TDGL and mKdV equations for car-following model considering traffic jerk and velocity difference

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• 作者：Han Song ; Hongxia Ge ; Fuzhou Chen ; Rongjun Cheng
• 关键词：Traffic flow ; Traffic jerk ; TDGL equation ; mKdV equation
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：87
• 期：3
• 页码：1809-1817
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

By introducing optimal velocity car-following model by Bando et al., we present an improved car-following model which is based on an optimal velocity model considering traffic jerk and full velocity difference. The nature of the model is researched by using linear and nonlinear analysis method. The analytical method and numerical simulation results show that the proposed model can describe the phase transition and critical phenomenon with the thermodynamic theory. In order to describe the traffic flow near the critical point, the time-dependent Ginzburg–Landau (TDGL) equation and the modified Korteweg–de Vries (mKdV) equation are derived. Additionally, the connection between the TDGL and the mKdV equation is also given. Theoretical analysis is demonstrated by numerical simulation.