Time-Evolving Measures and Macroscopic Modeling of Pedestrian Flow
By Benedetto Piccoli, Andrea Tosin. 2008
192 citations recorded by the source corpus.
This paper introduces a new model of pedestrian flow, formulated within a measure-theoretic framework. It consists of a macroscopic representation of the system via a family of measures which, pushed forward by some flow maps, provide an estimate of the space occupancy by pedestrians at successive times. From the modeling point of view, this setting is particularly suitable for treating nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. In addition, the analysis and numerical approximation of the resulting mathematical structures, which are the principal objectives of this work, follow more easily than for models based on standard hyperbolic conservation laws.
Subfields: Control and Systems Engineering, Ocean Engineering, Safety, Risk, Reliability and Quality
View Paper: https://www.semanticscholar.org/paper/7e8580124e692e5c2fcf4b0fcdeb9800156e200c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Control and Systems Engineering
- Mauro Garavello
- Magali L'ecureux-Mercier
- Rinaldo M. Colombo
- Filippo Santambrogio
- Benedetto Piccoli
- Francesco Rossi
- Michael Herty
- M. Mercier
In Ocean Engineering
- Filippo Santambrogio
- Mauro Garavello
- Benedetto Piccoli
- Magali L'ecureux-Mercier
- Francesco Rossi
- Rinaldo M. Colombo
- Michael Herty
- M. Mercier
In Safety, Risk, Reliability and Quality
- Rinaldo M. Colombo
- Francesco Rossi
- Magali L'ecureux-Mercier
- M. Mercier
- Mauro Garavello
- Michael Herty
- Benedetto Piccoli
Citations in the corpus
- Control of the Continuity Equation with a Non Local Flow (2009, methodology): “boundaries, obstacles or other geometric constraint can be described through ~ v, see [13, 27 ].”
- Heterophilious Dynamics Enhances Consensus (2013, background): “Self-organized dynamics is found in many other areas, from pedestrian and traffic dynamics [64, 92], social networks and economics [48, 66, 69, 77, 83], complex networks [5, 44, 91], and opinion dynamics [7, 23, 42, 49, 50, 63, 75, 105, 110, 109], all the way to applications in marketing [2, 3], pro”
- A CLASS OF NONLOCAL MODELS FOR PEDESTRIAN TRAFFIC (2011, methodology): “The model introduced in [13, 29] relies on this measure valued conservation law: ∂tμ+ div (μ v) = 0 where v = ν(x) + ∫”
- Generalized Wasserstein Distance and its Application to Transport Equations with Source (2012, methodology): “This equation is intensively used for the modelling of crowd dynamics, where μt represents a pedestrian density (see for example [6,8,12–14,16–18]).”
- A MACROSCOPIC CROWD MOTION MODEL OF GRADIENT FLOW TYPE (2010, background): “Crowd motion; Gradient Flow; Wasserstein distance; Continuity equation.”