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Networks and Heterogeneous Media

2015, Volume 10, Issue 3: 579-608. doi: 10.3934/nhm.2015.10.579
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Time-delayed follow-the-leader model for pedestrians walking in line

  • 1.
    Université de Toulouse; UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse; F-31062 Toulouse
  • 2.
    Donghua University, No. 2999 North Renmin Road, Songjiang, Shanghai 201620
  • 3.
    INRIA Rennes - Bretagne Atlantique, Campus de Beaulieu, 35042 Rennes
  • 4.
    Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome
  • 5.
    Laboratoire de Physique Théorique, Université Paris Sud, btiment 210, 91405 Orsay cedex
  • 6.
    Golaem S.A.S., Bâtiment Germanium, 80 avenue des Buttes de Coësmes, 35 700 Rennes
  • 7.
    Imperial College London, South Kensington Campus, London SW7 2AZ
  • Received: 01 October 2014 Revised: 01 January 2015

  • Primary: 90B06, 90B20; Secondary: 91C99, 65L99.

  • We use the results of a pedestrian tracking experiment to identify a follow-the-leader model for pedestrians walking-in-line. We demonstrate the existence of a time-delay between a subject's response and the predecessor's corresponding behavior. This time-delay induces an instability which can be damped out by a suitable relaxation. By comparisons with the experimental data, we show that the model reproduces well the emergence of large-scale structures such as congestions waves. The resulting model can be used either for modeling pedestrian queuing behavior or can be incorporated into bi-dimensional models of pedestrian traffic.

    Citation: Jérôme Fehrenbach, Jacek Narski, Jiale Hua, Samuel Lemercier, Asja Jelić, Cécile Appert-Rolland, Stéphane Donikian, Julien Pettré, Pierre Degond. Time-delayed follow-the-leader model for pedestrians walking in line[J]. Networks and Heterogeneous Media, 2015, 10(3): 579-608. doi: 10.3934/nhm.2015.10.579

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  • We use the results of a pedestrian tracking experiment to identify a follow-the-leader model for pedestrians walking-in-line. We demonstrate the existence of a time-delay between a subject's response and the predecessor's corresponding behavior. This time-delay induces an instability which can be damped out by a suitable relaxation. By comparisons with the experimental data, we show that the model reproduces well the emergence of large-scale structures such as congestions waves. The resulting model can be used either for modeling pedestrian queuing behavior or can be incorporated into bi-dimensional models of pedestrian traffic.


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