中国物理B ›› 2008, Vol. 17 ›› Issue (2): 473-478.doi: 10.1088/1674-1056/17/2/022

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An extended master-equation approach applied to aggregation in freeway traffic

黄永畅1, 李俊卫2, 林柏梁2   

  1. (1)Institute of Theoretical Physics, College of Applied Sciences, Beijing University of Technology, Beijing, 100022, China; (2)State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, 100044, China
  • 收稿日期:2007-04-18 修回日期:2007-08-25 出版日期:2008-02-20 发布日期:2008-02-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10435080 and 60674011), exoteric project Foundation of State Key Laboratory of Rail Traffic Control and Safety (Beijing Jiaotong University).

An extended master-equation approach applied to aggregation in freeway traffic

Li Jun-Wei(李俊卫)a), Lin Bo-Liang(林柏梁)a), and Huang Yong-Chang(黄永畅)b)   

  1. a State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China; b Institute of Theoretical Physics, College of Applied Sciences, Beijing University of Technology, Beijing 100022, China
  • Received:2007-04-18 Revised:2007-08-25 Online:2008-02-20 Published:2008-02-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10435080 and 60674011), exoteric project Foundation of State Key Laboratory of Rail Traffic Control and Safety (Beijing Jiaotong University).

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摘要： We restudy the master-equation approach applied to aggregation in a one-dimensional freeway, where the decay transition probabilities for the jump processes are reconstructed based on a car-following model. According to the reconstructed transition probabilities, the clustering behaviours and the stochastic properties of the master equation in a one-lane freeway traffic model are investigated in detail. The numerical results show that the size of the clusters initially below the critical size of the unstable cluster and initially above that of the unstable cluster all enter the same stable state, which also accords with the nucleation theory and is known from the result in earlier work. Moreover, we have obtained more reasonable parameters of the master equation based on some results of cellular automata models.

关键词: master equation, traffic jam, nucleation theory

Abstract: We restudy the master-equation approach applied to aggregation in a one-dimensional freeway, where the decay transition probabilities for the jump processes are reconstructed based on a car-following model. According to the reconstructed transition probabilities, the clustering behaviours and the stochastic properties of the master equation in a one-lane freeway traffic model are investigated in detail. The numerical results show that the size of the clusters initially below the critical size of the unstable cluster and initially above that of the unstable cluster all enter the same stable state, which also accords with the nucleation theory and is known from the result in earlier work. Moreover, we have obtained more reasonable parameters of the master equation based on some results of cellular automata models.

Key words: master equation, traffic jam, nucleation theory

中图分类号:  (Land transportation)

  • 89.40.Bb
45.70.Vn (Granular models of complex systems; traffic flow) 05.40.Fb (Random walks and Levy flights) 05.50.+q (Lattice theory and statistics)