Time-delayed follow-the-leader model for pedestrians walking in line

Jérôme  Fehrenbach; Jacek  Narski; Jiale  Hua; Samuel  Lemercier; Asja  Jelić; Cécile Appert-Rolland; Stéphane  Donikian; Julien Pettré; Pierre  Degond

doi:10.3934/nhm.2015.10.579

Article Contents

2015, Volume 10, Issue 3: 579-608. Doi: 10.3934/nhm.2015.10.579

This issue Previous Article Keep right or left? Towards a cognitive-mathematical model for pedestrians Next Article Analyzing human-swarm interactions using control Lyapunov functions and optimal control

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: October 2014

Revised: January 2015

Published: September 2015

Abstract / Introduction Related Papers Cited by

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.

Keywords:

Mathematics Subject Classification: Primary: 90B06, 90B20; Secondary: 91C99, 65L99.

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