Modeling crowd dynamics through coarse-grained data analysis

Sebastien Motsch; Mehdi Moussaïd; Elsa G. Guillot; Mathieu Moreau; Julien Pettré; Guy Theraulaz; Cécile Appert-Rolland; Pierre Degond; Sebastien Motsch; Mehdi Moussaïd; Elsa G. Guillot; Mathieu Moreau; Julien Pettré; Guy Theraulaz; Cécile Appert-Rolland; Pierre Degond

doi:10.3934/mbe.2018059

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 6: 1271-1290. doi: 10.3934/mbe.2018059

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Modeling crowd dynamics through coarse-grained data analysis

1.
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, USA
2.
Adaptive Behavior and Cognition Group, Max Planck Institut for Human Development, Berlin, Germany
3.
Centre de Recherches sur la Cognition Animale, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS) & Université de Toulouse 3 Paul Sabatier, 31062 Toulouse, France
4.
INRIA Rennes-Bretagne Atlantique, Campus de Beaulieu, Rennes, France
5.
CNRS, Laboratoire de Physique Théorique, Orsay, France
6.
Department of Mathematics, Imperial College London, London SW7 2AZ, UK

Received: 03 June 2017 Revised: 25 April 2018 Published: 01 December 2018
MSC : Primary: 93A30, 90B20; Secondary: 35B30

Understanding and predicting the collective behaviour of crowds is essential to improve the efficiency of pedestrian flows in urban areas and minimize the risks of accidents at mass events. We advocate for the development of crowd traffic management systems, whereby observations of crowds can be coupled to fast and reliable models to produce rapid predictions of the crowd movement and eventually help crowd managers choose between tailored optimization strategies. Here, we propose a Bi-directional Macroscopic (BM) model as the core of such a system. Its key input is the fundamental diagram for bi-directional flows, i.e. the relation between the pedestrian fluxes and densities. We design and run a laboratory experiments involving a total of 119 participants walking in opposite directions in a circular corridor and show that the model is able to accurately capture the experimental data in a typical crowd forecasting situation. Finally, we propose a simple segregation strategy for enhancing the traffic efficiency, and use the BM model to determine the conditions under which this strategy would be beneficial. The BM model, therefore, could serve as a building block to develop on the fly prediction of crowd movements and help deploying real-time crowd optimization strategies.
- Pedestrian traffic,
- bi-directional flux,
- collective behaviour,
- data-based modeling,
- macroscopic model
Citation: Sebastien Motsch, Mehdi Moussaïd, Elsa G. Guillot, Mathieu Moreau, Julien Pettré, Guy Theraulaz, Cécile Appert-Rolland, Pierre Degond. Modeling crowd dynamics through coarse-grained data analysis[J]. Mathematical Biosciences and Engineering, 2018, 15(6): 1271-1290. doi: 10.3934/mbe.2018059

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Abstract

Understanding and predicting the collective behaviour of crowds is essential to improve the efficiency of pedestrian flows in urban areas and minimize the risks of accidents at mass events. We advocate for the development of crowd traffic management systems, whereby observations of crowds can be coupled to fast and reliable models to produce rapid predictions of the crowd movement and eventually help crowd managers choose between tailored optimization strategies. Here, we propose a Bi-directional Macroscopic (BM) model as the core of such a system. Its key input is the fundamental diagram for bi-directional flows, i.e. the relation between the pedestrian fluxes and densities. We design and run a laboratory experiments involving a total of 119 participants walking in opposite directions in a circular corridor and show that the model is able to accurately capture the experimental data in a typical crowd forecasting situation. Finally, we propose a simple segregation strategy for enhancing the traffic efficiency, and use the BM model to determine the conditions under which this strategy would be beneficial. The BM model, therefore, could serve as a building block to develop on the fly prediction of crowd movements and help deploying real-time crowd optimization strategies.

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