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Statistical characteristics of evacuation without visibility in random walk model

Author

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  • Nagatani, Takashi
  • Nagai, Ryoichi

Abstract

The evacuation process from a dark room with an exit is investigated by the use of the biased random walk model. We clarify the statistical properties of the walker escaping from the room through the exit. The evacuation from the room without visibility consists of two processes: (1) the biased random walk from an initial position to the wall and (2) the second walk following the wall. The following statistical quantities are derived by using a lot of simulating trajectories: the probability density distributions of (1) the number of steps of the biased random walk to the wall, (2) the first contact point on the wall, and (3) the number of steps of the second walk on the wall. The third statistical distribution is connected closely with the first and second distributions. Their distributions depend highly on the scenarios of the walker. We show the effects of the initial position, drift, and scenario on the mean escape time.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:341:y:2004:i:c:p:638-648
    DOI: 10.1016/j.physa.2004.04.124
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    Citations

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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. Fang, Zhiming & Song, Weiguo & Zhang, Jun & Wu, Hao, 2010. "Experiment and modeling of exit-selecting behaviors during a building evacuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 815-824.
    3. Wang, Guanning & Chen, Tao & Hu, Xiangmin & Zheng, Huijie & Jiang, Wenyu, 2022. "Wall-following searching or area coverage searching? Simulation study of the panic evacuation considering the guidance of a single rescuer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    4. Cao, Shuchao & Song, Weiguo & Lv, Wei & Fang, Zhiming, 2015. "A multi-grid model for pedestrian evacuation in a room without visibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 45-61.
    5. Li, Xingli & Guo, Fang & Kuang, Hua & Geng, Zhongfei & Fan, Yanhong, 2019. "An extended cost potential field cellular automaton model for pedestrian evacuation considering the restriction of visual field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 47-56.
    6. 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.
    7. Shang, Hua-Yan & Huang, Hai-Jun & Zhang, Yi-Ming, 2015. "An extended mobile lattice gas model allowing pedestrian step size variable," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 283-293.
    8. Fang, Jun & Qin, Zheng & Hu, Hao & Xu, Zhaohui & Li, Huan, 2012. "The fundamental diagram of pedestrian model with slow reaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6112-6120.
    9. Liu, Xuan & Song, Weiguo & Zhang, Jun, 2009. "Extraction and quantitative analysis of microscopic evacuation characteristics based on digital image processing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(13), pages 2717-2726.

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