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Trapping in bottlenecks: Interplay between microscopic dynamics and large scale effects

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  • Cirillo, E.N.M.
  • Colangeli, M.
  • Muntean, A.

Abstract

We investigate the appearance of trapping states in pedestrian flows through bottlenecks as a result of the interplay between the geometry of the system and the microscopic stochastic dynamics. We model the flow through a bottleneck via a Zero Range Process on a one-dimensional periodic lattice. Particle are removed from the lattice sites with rates proportional to the local occupation numbers. The bottleneck is modeled by a particular site of the lattice whose updating rate saturates to a constant value as soon as the local occupation number exceeds a fixed threshold. We show that for any finite value of the threshold the stationary particle current saturates to the limiting bottleneck rate when the total particle density in the system exceeds a critical value corresponding to the bottleneck rate itself.

Suggested Citation

  • Cirillo, E.N.M. & Colangeli, M. & Muntean, A., 2017. "Trapping in bottlenecks: Interplay between microscopic dynamics and large scale effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 488(C), pages 30-38.
    • Handle: RePEc:eee:phsmap:v:488:y:2017:i:c:p:30-38
    DOI: 10.1016/j.physa.2017.07.001
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    References listed on IDEAS

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    1. 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.
    2. Tajima, Yusuke & Takimoto, Kouhei & Nagatani, Takashi, 2001. "Scaling of pedestrian channel flow with a bottleneck," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 294(1), pages 257-268.
    3. Cirillo, Emilio N.M. & Krehel, Oleh & Muntean, Adrian & van Santen, Rutger & Sengar, Aditya, 2016. "Residence time estimates for asymmetric simple exclusion dynamics on strips," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 436-457.
    4. Nagatani, Takashi, 2001. "Dynamical transition and scaling in a mean-field model of pedestrian flow at a bottleneck," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(3), pages 558-566.
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    Cited by:

    1. Xiaohong Li & Jianan Zhou & Feng Chen & Zan Zhang, 2018. "Cluster Risk of Walking Scenarios Based on Macroscopic Flow Model and Crowding Force Analysis," Sustainability, MDPI, vol. 10(2), pages 1-16, February.
    2. Qiu, Guo & Song, Rui & He, Shiwei & Yin, Weichuan, 2018. "The pedestrian flow characteristics of Y-shaped channel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 199-212.

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