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Traffic user equilibrium and proportionality

Author

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  • Borchers, Marlies
  • Breeuwsma, Paul
  • Kern, Walter
  • Slootbeek, Jaap
  • Still, Georg
  • Tibben, Wouter

Abstract

We discuss the problem of proportionality and uniqueness for route flows in the classical traffic user equilibrium model. It is well-known that under appropriate assumptions the user equilibrium (f,x) is unique in the link flow x but typically not in the route flow f. We consider the concept of proportionality in detail and re-discuss the well-known relation between the so-called bypass proportionality and entropy maximization. We exhibit special proportionality conditions which uniquely determine the route flow f. The results are illustrated with some simple example networks.

Suggested Citation

  • Borchers, Marlies & Breeuwsma, Paul & Kern, Walter & Slootbeek, Jaap & Still, Georg & Tibben, Wouter, 2015. "Traffic user equilibrium and proportionality," Transportation Research Part B: Methodological, Elsevier, vol. 79(C), pages 149-160.
    • Handle: RePEc:eee:transb:v:79:y:2015:i:c:p:149-160
    DOI: 10.1016/j.trb.2015.06.004
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    References listed on IDEAS

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    1. Nie, Yu (Marco), 2010. "A class of bush-based algorithms for the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 73-89, January.
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    3. Bar-Gera, Hillel & Boyce, David & Nie, Yu (Marco), 2012. "User-equilibrium route flows and the condition of proportionality," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 440-462.
    4. Hillel Bar-Gera, 2006. "Primal Method for Determining the Most Likely Route Flows in Large Road Networks," Transportation Science, INFORMS, vol. 40(3), pages 269-286, August.
    5. Kumar, Amit & Peeta, Srinivas, 2015. "Entropy weighted average method for the determination of a single representative path flow solution for the static user equilibrium traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 213-229.
    6. Roger L. Tobin & Terry L. Friesz, 1988. "Sensitivity Analysis for Equilibrium Network Flow," Transportation Science, INFORMS, vol. 22(4), pages 242-250, November.
    7. Florian, Michael & Morosan, Calin D., 2014. "On uniqueness and proportionality in multi-class equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 173-185.
    8. Bar-Gera, Hillel, 2010. "Traffic assignment by paired alternative segments," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1022-1046, September.
    9. Lu, Shu & (Marco) Nie, Yu, 2010. "Stability of user-equilibrium route flow solutions for the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 609-617, May.
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    Citations

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    Cited by:

    1. Jun Xie & Yu (Marco) Nie, 2019. "A New Algorithm for Achieving Proportionality in User Equilibrium Traffic Assignment," Transportation Science, INFORMS, vol. 53(2), pages 566-584, March.
    2. Xie, Jun & (Marco) Nie, Yu & Liu, Xiaobo, 2017. "Testing the proportionality condition with taxi trajectory data," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 583-601.
    3. Jiayang Li & Qianni Wang & Liyang Feng & Jun Xie & Yu Marco Nie, 2024. "A Day-to-Day Dynamical Approach to the Most Likely User Equilibrium Problem," Papers 2401.08013, arXiv.org.
    4. Eikenbroek, Oskar A.L. & Still, Georg J. & van Berkum, Eric C. & Kern, Walter, 2018. "The Boundedly Rational User Equilibrium: A parametric analysis with application to the Network Design Problem," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 1-17.
    5. Cominetti, Roberto & Dose, Valerio & Scarsini, Marco, 2024. "Monotonicity of equilibria in nonatomic congestion games," European Journal of Operational Research, Elsevier, vol. 316(2), pages 754-766.

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