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Time-Evolving Measures and Macroscopic Modeling of Pedestrian Flow

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Rutgers University - Camden, 311 N 5th Street, Camden, NJ, 08102, USA

    Benedetto Piccoli

  2. Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185, Rome, Italy

    Andrea Tosin

Authors
  1. Benedetto Piccoli
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  2. Andrea Tosin
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Correspondence to Benedetto Piccoli.

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Communicated by C. M. Dafermos

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Piccoli, B., Tosin, A. Time-Evolving Measures and Macroscopic Modeling of Pedestrian Flow. Arch Rational Mech Anal 199, 707–738 (2011). https://doi.org/10.1007/s00205-010-0366-y

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  • DOI: https://doi.org/10.1007/s00205-010-0366-y

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