Nonlinear analysis of an improved continuum model considering mean-field velocity difference |
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Authors: | Zihao Wang Rongjun Cheng Hongxia Ge |
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Affiliation: | 1. Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China;2. Jiangsu Province Collaborative Innovation Center for Modern Urban Traffic Technologies, Nanjing 210096, China;3. National Traffic Management Engineering and Technology Research Centre Ningbo University Sub-centre, Ningbo 315211, China |
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Abstract: | Based on the velocity gradient model, an extended continuum model with consideration of the mean-field velocity difference is proposed in this paper. By using the linear stability theory, the linear stability criterion of the new model is gained, which proved that mean-field velocity difference has significant influence on stability of traffic flow. The KdV–Burgers equation is derived by using non-linear analysis method and the evolution of density wave near the neutral stability line is explored. Numerical simulations are carried out how mean-field velocity difference affect the stability of traffic flow, and energy consumption is also studied for this new macro model. At the same time, complicated traffic phenomena such as local cluster effects, shock waves and rarefaction waves can be reproduced in the new model by numerical simulation. Numerical results are consistent with the theoretical analysis, which indicates that the mean-field velocity difference not only suppresses traffic jam, but also depresses energy consumption. |
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Keywords: | Traffic flow KdV equation Mean-field velocity difference FVD model |
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