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Dynamical transition and scaling in a mean-field model of pedestrian flow at a bottleneck

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  • Nagatani, Takashi

Abstract

A mean-field model is presented to mimic the pedestrian channel flow with a bottleneck. The pedestrian flow is described by the mean-field rate equation on the square lattice. The dynamical transition from the free flow to the choking flow is studied by carrying out a numerical simulation for the mean-field rate equation under open boundary conditions. The phase diagram is found numerically and analytically. The scaling behavior is investigated for the transition point and the saturated flow rate in the choking-flow region. It is shown that the transition point does not depend on the strength of drift. The transition point and saturated flow rate agree with those obtained by a one-dimensional approximation.

Suggested Citation

  • Nagatani, Takashi, 2001. "Dynamical transition and scaling in a mean-field model of pedestrian flow at a bottleneck," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(3), pages 558-566.
    • Handle: RePEc:eee:phsmap:v:300:y:2001:i:3:p:558-566
    DOI: 10.1016/S0378-4371(01)00366-1
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    Citations

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    Cited by:

    1. Cirillo, E.N.M. & Colangeli, M. & Muntean, A., 2017. "Trapping in bottlenecks: Interplay between microscopic dynamics and large scale effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 488(C), pages 30-38.
    2. Jie Xu & Yao Ning & Heng Wei & Wei Xie & Jianyuan Guo & Limin Jia & Yong Qin, 2015. "Route Choice in Subway Station during Morning Peak Hours: A Case of Guangzhou Subway," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-8, March.
    3. Wang, Li & Liu, Mao & Meng, Bo, 2013. "Incorporating topography in a cellular automata model to simulate residents evacuation in a mountain area in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(3), pages 520-528.
    4. Liu, Shaobo & Yang, Lizhong & Fang, Tingyong & Li, Jian, 2009. "Evacuation from a classroom considering the occupant density around exits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(9), pages 1921-1928.
    5. Haghani, Milad, 2021. "The knowledge domain of crowd dynamics: Anatomy of the field, pioneering studies, temporal trends, influential entities and outside-domain impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    6. Zhang, Jun & Song, Weiguo & Xu, Xuan, 2008. "Experiment and multi-grid modeling of evacuation from a classroom," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5901-5909.
    7. Tang, Tie-Qiao & Yang, Shao-Peng & Ou, Hui & Chen, Liang & Huang, Hai-Jun, 2018. "An aircraft boarding model accounting for group behavior," Journal of Air Transport Management, Elsevier, vol. 69(C), pages 182-189.
    8. Lei, Wenjun & Li, Angui & Gao, Ran & Zhou, Ning & Mei, Sen & Tian, Zhenguo, 2012. "Experimental study and numerical simulation of evacuation from a dormitory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5189-5196.

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