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arXiv · 1412.7537

Time-delayed Follow-the-Leader model for pedestrians walking in line

Jérôme Fehrenbach·Jacek Narski·Jiale Hua·Samuel Lemercier·Asja Jelic·Cécile Appert-Rolland·Stéphane Donikian·Julien Pettré·Pierre Degond
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Abstract

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. Acknowledgements: This work has been supported by the french 'Agence Nationale pour la Recherche (ANR)' in the frame of the contract "Pedigree" (ANR-08-SYSC-015-01). JH acknowledges support of the ANR and the Institut de Math{\'e}matiques de Toulouse, where he conducted this research. AJ acknowledges support of the ANR and of the Laboratoire de physique t A c orique in Orsay where she conducted this research. PD is on leave from CNRS, Institut de Mat A c matiques de Toulouse, France.

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Jérôme Fehrenbach, Jacek Narski, Jiale Hua, Samuel Lemercier, Asja Jelic, Cécile Appert-Rolland, Stéphane Donikian, Julien Pettré, Pierre Degond. 2014-12-23. Time-delayed Follow-the-Leader model for pedestrians walking in line. https://doi.org/10.3934/nhm.2015.10.579

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