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Modeling tagged pedestrian motion: A mean-field type game approach

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  • Aurell, Alexander
  • Djehiche, Boualem

Abstract

This paper suggests a model for the motion of tagged pedestrians: Pedestrians moving towards a specified targeted destination, which they are forced to reach. It aims to be a decision-making tool for the positioning of fire fighters, security personnel and other services in a pedestrian environment. Taking interaction with the surrounding crowd into account leads to a differential nonzero-sum game model where the tagged pedestrians compete with the surrounding crowd of ordinary pedestrians. When deciding how to act, pedestrians consider crowd distribution-dependent effects, like congestion and crowd aversion. Including such effects in the parameters of the game, makes it a mean-field type game. The equilibrium control is characterized, and special cases are discussed. Behavior in the model is studied by numerical simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:121:y:2019:i:c:p:168-183
    DOI: 10.1016/j.trb.2019.01.011
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    References listed on IDEAS

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    1. Hughes, Roger L., 2002. "A continuum theory for the flow of pedestrians," Transportation Research Part B: Methodological, Elsevier, vol. 36(6), pages 507-535, July.
    2. Jin, Cheng-Jie & Jiang, Rui & Yin, Jun-Lin & Dong, Li-Yun & Li, Dawei, 2017. "Simulating bi-directional pedestrian flow in a cellular automaton model considering the body-turning behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 666-681.
    3. Alexander Aurell, 2018. "Mean-Field Type Games between Two Players Driven by Backward Stochastic Differential Equations," Games, MDPI, vol. 9(4), pages 1-26, November.
    4. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    5. Burstedde, C & Klauck, K & Schadschneider, A & Zittartz, J, 2001. "Simulation of pedestrian dynamics using a two-dimensional cellular automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 507-525.
    6. 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.
    7. 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.
    8. Hoogendoorn, S. P. & Bovy, P. H. L., 2004. "Pedestrian route-choice and activity scheduling theory and models," Transportation Research Part B: Methodological, Elsevier, vol. 38(2), pages 169-190, February.
    9. Ermal Feleqi, 2013. "The Derivation of Ergodic Mean Field Game Equations for Several Populations of Players," Dynamic Games and Applications, Springer, vol. 3(4), pages 523-536, December.
    10. repec:dau:papers:123456789/5946 is not listed on IDEAS
    11. Boualem Djehiche & Hamidou Tembine & Raul Tempone, 2014. "A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control," Papers 1404.1441, arXiv.org.
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    1. Alexander Aurell, 2018. "Mean-Field Type Games between Two Players Driven by Backward Stochastic Differential Equations," Games, MDPI, vol. 9(4), pages 1-26, November.
    2. Shin, Youngchul & Moon, Ilkyeong, 2023. "Robust building evacuation planning in a dynamic network flow model under collapsible nodes and arcs," Socio-Economic Planning Sciences, Elsevier, vol. 86(C).
    3. Hancheng Guo & Jie Xiong & Jiayu Zheng, 2024. "Stochastic Maximum Principle for Generalized Mean-Field Delay Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 201(1), pages 352-377, April.

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