IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v79y2015icp149-160.html
   My bibliography  Save this article

Traffic user equilibrium and proportionality

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261515001277
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2015.06.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bar-Gera, Hillel & Hellman, Fredrik & Patriksson, Michael, 2013. "Computational precision of traffic equilibria sensitivities in automatic network design and road pricing," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 485-500.
    2. 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.
    3. 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.
    4. 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.
    5. Roger L. Tobin & Terry L. Friesz, 1988. "Sensitivity Analysis for Equilibrium Network Flow," Transportation Science, INFORMS, vol. 22(4), pages 242-250, November.
    6. Bar-Gera, Hillel, 2010. "Traffic assignment by paired alternative segments," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1022-1046, September.
    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. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Jafari, Ehsan & Boyles, Stephen D., 2016. "Improved bush-based methods for network contraction," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 298-313.
    3. Xie, Chi, 2016. "New insights and improvements of using paired alternative segments for traffic assignmentAuthor-Name: Xie, Jun," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 406-424.
    4. 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.
    5. 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.
    6. Jafari, Ehsan & Pandey, Venktesh & Boyles, Stephen D., 2017. "A decomposition approach to the static traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 270-296.
    7. 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.
    8. Rinaldi, Marco & Tampère, Chris M.J. & Viti, Francesco, 2018. "On characterizing the relationship between route choice behaviour and optimal traffic control solution space," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 892-906.
    9. O'Hare, Steven J. & Connors, Richard D. & Watling, David P., 2016. "Mechanisms that govern how the Price of Anarchy varies with travel demand," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 55-80.
    10. 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.
    11. 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.
    12. David Di Lorenzo & Alessandro Galligari & Marco Sciandrone, 2015. "A convergent and efficient decomposition method for the traffic assignment problem," Computational Optimization and Applications, Springer, vol. 60(1), pages 151-170, January.
    13. Xu, Zhandong & Xie, Jun & Liu, Xiaobo & Nie, Yu (Marco), 2020. "Hyperpath-based algorithms for the transit equilibrium assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    14. Yang Liu & Yu (Marco) Nie, 2017. "A Credit-Based Congestion Management Scheme in General Two-Mode Networks with Multiclass Users," Networks and Spatial Economics, Springer, vol. 17(3), pages 681-711, September.
    15. Liu, Zhiyuan & Chen, Xinyuan & Hu, Jintao & Wang, Shuaian & Zhang, Kai & Zhang, Honggang, 2023. "An alternating direction method of multipliers for solving user equilibrium problem," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1072-1084.
    16. Zhang, Honggang & Liu, Zhiyuan & Wang, Jian & Wu, Yunchi, 2023. "A novel flow update policy in solving traffic assignment problems: Successive over relaxation iteration method," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 174(C).
    17. Michael W. Levin & Melissa Duell & S. Travis Waller, 2020. "Arrival Time Reliability in Strategic User Equilibrium," Networks and Spatial Economics, Springer, vol. 20(3), pages 803-831, September.
    18. Bliemer, Michiel C.J. & Raadsen, Mark P.H. & Smits, Erik-Sander & Zhou, Bojian & Bell, Michael G.H., 2014. "Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 363-384.
    19. Du, Muqing & Chen, Anthony, 2022. "Sensitivity analysis for transit equilibrium assignment and applications to uncertainty analysis," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 175-202.
    20. Liu, Ronghui & Smith, Mike, 2015. "Route choice and traffic signal control: A study of the stability and instability of a new dynamical model of route choice and traffic signal control," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 123-145.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:79:y:2015:i:c:p:149-160. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.