IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v52y2018i3p547-563.html
   My bibliography  Save this article

Two-Dimensional Approximate Godunov Scheme and What It Means For Continuum Pedestrian Flow Models

Author

Listed:
  • Femke van Wageningen-Kessels

    (Department of Transport and Planning, Delft University of Technology, 2628 CD Delft, Netherlands; German University of Technology in Oman, Halban, Muscat, Sultinate of Oman)

  • Winnie Daamen

    (Department of Transport and Planning, Delft University of Technology, 2628 CD Delft, Netherlands)

  • Serge P. Hoogendoorn

    (Department of Transport and Planning, Delft University of Technology, 2628 CD Delft, Netherlands)

Abstract

An efficient simulation method for two-dimensional continuum pedestrian flow models is introduced. It is a two-dimensional adaptation of the Godunov scheme for one-dimensional road traffic flow models. It is further extended to include multiple classes, representing groups of pedestrians with different behavior, origin, and destination. The method can be applied to continuum pedestrian flow models in a wide range of applications from the design of train stations and other travel hubs to the study of crowd behavior and safety at sports, religious, and cultural events. The combination of the efficient simulation method with continuum models enables the user to get simulation results much quicker than before. This opens doors to real-time crowd control and to more advanced optimization of planning and control. Test results show the importance of choosing appropriate numerical settings, including grid cell and time step size for realistic simulation results.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:52:y:2018:i:3:p:547-563
    DOI: 10.1287/trsc.2017.0793
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/trsc.2017.0793
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.2017.0793?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. Mehdi Moussaïd & Elsa G Guillot & Mathieu Moreau & Jérôme Fehrenbach & Olivier Chabiron & Samuel Lemercier & Julien Pettré & Cécile Appert-Rolland & Pierre Degond & Guy Theraulaz, 2012. "Traffic Instabilities in Self-Organized Pedestrian Crowds," PLOS Computational Biology, Public Library of Science, vol. 8(3), pages 1-10, March.
    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. 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.
    4. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    5. 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.
    6. 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.
    7. 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.
    8. Ansorge, Rainer, 1990. "What does the entropy condition mean in traffic flow theory?," Transportation Research Part B: Methodological, Elsevier, vol. 24(2), pages 133-143, April.
    9. Dirk Helbing & Lubos Buzna & Anders Johansson & Torsten Werner, 2005. "Self-Organized Pedestrian Crowd Dynamics: Experiments, Simulations, and Design Solutions," Transportation Science, INFORMS, vol. 39(1), pages 1-24, February.
    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. Hänseler, Flurin S. & Lam, William H.K. & Bierlaire, Michel & Lederrey, Gael & Nikolić, Marija, 2017. "A dynamic network loading model for anisotropic and congested pedestrian flows," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 149-168.
    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. 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.
    4. Aghamohammadi, Rafegh & Laval, Jorge A., 2020. "A continuum model for cities based on the macroscopic fundamental diagram: A semi-Lagrangian solution method," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 101-116.
    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. 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.
    7. Flötteröd, Gunnar & Lämmel, Gregor, 2015. "Bidirectional pedestrian fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 194-212.
    8. 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.
    9. 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.
    10. Qingyan Ning & Maosheng Li, 2022. "Modeling Pedestrian Detour Behavior By-Passing Conflict Areas," Sustainability, MDPI, vol. 14(24), pages 1-17, December.
    11. Mazaré, Pierre-Emmanuel & Dehwah, Ahmad H. & Claudel, Christian G. & Bayen, Alexandre M., 2011. "Analytical and grid-free solutions to the Lighthill–Whitham–Richards traffic flow model," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1727-1748.
    12. Jin, Wen-Long & Gan, Qi-Jian & Gayah, Vikash V., 2013. "A kinematic wave approach to traffic statics and dynamics in a double-ring network," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 114-131.
    13. 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).
    14. Blandin, Sébastien & Argote, Juan & Bayen, Alexandre M. & Work, Daniel B., 2013. "Phase transition model of non-stationary traffic flow: Definition, properties and solution method," Transportation Research Part B: Methodological, Elsevier, vol. 52(C), pages 31-55.
    15. Mollier, Stéphane & Delle Monache, Maria Laura & Canudas-de-Wit, Carlos & Seibold, Benjamin, 2019. "Two-dimensional macroscopic model for large scale traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 309-326.
    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. Carolina Osorio & Gunnar Flötteröd, 2015. "Capturing Dependency Among Link Boundaries in a Stochastic Dynamic Network Loading Model," Transportation Science, INFORMS, vol. 49(2), pages 420-431, May.
    19. Jin, Wen-Long, 2010. "Continuous kinematic wave models of merging traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1084-1103, September.
    20. Zhang, H. M. & Recker, W. W., 1999. "On optimal freeway ramp control policies for congested traffic corridors," Transportation Research Part B: Methodological, Elsevier, vol. 33(6), pages 417-436, August.

    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:inm:ortrsc:v:52:y:2018:i:3:p:547-563. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.