Pedestrian flows in bounded domains with obstacles

Benedetto Piccoli, Andrea Tosin

Research output: Contribution to journalArticle

77 Scopus citations


In this paper, we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space occupancy by pedestrians is described via a sequence of Radon-positive measures generated by a push-forward recursive relation. We assume that two fundamental aspects of pedestrian behavior rule the dynamics of the system: on the one hand, the will to reach specific targets, which determines the main direction of motion of the walkers; on the other hand, the tendency to avoid crowding, which introduces interactions among the individuals. The resulting model is able to reproduce several experimental evidences of pedestrian flows pointed out in the specialized literature, being at the same time much easier to handle, from both the analytical and the numerical point of view, than other models relying on nonlinear hyperbolic conservation laws. This makes it suitable to address two-dimensional applications of practical interest, chiefly the motion of pedestrians in complex domains scattered with obstacles.

Original languageEnglish (US)
Pages (from-to)85-107
Number of pages23
JournalContinuum Mechanics and Thermodynamics
Issue number2
StatePublished - Jul 1 2009
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Mechanics of Materials
  • Physics and Astronomy(all)


  • Macroscopic modeling
  • Measure theory
  • Pedestrian flow
  • Push forward

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