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The “backward-looking” effect in the continuum model considering a new backward equilibrium velocity function

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Abstract

In this paper, a new continuum traffic model is developed considering the backward-looking effect through a new positive backward equilibrium speed function. As compared with the conventional full velocity difference model, the backward equilibrium velocity function, which is largely acceptably grounded from mathematical and physical perspectives, plays an important role in significantly enhancing the stability of the traffic flow field. A linear stability condition is derived to demonstrate the flow neutralization capacity of the model, whereas the Korteweg–de Vries–Burgers equation and the attendant analytical solution are deduced using nonlinear analysis to observe the traffic flow behavior near the neutral stability condition. A numerical simulation, used to determine the flow stability enhancement efficiency of the model, is also conducted to verify the theoretical results.

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Acknowledgements

This study was partially supported by the Grant-in-Aid for Scientific Research (KAKENHI) from JSPS (Grant No. JP 19KK0262, JP 20H02314, JP 20K21062) awarded to Professor Tanimoto.

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Authors and Affiliations

  1. Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka, 816-8580, Japan

    Md. Anowar Hossain & Jun Tanimoto

  2. Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka, 816-8580, Japan

    Jun Tanimoto

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  1. Md. Anowar Hossain
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Correspondence to Md. Anowar Hossain.

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Hossain, M.A., Tanimoto, J. The “backward-looking” effect in the continuum model considering a new backward equilibrium velocity function. Nonlinear Dyn 106, 2061–2072 (2021). https://doi.org/10.1007/s11071-021-06894-2

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