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Asymptotic solutions for a multi-anticipative car-following model

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  • Wagner, Christoph

Abstract

Using a long wave expansion we study the asymptotic solutions near a critical point of a multi-anticipative car-following model. A suitable rescaling of the variables then yields a modified Korteweg–de Vries (MKdV) equation with higher order corrections. An equation of this general form has already been investigated in detail in case of a simple model which allows us to use these results. We are thus led to the conclusion that the characteristic features of the multi-interaction model in the congested state can be obtained from the simple model by appropriately scaling the results.

Suggested Citation

  • Wagner, Christoph, 1998. "Asymptotic solutions for a multi-anticipative car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 260(1), pages 218-224.
    • Handle: RePEc:eee:phsmap:v:260:y:1998:i:1:p:218-224
    DOI: 10.1016/S0378-4371(98)00306-9
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    Cited by:

    1. Sun, Lu & Jafaripournimchahi, Ammar & Hu, Wusheng, 2020. "A forward-looking anticipative viscous high-order continuum model considering two leading vehicles for traffic flow through wireless V2X communication in autonomous and connected vehicle environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    2. Yeo, Hwasoo, 2008. "Asymmetric Microscopic Driving Behavior Theory," University of California Transportation Center, Working Papers qt1tn1m968, University of California Transportation Center.
    3. Li, Yongfu & Zhao, Hang & Zhang, Li & Zhang, Chao, 2018. "An extended car-following model incorporating the effects of lateral gap and gradient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 177-189.
    4. Helbing, Dirk & Batic, Davide & Schönhof, Martin & Treiber, Martin, 2002. "Modelling widely scattered states in ‘synchronized’ traffic flow and possible relevance for stock market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 303(1), pages 251-260.
    5. Ngoduy, D. & Hoogendoorn, S.P. & Liu, R., 2009. "Continuum modeling of cooperative traffic flow dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(13), pages 2705-2716.

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