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

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  • Huang, Ling
  • Wong, S.C.
  • Zhang, Mengping
  • Shu, Chi-Wang
  • Lam, William H.K.

Abstract

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.

Suggested Citation

  • Huang, Ling & Wong, S.C. & Zhang, Mengping & Shu, Chi-Wang & Lam, William H.K., 2009. "Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 127-141, January.
    • Handle: RePEc:eee:transb:v:43:y:2009:i:1:p:127-141
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    References listed on IDEAS

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    1. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    2. Ho, H.W. & Wong, S.C. & Loo, Becky P.Y., 2006. "Combined distribution and assignment model for a continuum traffic equilibrium problem with multiple user classes," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 633-650, September.
    3. William Lam & Jodie Lee & C. Cheung, 2002. "A study of the bi-directional pedestrian flow characteristics at Hong Kong signalized crosswalk facilities," Transportation, Springer, vol. 29(2), pages 169-192, May.
    4. Lam, William H. K. & Cheung, Chung-Yu & Lam, C. F., 1999. "A study of crowding effects at the Hong Kong light rail transit stations," Transportation Research Part A: Policy and Practice, Elsevier, vol. 33(5), pages 401-415, June.
    5. Lam, William H. K. & Lee, Jodie Y. S. & Chan, K. S. & Goh, P. K., 2003. "A generalised function for modeling bi-directional flow effects on indoor walkways in Hong Kong," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(9), pages 789-810, November.
    6. Hughes, Roger L., 2002. "A continuum theory for the flow of pedestrians," Transportation Research Part B: Methodological, Elsevier, vol. 36(6), pages 507-535, July.
    7. Tong, C. O. & Wong, S. C., 2000. "A predictive dynamic traffic assignment model in congested capacity-constrained road networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(8), pages 625-644, November.
    8. Wong, S. C., 1994. "An alternative formulation of D'Este's trip assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 28(3), pages 187-196, June.
    9. Hoogendoorn, S. P. & Bovy, P. H. L., 2004. "Pedestrian route-choice and activity scheduling theory and models," Transportation Research Part B: Methodological, Elsevier, vol. 38(2), pages 169-190, February.
    10. Shokri Z. Selim & Ala H. Al-Rabeh, 1991. "On the Modeling of Pedestrian Flow on the Jamarat Bridge," Transportation Science, INFORMS, vol. 25(4), pages 257-263, November.
    11. Lam, W.H.K. & Tam, Mei-ling & Wong, S.C. & Wirasinghe, S.C., 2003. "Wayfinding in the passenger terminal of Hong Kong International Airport," Journal of Air Transport Management, Elsevier, vol. 9(2), pages 73-81.
    12. Wong, S. C., 1998. "Multi-commodity traffic assignment by continuum approximation of network flow with variable demand," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 567-581, November.
    13. S. C. Wong & S. H. Sun, 2001. "A combined distribution and assignment model for continuous facility location problem," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 35(2), pages 267-281.
    14. Dirk Helbing & Lubos Buzna & Anders Johansson & Torsten Werner, 2005. "Self-Organized Pedestrian Crowd Dynamics: Experiments, Simulations, and Design Solutions," Transportation Science, INFORMS, vol. 39(1), pages 1-24, February.
    15. Ho, H.W. & Wong, S.C. & Yang, Hai & Loo, Becky P.Y., 2005. "Cordon-based congestion pricing in a continuum traffic equilibrium system," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 813-834.
    16. Hoogendoorn, Serge P. & Bovy, Piet H. L., 2004. "Dynamic user-optimal assignment in continuous time and space," Transportation Research Part B: Methodological, Elsevier, vol. 38(7), pages 571-592, August.
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