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A hierarchy of the optimal velocity model with optimal path for pedestrian evacuation: From microscopic to macroscopic models

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  • Makmul, J.

Abstract

We study the evacuation process of pedestrians by adopting an optimal velocity model. The Eikonal equation is coupled to the optimal velocity model for optimal path to guide the movement directions of pedestrians. It depends on pedestrian density. We derive the corresponding mean field equation, hydrodynamic and scalar models from the scaled microscopic optimal velocity model. Several numerical experiments are performed in a corridor with two exits. We show and compare results on the microscopic as well as on the hydrodynamic and scalar models. Results from microscopic model are closed to the hydrodynamic and scalar models when a large number of particles are considered in microscopic simulation. The computation time increases as number of particles in microscopic simulation increases. The computation times of the hydrodynamic and scalar models are less than the computation time of the microscopic model with large number of particles. Hence it is beneficial to apply the hydrodynamic and scalar models over the microscopic model when a large number of particles in microscopic system are considered.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:643:y:2024:i:c:s0378437124003029
    DOI: 10.1016/j.physa.2024.129793
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    References listed on IDEAS

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    1. 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.
    2. Jiang, Yan-qun & Zhang, Peng & Wong, S.C. & Liu, Ru-xun, 2010. "A higher-order macroscopic model for pedestrian flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4623-4635.
    3. Tobias Kretz & Andree Große & Stefan Hengst & Lukas Kautzsch & Andrej Pohlmann & Peter Vortisch, 2011. "Quickest Paths In Simulations Of Pedestrians," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 14(05), pages 733-759.
    4. 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.
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