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On a mean field game approach modeling congestion and aversion in pedestrian crowds

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  • Lachapelle, Aimé
  • Wolfram, Marie-Therese

Abstract

In this paper we present a new class of pedestrian crowd models based on the mean field games theory introduced by Lasry and Lions in 2006. This macroscopic approach is based on a microscopic model, that considers smart pedestrians who rationally interact and anticipate the future. This leads to a forward-backward structure in time. We focus on two-population interactions and validate the modeling with simple examples. Two complementary classes of problems are addressed, namely the case of crowd aversion and the one of congestion. In both cases we describe the model and present numerical solvers (based on the optimization formulation and the partial differential equations respectively). Finally we present numerical tests involving anticipation phenomena and complex group behaviors such as lane formation.

Suggested Citation

  • Lachapelle, Aimé & Wolfram, Marie-Therese, 2011. "On a mean field game approach modeling congestion and aversion in pedestrian crowds," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1572-1589.
    • Handle: RePEc:eee:transb:v:45:y:2011:i:10:p:1572-1589
    DOI: 10.1016/j.trb.2011.07.011
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    References listed on IDEAS

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    1. Zheng, Xiaoping & Cheng, Yuan, 2011. "Conflict game in evacuation process: A study combining Cellular Automata model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(6), pages 1042-1050.
    2. repec:dau:papers:123456789/3001 is not listed on IDEAS
    3. Guesnerie, Roger, 1992. "An Exploration of the Eductive Justifications of the Rational-Expectations Hypothesis," American Economic Review, American Economic Association, vol. 82(5), pages 1254-1278, December.
    4. Tanimoto, Jun & Hagishima, Aya & Tanaka, Yasukaka, 2010. "Study of bottleneck effect at an emergency evacuation exit using cellular automata model, mean field approximation analysis, and game theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5611-5618.
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    Cited by:

    1. Cheng, Yuan & Zheng, Xiaoping, 2018. "Emergence of cooperation during an emergency evacuation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 485-494.
    2. Aurell, Alexander & Djehiche, Boualem, 2019. "Modeling tagged pedestrian motion: A mean-field type game approach," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 168-183.
    3. Xu, Qiancheng & Chraibi, Mohcine & Tordeux, Antoine & Zhang, Jun, 2019. "Generalized collision-free velocity model for pedestrian dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    4. Abdelghany, Ahmed & Abdelghany, Khaled & Mahmassani, Hani, 2016. "A hybrid simulation-assignment modeling framework for crowd dynamics in large-scale pedestrian facilities," Transportation Research Part A: Policy and Practice, Elsevier, vol. 86(C), pages 159-176.
    5. 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.
    6. Cristiani, E. & Menci, M. & Malagnino, A. & Amaro, G.G., 2023. "An all-densities pedestrian simulator based on a dynamic evaluation of the interpersonal distances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    7. Zhou, Zi-Xuan & Nakanishi, Wataru & Asakura, Yasuo, 2021. "Data-driven framework for the adaptive exit selection problem in pedestrian flow: Visual information based heuristics approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    8. Ji, Xiangfeng & Zhang, Jian & Hu, Yongkai & Ran, Bin, 2016. "Pedestrian movement analysis in transfer station corridor: Velocity-based and acceleration-based," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 416-434.

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