IDEAS home Printed from https://ideas.repec.org/a/wly/jnlamp/v2016y2016i1n6902086.html

Comparing First‐Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive Agents

Author

Listed:
  • Alessandro Corbetta
  • Andrea Tosin

Abstract

A comparison between first‐order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number N of pedestrians. The novelty is the fact of considering massive agents, namely, particles whose individual mass does not become infinitesimal when N grows. This implies that the total mass of the system is not constant but grows with N. The main result is that the two types of models approach one another in the limit N → ∞, provided the strength and/or the domain of pedestrian interactions are properly modulated by N at either scale. This is consistent with the idea that pedestrians may adapt their interpersonal attitudes according to the overall level of congestion.

Suggested Citation

  • Alessandro Corbetta & Andrea Tosin, 2016. "Comparing First‐Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive Agents," Advances in Mathematical Physics, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnlamp:v:2016:y:2016:i:1:n:6902086
    DOI: 10.1155/2016/6902086
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2016/6902086
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2016/6902086?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Francesco Zanlungo & Tetsushi Ikeda & Takayuki Kanda, 2012. "A Microscopic “Social Norm” Model to Obtain Realistic Macroscopic Velocity and Density Pedestrian Distributions," PLOS ONE, Public Library of Science, vol. 7(12), pages 1-10, December.
    2. Anders Johansson & Dirk Helbing & Pradyumn K. Shukla, 2007. "Specification Of The Social Force Pedestrian Model By Evolutionary Adjustment To Video Tracking Data," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 10(supp0), pages 271-288.
    3. Hughes, Roger L., 2002. "A continuum theory for the flow of pedestrians," Transportation Research Part B: Methodological, Elsevier, vol. 36(6), pages 507-535, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ziyou Gao & Yunchao Qu & Xingang Li & Jiancheng Long & Hai-Jun Huang, 2014. "Simulating the Dynamic Escape Process in Large Public Places," Operations Research, INFORMS, vol. 62(6), pages 1344-1357, December.
    2. 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.
    3. Sun, Yi, 2018. "Kinetic Monte Carlo simulations of two-dimensional pedestrian flow models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 836-847.
    4. Xu, Qiancheng & Chraibi, Mohcine & Tordeux, Antoine & Zhang, Jun, 2019. "Generalized collision-free velocity model for pedestrian dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    5. Zhang, Hui & Xu, Jie & Jia, Limin & Shi, Yihan, 2021. "Research on walking efficiency of passengers around corner of subway station," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    6. Tanimoto, Jun & Hagishima, Aya & Tanaka, Yasukaka, 2010. "Study of bottleneck effect at an emergency evacuation exit using cellular automata model, mean field approximation analysis, and game theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5611-5618.
    7. Krbálek, Milan & Hrabák, Pavel & Bukáček, Marek, 2018. "Pedestrian headways — Reflection of territorial social forces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 38-49.
    8. Huang, Zhongyi & Chraibi, Mohcine & Cao, Shuchao & Huang, Chuanli & Fang, Zhiming & Song, Weiguo, 2019. "A microscopic method for the evaluating of continuous pedestrian dynamic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    9. Makmul, J., 2024. "A hierarchy of the optimal velocity model with optimal path for pedestrian evacuation: From microscopic to macroscopic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).
    10. Giovanni Musolino & Reza Ahmadian & Junqiang Xia, 2022. "Enhancing pedestrian evacuation routes during flood events," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 112(3), pages 1941-1965, July.
    11. Saberi, Meead & Aghabayk, Kayvan & Sobhani, Amir, 2015. "Spatial fluctuations of pedestrian velocities in bidirectional streams: Exploring the effects of self-organization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 120-128.
    12. Wang, Jiayue & Boltes, Maik & Seyfried, Armin & Zhang, Jun & Ziemer, Verena & Weng, Wenguo, 2018. "Linking pedestrian flow characteristics with stepping locomotion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 106-120.
    13. Ma, Liang & Chen, Bin & Wang, Xiaodong & Zhu, Zhengqiu & Wang, Rongxiao & Qiu, Xiaogang, 2019. "The analysis on the desired speed in social force model using a data driven approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 894-911.
    14. Hu, Xiangmin & Chen, Tao & Deng, Kaifeng & Wang, Guanning, 2023. "Effects of aggressiveness on pedestrian room evacuation using extended cellular automata model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    15. Qingyan Ning & Maosheng Li, 2022. "Modeling Pedestrian Detour Behavior By-Passing Conflict Areas," Sustainability, MDPI, vol. 14(24), pages 1-17, December.
    16. Zhao, Dongyue & Hu, Haixing & Tong, Yunhe & Ren, Shihua & Zhao, Xiaolong & Qi, Qi, 2026. "Information-driven behavioural dynamics in indoor gas-leak evacuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 688(C).
    17. Wang, Shuaian & Zhang, Wei & Qu, Xiaobo, 2018. "Trial-and-error train fare design scheme for addressing boarding/alighting congestion at CBD stations," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 318-335.
    18. Lili Lu, A. & Gang Ren, B. & Wei Wang, C. & Ching-Yao Chan, D., 2015. "Application of SFCA pedestrian simulation model to the signalized crosswalk width design," Transportation Research Part A: Policy and Practice, Elsevier, vol. 80(C), pages 76-89.
    19. Haghani, Milad & Sarvi, Majid & Shahhoseini, Zahra, 2019. "When ‘push’ does not come to ‘shove’: Revisiting ‘faster is slower’ in collective egress of human crowds," Transportation Research Part A: Policy and Practice, Elsevier, vol. 122(C), pages 51-69.
    20. Zheng, Xiaoping & Li, Wei & Guan, Chao, 2010. "Simulation of evacuation processes in a square with a partition wall using a cellular automaton model for pedestrian dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(11), pages 2177-2188.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlamp:v:2016:y:2016:i:1:n:6902086. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/3197 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.