 2.
    T. Musya and H. Higuchi, J. Phys. Soc. Jpn. 17, 811 (1978).CrossRefGoogle Scholar
  3. 3.
    T. Tokihiro, D. Takahashi, J. Matsukidaira, and J. Satsuma, Phys. Rev. Lett. 76, 3247 (1996).CrossRefGoogle Scholar
  4. 4.
    K. Nishinari and D. Takahashi, J. Phys. A 32, 93 (1999).MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    K. Nishinari and D. Takahashi, J. Phys. A 33, 7709 (2000).MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    K. Nishinari, J. Phys. A to appear.Google Scholar
  7. 7.
    M. Fukui and Y. Ishibashi, J. Phys. Soc. Jpn. 65, 1868 (1996).CrossRefGoogle Scholar
  8. 8.
    M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, Phys. Rev. E. 51, 1035 (1995).CrossRefGoogle Scholar
  9. 9.
    K. Nakanishi, K. Itoh, Y. Igarashi, and M. Bando, Phys. Rev. E 55, 6519 (1997).CrossRefGoogle Scholar
  10. 10.
    M. Takayasu and H. Takayasu, Fractals 1, 860 (1993).MATHCrossRefGoogle Scholar
  11. 11.
    K. Nagel and M. Schreckenberg, J. Phys. I France 2, 2221 (1992).CrossRefGoogle Scholar
  12. 12.
    A. Schadschneider and M. Schreckenberg, Ann. Phys. 6, 541 (1997).MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    K. Nishinari and M. Hayashi (editors), Traffic Statistics in Tomei Express Way, (The Mathematical Society of Traffic Flow, Japan, 1999 ).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

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

Personalised recommendations