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Scaling of pedestrian channel flow with a bottleneck

Author

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  • Tajima, Yusuke
  • Takimoto, Kouhei
  • Nagatani, Takashi

Abstract

Pedestrian channel flow at a bottleneck is investigated under the open boundaries by using the lattice-gas model of biased random walkers. It is shown that a dynamical phase transition occurs from the free flow to the choking flow at a critical density pc with increasing density. The flow rate saturates at higher density than the critical density. In the choking-flow region, a scaling behavior is found as follows: the saturated flow rate Js scales as Js∝d0.93±0.02 and the critical density pc scales as pc∝(d/W)1.16±0.02, where d is the width of the bottleneck and W is the width of channel. The plot of the rescaled flow rate against the rescaled density collapses onto a single curve.

Suggested Citation

  • Tajima, Yusuke & Takimoto, Kouhei & Nagatani, Takashi, 2001. "Scaling of pedestrian channel flow with a bottleneck," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 294(1), pages 257-268.
    • Handle: RePEc:eee:phsmap:v:294:y:2001:i:1:p:257-268
    DOI: 10.1016/S0378-4371(01)00109-1
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    Citations

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    Cited by:

    1. Hänseler, Flurin S. & Bierlaire, Michel & Farooq, Bilal & Mühlematter, Thomas, 2014. "A macroscopic loading model for time-varying pedestrian flows in public walking areas," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 60-80.
    2. Li, Maoyu & Zhou, Zhizuan & Zhou, Xiaodong & Zhang, Ping & Cheng, Han & Jiang, Jiajia & Jiang, Nan & Yang, Lizhong, 2022. "How bottleneck width and restricted walking height affect pedestrian motion: Experimental analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    3. 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.
    4. Varas, A. & Cornejo, M.D. & Mainemer, D. & Toledo, B. & Rogan, J. & Muñoz, V. & Valdivia, J.A., 2007. "Cellular automaton model for evacuation process with obstacles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 631-642.
    5. Li, Na & Guo, Ren-Yong, 2020. "Simulation of bi-directional pedestrian flow through a bottleneck: Cell transmission model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    6. Song, Weiguo & Xu, Xuan & Wang, Bing-Hong & Ni, Shunjiang, 2006. "Simulation of evacuation processes using a multi-grid model for pedestrian dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 492-500.
    7. Rastogi, R. & Ilango, T. & Chandra, S., 2013. "Pedestrian flow characteristics for different pedestrian facilities and situations," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 53, pages 1-5.
    8. 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).
    9. Guo, Xiwei & Chen, Jianqiao & You, Suozhu & Wei, Junhong, 2013. "Modeling of pedestrian evacuation under fire emergency based on an extended heterogeneous lattice gas model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 1994-2006.
    10. Xie, Qimiao & Wu, Yaxin & Wang, Yitian & Zhang, Hui, 2024. "A multi-grid evacuation model considering the effects of different turning types," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 635(C).
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Zhang, Xinwei & Zhang, Peihong & Zhong, Maohua, 2021. "A dual adaptive cellular automaton model based on a composite field and pedestrian heterogeneity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    16. Zheng, Ying & Jia, Bin & Li, Xin-Gang & Zhu, Nuo, 2011. "Evacuation dynamics with fire spreading based on cellular automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(18), pages 3147-3156.

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