IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v7y2017i4d10.1007_s13235-016-0202-6.html
   My bibliography  Save this article

A Semi-Lagrangian Scheme for a Modified Version of the Hughes’ Model for Pedestrian Flow

Author

Listed:
  • Elisabetta Carlini

    (Sapienza Università di Roma)

  • Adriano Festa

    (Austrian Academy of Sciences (ÖAW))

  • Francisco J. Silva

    (Université de Limoges)

  • Marie-Therese Wolfram

    (Austrian Academy of Sciences (ÖAW)
    University of Warwick)

Abstract

In this paper, we present a semi-Lagrangian scheme for a regularized version of the Hughes’ model for pedestrian flow. Hughes originally proposed a coupled nonlinear PDE system describing the evolution of a large pedestrian group trying to exit a domain as fast as possible. The original model corresponds to a system of a conservation law for the pedestrian density and an eikonal equation to determine the weighted distance to the exit. We consider this model in the presence of small diffusion and discuss the numerical analysis of the proposed semi-Lagrangian scheme. Furthermore, we illustrate the effect of small diffusion on the exit time with various numerical experiments.

Suggested Citation

  • Elisabetta Carlini & Adriano Festa & Francisco J. Silva & Marie-Therese Wolfram, 2017. "A Semi-Lagrangian Scheme for a Modified Version of the Hughes’ Model for Pedestrian Flow," Dynamic Games and Applications, Springer, vol. 7(4), pages 683-705, December.
    • Handle: RePEc:spr:dyngam:v:7:y:2017:i:4:d:10.1007_s13235-016-0202-6
    DOI: 10.1007/s13235-016-0202-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-016-0202-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13235-016-0202-6?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Huang, Ling & Wong, S.C. & Zhang, Mengping & Shu, Chi-Wang & Lam, William H.K., 2009. "Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 127-141, January.
    2. N/A, 2011. "The UK economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 215(1), pages 3-3, January.
    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.
    4. Gobet, Emmanuel, 2000. "Weak approximation of killed diffusion using Euler schemes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 167-197, June.
    5. Manuel Santos & John Rust, "undated". "Convergence Properties of Policy Iteration," Working Papers 2133377, Department of Economics, W. P. Carey School of Business, Arizona State University.
    6. Blue, Victor J. & Adler, Jeffrey L., 2001. "Cellular automata microsimulation for modeling bi-directional pedestrian walkways," Transportation Research Part B: Methodological, Elsevier, vol. 35(3), pages 293-312, March.
    7. N/A, 2011. "The UK economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 217(1), pages 3-3, July.
    8. Burstedde, C & Klauck, K & Schadschneider, A & Zittartz, J, 2001. "Simulation of pedestrian dynamics using a two-dimensional cellular automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 507-525.
    9. Martin L. Puterman & Shelby L. Brumelle, 1979. "On the Convergence of Policy Iteration in Stationary Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 60-69, February.
    10. M. Falcone, 2006. "Numerical Methods For Differential Games Based On Partial Differential Equations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 231-272.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Albi, G. & Herty, M. & Pareschi, L., 2019. "Linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 460-477.

    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. 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.
    2. 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.
    3. Sun, Yi, 2019. "Simulations of bi-direction pedestrian flow using kinetic Monte Carlo methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 519-531.
    4. Sun, Yi, 2020. "Kinetic Monte Carlo simulations of bi-direction pedestrian flow with different walk speeds," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    5. Cui, Xiaoting & Ji, Jingwei & Bai, Xuehe & Cao, Yin & Wu, Tong, 2022. "Research and realization of parallel algorithms for large scale crowd evacuation in emergency," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 713-724.
    6. Canca, David & Zarzo, Alejandro & Algaba, Encarnación & Barrena, Eva, 2013. "Macroscopic attraction-based simulation of pedestrian mobility: A dynamic individual route-choice approach," European Journal of Operational Research, Elsevier, vol. 231(2), pages 428-442.
    7. 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).
    8. Qingyan Ning & Maosheng Li, 2022. "Modeling Pedestrian Detour Behavior By-Passing Conflict Areas," Sustainability, MDPI, vol. 14(24), pages 1-17, December.
    9. Zhou, Zi-Xuan & Nakanishi, Wataru & Asakura, Yasuo, 2021. "Data-driven framework for the adaptive exit selection problem in pedestrian flow: Visual information based heuristics approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    10. 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.
    11. Li, Shuang & Yu, Xiaohui & Zhang, Yanjuan & Zhai, Changhai, 2018. "A numerical simulation strategy on occupant evacuation behaviors and casualty prediction in a building during earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1238-1250.
    12. 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).
    13. Ji, Xiangfeng & Zhang, Jian & Ran, Bin, 2013. "A study on pedestrian choice between stairway and escalator in the transfer station based on floor field cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 5089-5100.
    14. Yue, Hao & Guan, Hongzhi & Zhang, Juan & Shao, Chunfu, 2010. "Study on bi-direction pedestrian flow using cellular automata simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 527-539.
    15. Tianran Han & Jianming Zhao & Wenquan Li, 2020. "Smart-Guided Pedestrian Emergency Evacuation in Slender-Shape Infrastructure with Digital Twin Simulations," Sustainability, MDPI, vol. 12(22), pages 1-18, November.
    16. Leng, Biao & Wang, Jianyuan & Xiong, Zhang, 2015. "Pedestrian simulations in hexagonal cell local field model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 532-543.
    17. Huang, Hai-Jun & Xia, Tian & Tian, Qiong & Liu, Tian-Liang & Wang, Chenlan & Li, Daqing, 2020. "Transportation issues in developing China's urban agglomerations," Transport Policy, Elsevier, vol. 85(C), pages 1-22.
    18. 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).
    19. Maity, Somnath & Sundar, S., 2022. "A coupled model for macroscopic behavior of crowd in flood induced evacuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    20. Ji, Xiangfeng & Zhou, Xuemei & Ran, Bin, 2013. "A cell-based study on pedestrian acceleration and overtaking in a transfer station corridor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1828-1839.

    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:spr:dyngam:v:7:y:2017:i:4:d:10.1007_s13235-016-0202-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.