Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm

Ling Huang, S. C. Wong, Mengping Zhang, Chi Wang Shu, Hing Keung William Lam

Research output: Journal article publicationJournal articleAcademic researchpeer-review

187 Citations (Scopus)


In this paper, we revisit Hughes' dynamic continuum model for pedestrian flow in a two-dimensional walking facility that is represented as a continuum within which pedestrians can freely move in any direction [Hughes, R.L., 2002. A continuum theory for the flow of pedestrians. Transportation Research Part B, 36 (6), 507-535]. We first reformulate Hughes' model, and then show that the pedestrian route choice strategy in Hughes' model satisfies the reactive dynamic user equilibrium principle in which a pedestrian chooses a route to minimize the instantaneous travel cost to the destination. In this model, the pedestrian demand is time varying. The pedestrian density, flux, and walking speed are governed by the conservation equation. A generalized cost function is considered. The reformulated problem is solved by the efficient weighted essentially non-oscillatory scheme for the conservation equation and the fast sweeping method for the Eikonal equation. A numerical example is used to demonstrate the effectiveness of the proposed solution procedure.
Original languageEnglish
Pages (from-to)127-141
Number of pages15
JournalTransportation Research Part B: Methodological
Issue number1
Publication statusPublished - 1 Jan 2009


  • Continuum modeling
  • Eikonal equation
  • Pedestrian flow
  • Reactive dynamic user equilibrium
  • WENO scheme

ASJC Scopus subject areas

  • Transportation

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