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)
aState Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China; bInstitute of Theoretical Physics, College of Applied Sciences, Beijing University of Technology, Beijing 100022, China
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.
Received: 18 April 2007
Revised: 25 August 2007
Accepted manuscript online:
Fund: 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).
Cite this article:
Li Jun-Wei(李俊卫), Lin Bo-Liang(林柏梁), and Huang Yong-Chang(黄永畅) An extended master-equation approach applied to aggregation in freeway traffic 2008 Chin. Phys. B 17 473
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