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Non-unique flows in macroscopic first-order intersection models


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  • Corthout, Ruben
  • Flötteröd, Gunnar
  • Viti, Francesco
  • Tampère, Chris M.J.
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    Currently, most intersection models embedded in macroscopic Dynamic Network Loading (DNL) models are not well suited for urban and regional applications. This is so because so-called internal supply constraints, bounding flows due to crossing and merging conflicts inherent to the intersection itself, are missing. This paper discusses the problems that arise upon introducing such constraints. A general framework for the distribution of (internal) supply is adopted, which is based on the definition of priority parameters that describe the strength of each flow in the competition for a particular supply. Using this representation, it is shown that intersection models – with realistic behavioral assumptions, and in simple configurations – can produce non-unique flow patterns under identical boundary conditions. This solution non-uniqueness is thoroughly discussed and approaches on how it can be dealt with are provided. Also, it is revealed that the undesirable model properties are not solved – but rather enhanced – when diverting from a point-like to a spatial modeling approach.

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    Bibliographic Info

    Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

    Volume (Year): 46 (2012)
    Issue (Month): 3 ()
    Pages: 343-359

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    Handle: RePEc:eee:transb:v:46:y:2012:i:3:p:343-359

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    Keywords: Dynamic Network Loading; First-order macroscopic intersection model; Internal supply constraints; Priority parameters; Solution non-uniqueness;


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    1. Chevallier, Estelle & Leclercq, Ludovic, 2007. "A macroscopic theory for unsignalized intersections," Transportation Research Part B: Methodological, Elsevier, vol. 41(10), pages 1139-1150, December.
    2. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    3. Sumalee, A. & Zhong, R.X. & Pan, T.L. & Szeto, W.Y., 2011. "Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 507-533, March.
    4. Carey, Malachy, 1992. "Nonconvexity of the dynamic traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 26(2), pages 127-133, April.
    5. Flötteröd, Gunnar & Rohde, Jannis, 2011. "Operational macroscopic modeling of complex urban road intersections," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 903-922, July.
    6. Troutbeck, Rod J. & Kako, Soichiro, 1999. "Limited priority merge at unsignalized intersections," Transportation Research Part A: Policy and Practice, Elsevier, vol. 33(3-4), pages 291-304, April.
    7. Tampère, Chris M.J. & Corthout, Ruben & Cattrysse, Dirk & Immers, Lambertus H., 2011. "A generic class of first order node models for dynamic macroscopic simulation of traffic flows," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 289-309, January.
    8. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: basic theory and complex boundary conditions," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 187-196, February.
    9. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: Solution methods," Transportation Research Part B: Methodological, Elsevier, vol. 39(10), pages 934-950, December.
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