IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v499y2025ics0096300325001316.html
   My bibliography  Save this article

A macroscopic pedestrian model with variable maximal density

Author

Listed:
  • Bartoli, Laura
  • Cacace, Simone
  • Cristiani, Emiliano
  • Ferretti, Roberto

Abstract

In this paper we propose a novel macroscopic (fluid dynamics) model for describing pedestrian flow in low and high density regimes. The model is characterized by the fact that the maximal density reachable by the crowd – usually a fixed model parameter – is instead a state variable. To do that, the model couples a conservation law, devised as usual for tracking the evolution of the crowd density, with a Burgers-like PDE with a nonlocal term describing the evolution of the maximal density. The variable maximal density is used here to describe the effects of the psychological/physical pushing forces which are observed in crowds during competitive or emergency situations.

Suggested Citation

  • Bartoli, Laura & Cacace, Simone & Cristiani, Emiliano & Ferretti, Roberto, 2025. "A macroscopic pedestrian model with variable maximal density," Applied Mathematics and Computation, Elsevier, vol. 499(C).
    • Handle: RePEc:eee:apmaco:v:499:y:2025:i:c:s0096300325001316
    DOI: 10.1016/j.amc.2025.129404
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300325001316
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2025.129404?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
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    2. Dirk Helbing & Illés Farkas & Tamás Vicsek, 2000. "Simulating dynamical features of escape panic," Nature, Nature, vol. 407(6803), pages 487-490, September.
    3. von Sivers, Isabella & Köster, Gerta, 2015. "Dynamic stride length adaptation according to utility and personal space," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 104-117.
    4. Li, Yang & Chen, Maoyin & Dou, Zhan & Zheng, Xiaoping & Cheng, Yuan & Mebarki, Ahmed, 2019. "A review of cellular automata models for crowd evacuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    5. Cristiani, E. & Menci, M. & Malagnino, A. & Amaro, G.G., 2023. "An all-densities pedestrian simulator based on a dynamic evaluation of the interpersonal distances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    6. 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.
    7. Anders Johansson & Dirk Helbing & Habib Z. Al-Abideen & Salim Al-Bosta, 2008. "From Crowd Dynamics To Crowd Safety: A Video-Based Analysis," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 497-527.
    8. Xu Chen & Martin Treiber & Venkatesan Kanagaraj & Haiying Li, 2018. "Social force models for pedestrian traffic – state of the art," Transport Reviews, Taylor & Francis Journals, vol. 38(5), pages 625-653, September.
    9. Liang, Haoyang & Du, Jie & Wong, S.C., 2021. "A Continuum model for pedestrian flow with explicit consideration of crowd force and panic effects," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 100-117.
    10. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    11. Aghamohammadi, Rafegh & Laval, Jorge A., 2020. "Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models," Transportation Research Part B: Methodological, Elsevier, vol. 137(C), pages 99-118.
    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. Cristiani, E. & Menci, M. & Malagnino, A. & Amaro, G.G., 2023. "An all-densities pedestrian simulator based on a dynamic evaluation of the interpersonal distances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    2. 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).
    3. 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).
    4. Rangel-Galván, Maricruz & Ballinas-Hernández, Ana L. & Rangel-Galván, Violeta, 2024. "Thermo-inspired model of self-propelled hard disk agents for heterogeneous bidirectional pedestrian flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 635(C).
    5. 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.
    6. 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.
    7. 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).
    8. Jiang, Yan-Qun & Zhang, Wei & Zhou, Shu-Guang, 2016. "Comparison study of the reactive and predictive dynamic models for pedestrian flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 51-61.
    9. Li, Zhenning & Xu, Chengzhong & Bian, Zilin, 2022. "A force-driven model for passenger evacuation in bus fires," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    10. Jiang, Yan-Qun & Zhou, Shu-Guang & Duan, Ya-Li & Huang, Xiao-Qian, 2023. "A viscous continuum model with smoke effect for pedestrian evacuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).
    11. 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.
    12. Jiang, Yan-Qun & Hu, Ying-Gang & Huang, Xiaoqian, 2022. "Modeling pedestrian flow through a bottleneck based on a second-order continuum model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    13. Mullick, Pratik & Appert-Rolland, Cécile & Warren, William H. & Pettré, Julien, 2025. "Eliminating bias in pedestrian density estimation: A Voronoi cell perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 657(C).
    14. Liu, Yixue & Mao, Zhanli, 2022. "An experimental study on the critical state of herd behavior in decision-making of the crowd evacuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    15. Liang, Haoyang & Du, Jie & Wong, S.C., 2021. "A Continuum model for pedestrian flow with explicit consideration of crowd force and panic effects," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 100-117.
    16. He, Mengchen & Qiu, Yunfei & Ge, Xinru & Huang, Ran & Chen, Juan & Wang, Qiao & Lo, Jacquline & Ma, Jian, 2024. "Effect of moving walkway arrangement on unidirectional crowd flow characteristics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).
    17. Tumash, Liudmila & Canudas-de-Wit, Carlos & Delle Monache, Maria Laura, 2022. "Multi-directional continuous traffic model for large-scale urban networks," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 374-402.
    18. Femke van Wageningen-Kessels & Winnie Daamen & Serge P. Hoogendoorn, 2018. "Two-Dimensional Approximate Godunov Scheme and What It Means For Continuum Pedestrian Flow Models," Transportation Science, INFORMS, vol. 52(3), pages 547-563, June.
    19. Tamang, Nutthavuth & Sun, Yi, 2023. "Application of the dynamic Monte Carlo method to pedestrian evacuation dynamics," Applied Mathematics and Computation, Elsevier, vol. 445(C).
    20. Syed, Ahmed & Thampi, Sumesh P. & Panchagnula, Mahesh V., 2022. "Order-stampede transitions in human crowds: The role of individualistic and cooperative forces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).

    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:eee:apmaco:v:499:y:2025:i:c:s0096300325001316. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.