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.
A discrete hughes model for pedestrian flow on graphs / CAMILLI, FABIO; FESTA, ADRIANO; TOZZA, SILVIA. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - ELETTRONICO. - 12:1(2017), pp. 93-112. [10.3934/nhm.2017004]
A discrete hughes model for pedestrian flow on graphs
TOZZA, SILVIA
2017
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.