Archive for Rational Mechanics and Analysis

, Volume 199, Issue 3, pp 707–738 | Cite as

Time-Evolving Measures and Macroscopic Modeling of Pedestrian Flow

  • Benedetto Piccoli
  • Andrea Tosin


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.


Spatial Approximation Intermediate Target Fundamental Diagram Nonlinear Hyperbolic Equation Pedestrian Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Mathematical SciencesRutgers University - CamdenCamdenUSA
  2. 2.Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle RicercheRomeItaly

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