A discrete Hughes model for pedestrian flow on graphs

Fabio Camilli; Adriano Festa; Silvia Tozza; Fabio Camilli; Adriano Festa; Silvia Tozza

doi:10.3934/nhm.2017004

Networks and Heterogeneous Media

2017, Volume 12, Issue 1: 93-112. doi: 10.3934/nhm.2017004

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A discrete Hughes model for pedestrian flow on graphs

1.
Dip. di Scienze di Base e Applicate per l'Ingegneria, "Sapienza" Università di Roma, via Scarpa 16, 00161 Roma, Italy
2.
RICAM, Austrian Academy of Sciences (ÖAW), Altenbergerstr. 69, 4040 Linz, Austria
3.
Dip. di Matematica, "Sapienza" Università di Roma, P.le Aldo Moro 5, 00185 Roma, Italy

Received: 01 April 2016 Revised: 01 December 2016
Primary: 90B20; Secondary: 35R02, 65M06

In this paper, we introduce a discrete time-finite state model for pedestrian flow on a graph in the spirit of the Hughes dynamic continuum model. The pedestrians, represented by a density function, move on the graph choosing a route to minimize the instantaneous travel cost to the destination. The density is governed by a conservation law whereas the minimization principle is described by a graph eikonal equation. We show that the discrete model is well-posed and the numerical examples reported confirm the validity of the proposed model and its applicability to describe real situations.
- Pedestrian flow,
- Hughes model,
- conservation law,
- graph eikonal equation,
- well-posed discrete model
Citation: Fabio Camilli, Adriano Festa, Silvia Tozza. A discrete Hughes model for pedestrian flow on graphs[J]. Networks and Heterogeneous Media, 2017, 12(1): 93-112. doi: 10.3934/nhm.2017004

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Abstract

In this paper, we introduce a discrete time-finite state model for pedestrian flow on a graph in the spirit of the Hughes dynamic continuum model. The pedestrians, represented by a density function, move on the graph choosing a route to minimize the instantaneous travel cost to the destination. The density is governed by a conservation law whereas the minimization principle is described by a graph eikonal equation. We show that the discrete model is well-posed and the numerical examples reported confirm the validity of the proposed model and its applicability to describe real situations.

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