The KdV-Burgers equation in a modified speed gradient continuum model

Based on the full velocity difference model, Jiang et al. put forward the speed gradient model through the micromacro linkage （Jiang R, Wu Q S and Zhu Z J 2001 Chin. Sci. Bull 46 345 and Jiang R, Wu Q S and Zhu Z J 2002 Trans. Res. B 36 405）. In this paper, the Taylor expansion is adopted to modify...

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Published inChinese physics B Vol. 22; no. 6; pp. 289 - 293
Main Author 赖玲玲 程荣军 李志鹏 葛红霞
Format Journal Article
LanguageEnglish
Published 01.06.2013
Subjects
Clusters
Continuums
Density
Fluctuation
Mathematical analysis
Mathematical models
Nonlinearity
Stability
Traffic flow
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ISSN1674-1056
2058-3834
1741-4199
DOI10.1088/1674-1056/22/6/060511

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Summary:Based on the full velocity difference model, Jiang et al. put forward the speed gradient model through the micromacro linkage （Jiang R, Wu Q S and Zhu Z J 2001 Chin. Sci. Bull 46 345 and Jiang R, Wu Q S and Zhu Z J 2002 Trans. Res. B 36 405）. In this paper, the Taylor expansion is adopted to modify the model. The backward travel problem is overcome by our model, which exists in many higher-order continuum models. The neutral stability condition of the model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the density fluctuation in traffic flow leads to a variety of density waves. Moreover, the Korteweg-de Vries-Burgers （KdV-Burgers） equation is derived to describe the traffic flow near the neutral stability line and the corresponding solution for traffic density wave is derived. The numerical simulation is carried out to investigate the local cluster effects. The results are consistent with the realistic traffic flow and also further verify the results of nonlinear analysis.
Bibliography:traffic flow, the speed gradient model, KdV-Burgers equation
Based on the full velocity difference model, Jiang et al. put forward the speed gradient model through the micromacro linkage （Jiang R, Wu Q S and Zhu Z J 2001 Chin. Sci. Bull 46 345 and Jiang R, Wu Q S and Zhu Z J 2002 Trans. Res. B 36 405）. In this paper, the Taylor expansion is adopted to modify the model. The backward travel problem is overcome by our model, which exists in many higher-order continuum models. The neutral stability condition of the model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the density fluctuation in traffic flow leads to a variety of density waves. Moreover, the Korteweg-de Vries-Burgers （KdV-Burgers） equation is derived to describe the traffic flow near the neutral stability line and the corresponding solution for traffic density wave is derived. The numerical simulation is carried out to investigate the local cluster effects. The results are consistent with the realistic traffic flow and also further verify the results of nonlinear analysis.
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ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/22/6/060511