The theoretical analysis of the anticipation lattice models for traffic flow
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Based on the anticipation lattice hydrodynamic models, which are described by the partial differential equations, the continuum version of the model is investigated through a reductive perturbation method. The linear stability theory is used to discuss the stability of the continuum model. The Korteweg–de Vries (for short, KdV) equation near the neutral stability line and the modified Korteweg–de Vries (for short, mKdV) equation near the critical point are obtained by using the nonlinear analysis method. And the corresponding solutions for the traffic density waves are derived, respectively. The results display that the anticipation factor has an important influence on traffic flow. From the simulation, it is shown that the traffic jam is suppressed efficiently with taking into account the anticipation effect, and the analytical result is consonant with the simulation one.
KeywordsTraffic flow Lattice hydrodynamic model KdV equation mKdV equation
Project supported by the National Natural Science Foundation of China (Grant Nos. 11072117, 11372166 and 61074142), the Scientific Research Fund of Zhejiang Provincial, China (Grant No. LY13A010005), Disciplinary Project of Ningbo, China (Grant No. SZXL1067) and the K.C. Wong Magna Fund in Ningbo University, China.
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