IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v32y1998i8p539-549.html
   My bibliography  Save this article

Algorithms for logit-based stochastic user equilibrium assignment

Author

Listed:
  • Maher, Mike

Abstract

The paper proposes an efficient algorithm for determining the stochastic user equilibrium solution for logit-based loading. The commonly used Method of Successive Averages typically has a very slow convergence rate. The new algorithm described here uses Williams' result [ Williams, (1977) On the formation of travel demand models and economic evaluation measures of user benefit. Environment and Planning 9A(3), 285-344] which enables the expected value of the perceived travel costs Srs to be readily calculated for any flow vector x. This enables the value of the Sheffi and Powell, 1982 objective function [Sheffi, Y. and Powell, W. B. (1982) An algorithm for the equilibrium assignment problem with random link times. Networks 12(2), 191-207], and its gradient in any specified search direction, to be calculated. It is then shown how, at each iteration, an optimal step length along the search direction can be easily estimated, rather than using the pre-set step lengths, thus giving much faster convergence. The basic algorithm uses the standard search direction (towards the auxiliary solution). In addition the performance of two further versions of the algorithm are investigated, both of which use an optimal step length but alternative search directions, based on the Davidon-Fletcher-Powell function minimisation method. The first is an unconstrained and the second a constrained version. Comparisons are made of all three versions of the algorithm, using a number of test networks ranging from a simple three-link network to one with almost 3000 links. It is found that for all but the smallest network the version using the standard search direction gives the fastest rate of convergence. Extensions to allow for multiple user classes and elastic demand are also possible.

Suggested Citation

  • Maher, Mike, 1998. "Algorithms for logit-based stochastic user equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 539-549, November.
  • Handle: RePEc:eee:transb:v:32:y:1998:i:8:p:539-549
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191-2615(98)00015-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Fisk, Caroline, 1980. "Some developments in equilibrium traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 14(3), pages 243-255, September.
    2. Mingyuan Chen & Attahiru Sule Alfa, 1991. "Algorithms for solving fisk's stochastic traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 25(6), pages 405-412, December.
    3. Leurent, Fabien M., 1997. "Curbing the computational difficulty of the logit equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 315-326, August.
    4. H C W L Williams, 1977. "On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit," Environment and Planning A, , vol. 9(3), pages 285-344, March.
    5. Akamatsu, Takashi, 1996. "Cyclic flows, Markov process and stochastic traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 369-386, October.
    6. Larry J. Leblanc, 1975. "An Algorithm for the Discrete Network Design Problem," Transportation Science, INFORMS, vol. 9(3), pages 183-199, August.
    7. Maher, M. J. & Hughes, P. C., 1997. "A probit-based stochastic user equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 341-355, August.
    Full references (including those not matched with items on IDEAS)

    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. Xie, Chi & Travis Waller, S., 2012. "Stochastic traffic assignment, Lagrangian dual, and unconstrained convex optimization," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1023-1042.
    2. Ahipaşaoğlu, Selin Damla & Meskarian, Rudabeh & Magnanti, Thomas L. & Natarajan, Karthik, 2015. "Beyond normality: A cross moment-stochastic user equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 333-354.
    3. Oyama, Yuki & Hara, Yusuke & Akamatsu, Takashi, 2022. "Markovian traffic equilibrium assignment based on network generalized extreme value model," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 135-159.
    4. Bekhor, Shlomo & Toledo, Tomer, 2005. "Investigating path-based solution algorithms to the stochastic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 39(3), pages 279-295, March.
    5. Zhou, Bojian & Li, Xuhong & He, Jie, 2014. "Exploring trust region method for the solution of logit-based stochastic user equilibrium problem," European Journal of Operational Research, Elsevier, vol. 239(1), pages 46-57.
    6. Han, Sangjin, 2003. "Dynamic traffic modelling and dynamic stochastic user equilibrium assignment for general road networks," Transportation Research Part B: Methodological, Elsevier, vol. 37(3), pages 225-249, March.
    7. Maher, M. J. & Hughes, P. C., 1997. "A probit-based stochastic user equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 341-355, August.
    8. Chen, Anthony & Pravinvongvuth, Surachet & Xu, Xiangdong & Ryu, Seungkyu & Chootinan, Piya, 2012. "Examining the scaling effect and overlapping problem in logit-based stochastic user equilibrium models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(8), pages 1343-1358.
    9. Huang, Hai-Jun & Bell, Michael G. H., 1998. "A study on logit assignment which excludes all cyclic flows," Transportation Research Part B: Methodological, Elsevier, vol. 32(6), pages 401-412, August.
    10. Guido Gentile, 2018. "New Formulations of the Stochastic User Equilibrium with Logit Route Choice as an Extension of the Deterministic Model," Service Science, INFORMS, vol. 52(6), pages 1531-1547, December.
    11. Watling, David Paul & Rasmussen, Thomas Kjær & Prato, Carlo Giacomo & Nielsen, Otto Anker, 2015. "Stochastic user equilibrium with equilibrated choice sets: Part I – Model formulations under alternative distributions and restrictions," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 166-181.
    12. Rasmussen, Thomas Kjær & Watling, David Paul & Prato, Carlo Giacomo & Nielsen, Otto Anker, 2015. "Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 146-165.
    13. Tan, Heqing & Xu, Xiangdong & Chen, Anthony, 2024. "On endogenously distinguishing inactive paths in stochastic user equilibrium: A convex programming approach with a truncated path choice model," Transportation Research Part B: Methodological, Elsevier, vol. 183(C).
    14. Leurent, Fabien M., 1997. "Curbing the computational difficulty of the logit equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 315-326, August.
    15. E. Nikolova & N. E. Stier-Moses, 2014. "A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times," Operations Research, INFORMS, vol. 62(2), pages 366-382, April.
    16. Castillo, Enrique & Menéndez, José María & Sánchez-Cambronero, Santos, 2008. "Predicting traffic flow using Bayesian networks," Transportation Research Part B: Methodological, Elsevier, vol. 42(5), pages 482-509, June.
    17. Du, Muqing & Tan, Heqing & Chen, Anthony, 2021. "A faster path-based algorithm with Barzilai-Borwein step size for solving stochastic traffic equilibrium models," European Journal of Operational Research, Elsevier, vol. 290(3), pages 982-999.
    18. Jiayang Li & Zhaoran Wang & Yu Marco Nie, 2023. "Wardrop Equilibrium Can Be Boundedly Rational: A New Behavioral Theory of Route Choice," Papers 2304.02500, arXiv.org, revised Feb 2024.
    19. Honggang Zhang & Zhiyuan Liu & Yicheng Zhang & Weijie Chen & Chenyang Zhang, 2024. "A Distributed Computing Method Integrating Improved Gradient Projection for Solving Stochastic Traffic Equilibrium Problem," Networks and Spatial Economics, Springer, vol. 24(2), pages 361-381, June.
    20. Kitthamkesorn, Songyot & Chen, Anthony, 2013. "A path-size weibit stochastic user equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 378-397.

    More about this item

    Statistics

    Access and download statistics

    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:32:y:1998:i:8:p:539-549. 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.