IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v33y1999i8p609-616.html
   My bibliography  Save this article

On the convergence of Bell's logit assignment formulation

Author

Listed:
  • Wong, S. C.

Abstract

In Bell M.G.H. (1995. Transportation Research B 29, 287-295), a new logit assignment formulation was developed, which considered all possible paths in the network while still retaining the absence of a need for path enumeration. In his formulation, it presumes that the sum of a geometric series of the weights matrix always converges and hence can be computed as the inversion of a matrix. In this paper, we investigate the convergence properties of this geometric series by means of an eigensystem interpretation which states that the series converges if and only if all the eigenvalues associated with the weights matrix fall into the unit circle in a complex plane. It is found that the geometric series converges unconditionally for acyclic networks, but not necessarily does so for general networks.

Suggested Citation

  • Wong, S. C., 1999. "On the convergence of Bell's logit assignment formulation," Transportation Research Part B: Methodological, Elsevier, vol. 33(8), pages 609-616, November.
    • Handle: RePEc:eee:transb:v:33:y:1999:i:8:p:609-616
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191-2615(99)00015-6
    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. Warren B. Powell & Yosef Sheffi, 1982. "The Convergence of Equilibrium Algorithms with Predetermined Step Sizes," Transportation Science, INFORMS, vol. 16(1), pages 45-55, February.
    2. 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.
    3. Akamatsu, Takashi, 1996. "Cyclic flows, Markov process and stochastic traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 369-386, October.
    4. Van Vliet, Dirck, 1981. "Selected node-pair analysis in dial's assignment algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 15(1), pages 65-68, February.
    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. Lo, Hing-Po & Chan, Chi-Pak, 2003. "Simultaneous estimation of an origin-destination matrix and link choice proportions using traffic counts," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(9), pages 771-788, November.

    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. Long, Jiancheng & Szeto, W.Y. & Huang, Hai-Jun, 2014. "A bi-objective turning restriction design problem in urban road networks," European Journal of Operational Research, Elsevier, vol. 237(2), pages 426-439.
    2. 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.
    3. 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.
    4. Bell, Michael G. H., 1995. "Alternatives to Dial's logit assignment algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 287-295, August.
    5. Oyama, Yuki & Hato, Eiji, 2019. "Prism-based path set restriction for solving Markovian traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 528-546.
    6. Huang, Hai-Jun & Li, Zhi-Chun, 2007. "A multiclass, multicriteria logit-based traffic equilibrium assignment model under ATIS," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1464-1477, February.
    7. Lo, Hing-Po & Chan, Chi-Pak, 2003. "Simultaneous estimation of an origin-destination matrix and link choice proportions using traffic counts," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(9), pages 771-788, November.
    8. Akamatsu, Takashi, 1996. "Cyclic flows, Markov process and stochastic traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 369-386, October.
    9. Selin Damla Ahipaşaoğlu & Uğur Arıkan & Karthik Natarajan, 2019. "Distributionally Robust Markovian Traffic Equilibrium," Transportation Science, INFORMS, vol. 53(6), pages 1546-1562, November.
    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. 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.
    12. Mogens Fosgerau & Mads Paulsen & Thomas Kj{ae}r Rasmussen, 2021. "A perturbed utility route choice model," Papers 2103.13784, arXiv.org, revised Sep 2021.
    13. Maria Mitradjieva & Per Olov Lindberg, 2013. "The Stiff Is Moving---Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment ," Transportation Science, INFORMS, vol. 47(2), pages 280-293, May.
    14. Maher, Mike, 1998. "Algorithms for logit-based stochastic user equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 539-549, November.
    15. Zhu, Daoli & Marcotte, Patrice, 1995. "Coupling the auxiliary problem principle with descent methods of pseudoconvex programming," European Journal of Operational Research, Elsevier, vol. 83(3), pages 670-685, June.
    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. Fosgerau, Mogens & Frejinger, Emma & Karlstrom, Anders, 2013. "A link based network route choice model with unrestricted choice set," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 70-80.
    18. Feng Xie & David Levinson, 2009. "Jurisdictional Control and Network Growth," Networks and Spatial Economics, Springer, vol. 9(3), pages 459-483, September.
    19. Andrea Raith & Judith Wang & Matthias Ehrgott & Stuart Mitchell, 2014. "Solving multi-objective traffic assignment," Annals of Operations Research, Springer, vol. 222(1), pages 483-516, November.
    20. Farahani, Reza Zanjirani & Miandoabchi, Elnaz & Szeto, W.Y. & Rashidi, Hannaneh, 2013. "A review of urban transportation network design problems," European Journal of Operational Research, Elsevier, vol. 229(2), pages 281-302.

    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:33:y:1999:i:8:p:609-616. 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.