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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K. Nishinari and D. Takahashi, J. Phys. A 31, 5439 (1998).
T. Musya and H. Higuchi, J. Phys. Soc. Jpn. 17, 811 (1978).
T. Tokihiro, D. Takahashi, J. Matsukidaira, and J. Satsuma, Phys. Rev. Lett. 76, 3247 (1996).
K. Nishinari and D. Takahashi, J. Phys. A 32, 93 (1999).
K. Nishinari and D. Takahashi, J. Phys. A 33, 7709 (2000).
K. Nishinari, J. Phys. A to appear.
M. Fukui and Y. Ishibashi, J. Phys. Soc. Jpn. 65, 1868 (1996).
M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, Phys. Rev. E. 51, 1035 (1995).
K. Nakanishi, K. Itoh, Y. Igarashi, and M. Bando, Phys. Rev. E 55, 6519 (1997).
M. Takayasu and H. Takayasu, Fractals 1, 860 (1993).
K. Nagel and M. Schreckenberg, J. Phys. I France 2, 2221 (1992).
A. Schadschneider and M. Schreckenberg, Ann. Phys. 6, 541 (1997).
K. Nishinari and M. Hayashi (editors), Traffic Statistics in Tomei Express Way, (The Mathematical Society of Traffic Flow, Japan, 1999 ).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nishinari, K. (2003). Euler and Lagrange Representation of Traffic Models. In: Fukui, M., Sugiyama, Y., Schreckenberg, M., Wolf, D.E. (eds) Traffic and Granular Flow’01. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10583-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-662-10583-2_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07304-5
Online ISBN: 978-3-662-10583-2
eBook Packages: Springer Book Archive