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

TL;DR

This paper develops a time-delayed follow-the-leader model for pedestrians walking in line, capturing response delays and instabilities, and demonstrating its ability to reproduce congestion waves observed in experiments.

Contribution

The paper introduces a novel pedestrian follow-the-leader model incorporating time-delay effects, validated against experimental data, and applicable to pedestrian queuing and traffic modeling.

Findings

Model reproduces large-scale congestion waves

Time-delay causes response instability

Damping relaxation stabilizes pedestrian flow

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.