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The flow of large crowds of pedestrians

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  • Hughes, R.L.

Abstract

Despite popular belief the motion of a crowd is governed by well-defined rules of behaviour. These rules imply a set of coupled, non-linear, partial differential equations for the density and velocity potential for each type of pedestrian in the crowd. As may be expected, the solution of these equations may, in different regions of space, be supercritical or subcritical with the possibility of a shock wave separating the regions. Less predictable is the remarkable finding that these coupled, non-linear, time dependent equations are conformally mappable and this finding enables solutions to be obtained easily for both supercritical and subcritical flows.

Suggested Citation

  • Hughes, R.L., 2000. "The flow of large crowds of pedestrians," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(4), pages 367-370.
    • Handle: RePEc:eee:matcom:v:53:y:2000:i:4:p:367-370
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    Cited by:

    1. Li, Xiao-Yang & Lin, Zhi-Yang & Zhang, Peng & Zhang, Xiao-Ning, 2023. "Reconstruction of density and cost potential field of Eikonal equation: Applications to discrete pedestrian flow models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).
    2. Xiaohong Li & Jianan Zhou & Feng Chen & Zan Zhang, 2018. "Cluster Risk of Walking Scenarios Based on Macroscopic Flow Model and Crowding Force Analysis," Sustainability, MDPI, vol. 10(2), pages 1-16, February.
    3. Fu, Zhijian & Zhou, Xiaodong & Zhu, Kongjin & Chen, Yanqiu & Zhuang, Yifan & Hu, Yuqi & Yang, Lizhong & Chen, Changkun & Li, Jian, 2015. "A floor field cellular automaton for crowd evacuation considering different walking abilities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 294-303.
    4. Subaih, Rudina & Tordeux, Antoine, 2024. "Modeling pedestrian single-file movement: Extending the interaction to the follower," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    5. He, Mengchen & Wang, Qiao & Chen, Juan & Xu, Shiwei & Ma, Jian, 2023. "Modeling pedestrian walking behavior in the flow field with moving walkways," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    6. Fu, Zhijian & Luo, Lin & Yang, Yue & Zhuang, Yifan & Zhang, Peitong & Yang, Lizhong & Yang, Hongtai & Ma, Jian & Zhu, Kongjin & Li, Yanlai, 2016. "Effect of speed matching on fundamental diagram of pedestrian flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 31-42.
    7. Lee, Ris S.C. & Hughes, Roger L., 2007. "Minimisation of the risk of trampling in a crowd," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(1), pages 29-37.
    8. Shi, Yihan & Xu, Jie & Zhang, Hui & Jia, Limin & Qin, Yong, 2022. "Walking model on passenger in merging passage of subway station considering overtaking behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    9. Milad Haghani & Majid Sarvi & Zahra Shahhoseini & Maik Boltes, 2016. "How Simple Hypothetical-Choice Experiments Can Be Utilized to Learn Humans’ Navigational Escape Decisions in Emergencies," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-24, November.
    10. Li-ya Yao & Li-shan Sun & Wu-hong Wang & Hui Xiong, 2012. "Concept Layout Model of Transportation Terminals," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-8, December.
    11. 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).
    12. Fu, Zhijian & Yang, Lizhong & Chen, Yanqiu & Zhu, Kongjin & Zhu, Shi, 2013. "The effect of individual tendency on crowd evacuation efficiency under inhomogeneous exit attraction using a static field modified FFCA model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 6090-6099.
    13. Zhang, J. & Seyfried, A., 2014. "Comparison of intersecting pedestrian flows based on experiments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 316-325.
    14. Reppas, Andreas I. & Spiliotis, Konstantinos & Siettos, Constantinos I., 2015. "Tuning the average path length of complex networks and its influence to the emergent dynamics of the majority-rule model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 186-196.
    15. Abdelghany, Ahmed & Abdelghany, Khaled & Mahmassani, Hani, 2016. "A hybrid simulation-assignment modeling framework for crowd dynamics in large-scale pedestrian facilities," Transportation Research Part A: Policy and Practice, Elsevier, vol. 86(C), pages 159-176.
    16. Adriano Festa & Paola Goatin & Fabio Vicini, 2023. "Navigation System-Based Routing Strategies in Traffic Flows on Networks," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 930-957, September.
    17. Hongjia Zhang & Yingshi Guo & Yunxing Chen & Qinyu Sun & Chang Wang, 2020. "Analysis of Pedestrian Street-Crossing Decision-Making Based on Vehicle Deceleration-Safety Gap," IJERPH, MDPI, vol. 17(24), pages 1-13, December.
    18. Srinivasan, Aravinda Ramakrishnan & Karan, Farshad Salimi Naneh & Chakraborty, Subhadeep, 2017. "Pedestrian dynamics with explicit sharing of exit choice during egress through a long corridor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 770-782.
    19. Zhang, Yijing & Lu, Linjun & Liu, Qiujia & Hu, Miaoqing, 2023. "Modeling of low-risk behavior of pedestrian movement based on dynamic data analysis," Transportation Research Part A: Policy and Practice, Elsevier, vol. 168(C).
    20. Jinghong Wang & Siuming Lo & Qingsong Wang & Jinhua Sun & Honglin Mu, 2013. "Risk of Large‐Scale Evacuation Based on the Effectiveness of Rescue Strategies Under Different Crowd Densities," Risk Analysis, John Wiley & Sons, vol. 33(8), pages 1553-1563, August.

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