A discrete Hughes' model for pedestrian flow on graphs
This work extends the Hughes continuum model to discrete graph structures, offering a new tool for modeling pedestrian dynamics in networked environments.
The authors propose a discrete Hughes-type model for pedestrian flow on graphs, proving its well-posedness and demonstrating its validity through numerical examples.
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 while the minimization principle is described by a graph eikonal equation. We show that the model is well posed and we implement some numerical examples to demonstrate the validity of the proposed model.