A reactive dynamic continuum user equilibrium model for bi-directional pedestrian flows

Yanqun Jiang, Tao Xiong, S. C. Wong, Chi Wang Shu, Mengping Zhang, Peng Zhang, Hing Keung William Lam

Research output: Journal article publicationJournal articleAcademic researchpeer-review

51 Citations (Scopus)


In this paper, a reactive dynamic user equilibrium model is extended to simulate two groups of pedestrians traveling on crossing paths in a continuous walking facility. Each group makes path choices to minimize the travel cost to its destination in a reactive manner based on instantaneous information. The model consists of a conservation law equation coupled with an Eikonal-type equation for each group. The velocity-density relationship of pedestrian movement is obtained via an experimental method. The model is solved using a finite volume method for the conservation law equation and a fast-marching method for the Eikonal-type equation on unstructured grids. The numerical results verify the rationality of the model and the validity of the numerical method. Based on this continuum model, a number of results, e.g., the formation of strips or moving clusters composed of pedestrians walking to the same destination, are also observed.
Original languageEnglish
Pages (from-to)1541-1555
Number of pages15
JournalActa Mathematica Scientia
Issue number6
Publication statusPublished - 1 Nov 2009


  • 76M12
  • conservation law
  • density-velocity relationship
  • Eikonal-type equation
  • fast marching method
  • finite volume method
  • pedestrian flows
  • unstructured grids

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)


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