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Continuum modelling of transportation networks

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  • Dafermos, Stella C.

Abstract

The standard discrete transportation models, which attempt to determine traffic flow on every link of a transportation network, are inapplicable to complex dense urban networks, in view of the amount of computation involved. In this paper we adopt a radically new point of view and construct a family of models based on the assumption of continuous traffic distribution over the network. We derive the flow conservation equations and the equilibrium conditions for user-optimized and system-optimized networks.

Suggested Citation

  • Dafermos, Stella C., 1980. "Continuum modelling of transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 14(3), pages 295-301, September.
    • Handle: RePEc:eee:transb:v:14:y:1980:i:3:p:295-301
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    Cited by:

    1. Richard Connors & David Watling, 2015. "Assessing the Demand Vulnerability of Equilibrium Traffic Networks via Network Aggregation," Networks and Spatial Economics, Springer, vol. 15(2), pages 367-395, June.
    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. David Watling & Giulio Cantarella, 2015. "Model Representation & Decision-Making in an Ever-Changing World: The Role of Stochastic Process Models of Transportation Systems," Networks and Spatial Economics, Springer, vol. 15(3), pages 843-882, September.
    4. Jiang, Yanqun & Wong, S.C. & Ho, H.W. & Zhang, Peng & Liu, Ruxun & Sumalee, Agachai, 2011. "A dynamic traffic assignment model for a continuum transportation system," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 343-363, February.
    5. Al-deek, Haitham M. & Kanafani, Adib K., 1989. "Some Theoretical Aspects Of The Benefits Of En-route Vehicle Guidance (ervg)," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt0c83x3gr, Institute of Transportation Studies, UC Berkeley.
    6. Du, Jie & Wong, S.C. & Shu, Chi-Wang & Xiong, Tao & Zhang, Mengping & Choi, Keechoo, 2013. "Revisiting Jiang’s dynamic continuum model for urban cities," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 96-119.
    7. 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.
    8. Hai Yang & S. C. Wong, 2000. "A Continuous Equilibrium Model for Estimating Market Areas of Competitive Facilities with Elastic Demand and Market Externality," Transportation Science, INFORMS, vol. 34(2), pages 216-227, May.

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