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The fundamental diagram of pedestrian model with slow reaction

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  • Fang, Jun
  • Qin, Zheng
  • Hu, Hao
  • Xu, Zhaohui
  • Li, Huan
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    Abstract

    The slow-to-start models are a classical cellular automata model in simulating vehicle traffic. However, to our knowledge, the slow-to-start effect has not been considered in modeling pedestrian dynamics. We verify the similar behavior between pedestrian and vehicle, and propose an new lattice gas (LG) model called the slow reaction (SR) model to describe the pedestrian’s delayed reaction in single-file movement. We simulate and reproduce Seyfried’s field experiments at the Research Centre Jülich, and use its empirical data to validate our SR model. We compare the SR model with the standard LG model. We tested different probabilities of slow reaction ps in the SR model and found the simulation data of ps=0.3 fit the empirical data best. The RMS error of the mean velocity of the SR model is smaller than that of the standard LG model. In the range of ps=0.1–0.3, our fundamental diagram between velocity and density by simulation coincides with field experiments. The distribution of individual velocity in the fundamental diagram in the SR model agrees with the empirical data better than that of the standard LG model. In addition, we observe stop-and-go waves and phase separation in pedestrian flow by simulation. We reproduced the phenomena of uneven distribution of interspaces by the SR model while the standard LG model did not. The SR model can reproduce the evolution of spatio-temporal structures of pedestrian flow with higher fidelity to Seyfried’s experiments than the standard LG model.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 391 (2012)
    Issue (Month): 23 ()
    Pages: 6112-6120

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    Handle: RePEc:eee:phsmap:v:391:y:2012:i:23:p:6112-6120

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Cellular automata model; Slow reaction model; Slow-to-start model; Field experiment; Single-file pedestrian flow;

    References

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    1. Jiang, Rui & Wu, Qing-Song, 2007. "Pedestrian behaviors in a lattice gas model with large maximum velocity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 683-693.
    2. Tajima, Yusuke & Takimoto, Kouhei & Nagatani, Takashi, 2002. "Pattern formation and jamming transition in pedestrian counter flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(3), pages 709-723.
    3. Matsui, Akiyoshi & Mashiko, Takashi & Nagatani, Takashi, 2009. "Traffic flow of mobile objects through obstacles: Turning and translational objects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(2), pages 157-173.
    4. Weng, W.G. & Shen, S.F. & Yuan, H.Y. & Fan, W.C., 2007. "A behavior-based model for pedestrian counter flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 668-678.
    5. Maniccam, S., 2006. "Adaptive decentralized congestion avoidance in two-dimensional traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 512-526.
    6. Fukamachi, Masahiro & Kuwajima, Ryota & Imanishi, Yasuhito & Nagatani, Takashi, 2007. "Velocity enhancement of slow particles in lattice–gas binary mixture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 425-434.
    7. Fukamachi, Masahiro & Nagatani, Takashi, 2007. "Sidle effect on pedestrian counter flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 269-278.
    8. Jian, Li & Lizhong, Yang & Daoliang, Zhao, 2005. "Simulation of bi-direction pedestrian movement in corridor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 619-628.
    9. Seyfried, Armin & Steffen, Bernhard & Lippert, Thomas, 2006. "Basics of modelling the pedestrian flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 232-238.
    10. Nagatani, Takashi & Nagai, Ryoichi, 2004. "Statistical characteristics of evacuation without visibility in random walk model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 638-648.
    11. Muramatsu, Masakuni & Irie, Tunemasa & Nagatani, Takashi, 1999. "Jamming transition in pedestrian counter flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 267(3), pages 487-498.
    12. Song, Weiguo & Xu, Xuan & Wang, Bing-Hong & Ni, Shunjiang, 2006. "Simulation of evacuation processes using a multi-grid model for pedestrian dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 492-500.
    13. Nagai, Ryoichi & Fukamachi, Masahiro & Nagatani, Takashi, 2006. "Evacuation of crawlers and walkers from corridor through an exit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 449-460.
    14. Yang, Lizhong & Li, Jian & Liu, Shaobo, 2008. "Simulation of pedestrian counter-flow with right-moving preference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3281-3289.
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    Cited by:
    1. Leng, Biao & Wang, Jianyuan & Zhao, Wenyuan & Xiong, Zhang, 2014. "An extended floor field model based on regular hexagonal cells for pedestrian simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 119-133.
    2. Rodriguez, E. & Espinosa-Paredes, G. & Alvarez-Ramirez, J., 2014. "Convection–diffusion effects in marathon race dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 498-507.

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