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Application of singular perturbation method in analyzing traffic density waves

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Journal of Shanghai University (English Edition)

Abstract

Car following model is one of microscopic models for describing traffic flow. Through linear stability analysis, the neutral stability lines and the critical points are obtained for the different types of car following models and two modified models. The singular perturbation method has been used to derive various nonlinear wave equations, such as the Korteweg-de-Vries (KdV) equation and the modified Korteweg-de-Vries (mKdV) equation, which could describe different density waves occurring in traffic flows under certain conditions. These density waves are mainly employed to depict the formation of traffic jams in the congested traffic flow. The general soliton solutions are given for the different types of car following models, and the results have been used to the modified models efficiently.

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Authors and Affiliations

  1. Faculty of Science, Ningbo University, Ningbo, 315211, Zhejiang, P. R. China

    Fei-ying Shen  (沈飞英) & Hong-xia Ge  (葛红霞)

  2. School of Energy and Power Engineering, Shandong University, Jinan, 250061, P. R. China

    Li Lei  (雷 丽)

Authors
  1. Fei-ying Shen  (沈飞英)
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  2. Hong-xia Ge  (葛红霞)
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  3. Li Lei  (雷 丽)
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Corresponding author

Correspondence to Hong-xia Ge  (葛红霞).

Additional information

(Communicated by NI Ming-kang)

Project supported by the National Basic Research Program of China (Grant No.2006CB705500), the National Natural Science Foundation of China (Grant Nos.10532060, 10602025, 10802042), and the Natural Science Foundation of Ningbo (Grant No.2007A610050)

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Shen, Fy., Ge, Hx. & Lei, L. Application of singular perturbation method in analyzing traffic density waves. J. Shanghai Univ.(Engl. Ed.) 13, 6–11 (2009). https://doi.org/10.1007/s11741-009-0102-3

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  • DOI: https://doi.org/10.1007/s11741-009-0102-3

Keywords

2000 Mathematics Subject Classification

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