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Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm

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  • Huang, Ling
  • Wong, S.C.
  • Zhang, Mengping
  • Shu, Chi-Wang
  • Lam, William H.K.

Abstract

In this paper, we revisit Hughes' dynamic continuum model for pedestrian flow in a two-dimensional walking facility that is represented as a continuum within which pedestrians can freely move in any direction [Hughes, R.L., 2002. A continuum theory for the flow of pedestrians. Transportation Research Part B, 36 (6), 507-535]. We first reformulate Hughes' model, and then show that the pedestrian route choice strategy in Hughes' model satisfies the reactive dynamic user equilibrium principle in which a pedestrian chooses a route to minimize the instantaneous travel cost to the destination. In this model, the pedestrian demand is time varying. The pedestrian density, flux, and walking speed are governed by the conservation equation. A generalized cost function is considered. The reformulated problem is solved by the efficient weighted essentially non-oscillatory scheme for the conservation equation and the fast sweeping method for the Eikonal equation. A numerical example is used to demonstrate the effectiveness of the proposed solution procedure.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:transb:v:43:y:2009:i:1:p:127-141
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    References listed on IDEAS

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    Cited by:

    1. Guo, Ren-Yong & Huang, Hai-Jun & Wong, S.C., 2012. "Route choice in pedestrian evacuation under conditions of good and zero visibility: Experimental and simulation results," Transportation Research Part B: Methodological, Elsevier, vol. 46(6), pages 669-686.
    2. 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.
    3. Guo, Ren-Yong & Huang, Hai-Jun & Wong, S.C., 2011. "Collection, spillback, and dissipation in pedestrian evacuation: A network-based method," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 490-506, March.
    4. repec:eee:phsmap:v:505:y:2018:i:c:p:836-847 is not listed on IDEAS
    5. van Wageningen-Kessels, Femke & Leclercq, Ludovic & Daamen, Winnie & Hoogendoorn, Serge P., 2016. "The Lagrangian coordinate system and what it means for two-dimensional crowd flow models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 272-285.
    6. repec:gam:jsusta:v:10:y:2018:i:2:p:385-:d:129848 is not listed on IDEAS
    7. 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.
    8. repec:eee:transb:v:100:y:2017:i:c:p:222-254 is not listed on IDEAS
    9. Jiang, Yanqun & Wong, S.C. & Ho, H.W. & Zhang, Peng & Liu, Ruxun & Sumalee, Agachai, 2011. "A dynamic traffic assignment model for a continuum transportation system," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 343-363, February.
    10. 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.
    11. 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.
    12. 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.
    13. Guo, Ning & Hu, Mao-Bin & Jiang, Rui, 2017. "Impact of variable body size on pedestrian dynamics by heuristics-based model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 109-114.
    14. Du, Jie & Wong, S.C. & Shu, Chi-Wang & Zhang, Mengping, 2015. "Reformulating the Hoogendoorn–Bovy predictive dynamic user-optimal model in continuum space with anisotropic condition," Transportation Research Part B: Methodological, Elsevier, vol. 79(C), pages 189-217.
    15. 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.
    16. Li, Baibing, 2013. "A model of pedestrians’ intended waiting times for street crossings at signalized intersections," Transportation Research Part B: Methodological, Elsevier, vol. 51(C), pages 17-28.
    17. 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.
    18. Jiang, Yan-Qun & Zhou, Shu-Guang & Tian, Fang-Bao, 2015. "A higher-order macroscopic model for bi-direction pedestrian flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 425(C), pages 69-78.
    19. Du, Jie & Wong, S.C. & Shu, Chi-Wang & Xiong, Tao & Zhang, Mengping & Choi, Keechoo, 2013. "Revisiting Jiang’s dynamic continuum model for urban cities," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 96-119.
    20. repec:eee:phsmap:v:487:y:2017:i:c:p:47-57 is not listed on IDEAS
    21. 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.
    22. repec:eee:phsmap:v:490:y:2018:i:c:p:1238-1250 is not listed on IDEAS
    23. Li, Shuang & Zhai, Changhai & Xie, Lili, 2015. "Occupant evacuation and casualty estimation in a building under earthquake using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 152-167.
    24. Wang, Jinhuan & Zhang, Lei & Shi, Qiongyu & Yang, Peng & Hu, Xiaoming, 2015. "Modeling and simulating for congestion pedestrian evacuation with panic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 396-409.
    25. repec:spr:dyngam:v:7:y:2017:i:4:d:10.1007_s13235-016-0202-6 is not listed on IDEAS

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