IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v32y1998i2p101-108.html
   My bibliography  Save this article

Some Remarks on Stochastic User Equilibrium

Author

Listed:
  • Hazelton, Martin L.

Abstract

The behavioural foundation of Stochastic User Equilibrium is that each traveller attempts to minimize his or her perceived travel costs, where these costs are composed of a deterministic measured cost and a random term which can be interpreted as perceptual error. In principle such a definition, which is in terms of random errors, should imply an equilibrium probability distribution over feasible flow patterns on the transport network. Such a probability distribution could potentially allow between day variability in network flows to be represented. However, traditionally a deterministic, large sample approximation has been used as the 'solution' of Stochastic User Equilibrium. In this paper a representation of Stochastic User Equilibrium as a probability distribution is developed. This distribution is defined by the conditional route selection of each individual given the choices of all other travellers. An interpretation of the resulting assignment model as the limit (in the infinite future) of a continuous time assignment process is discussed. The limiting behaviour as the travel demand becomes large is also investigated, and convergence to the traditional deterministic form of Stochastic User Equilibrium is proved.

Suggested Citation

  • Hazelton, Martin L., 1998. "Some Remarks on Stochastic User Equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 32(2), pages 101-108, February.
  • Handle: RePEc:eee:transb:v:32:y:1998:i:2:p:101-108
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191-2615(97)00015-5
    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. M. A. P. Taylor, 1982. "Travel Time Variability---The Case of Two Public Modes," Transportation Science, INFORMS, vol. 16(4), pages 507-521, November.
    2. Gary A. Davis & Nancy L. Nihan, 1993. "Large Population Approximations of a General Stochastic Traffic Assignment Model," Operations Research, INFORMS, vol. 41(1), pages 169-178, February.
    3. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    4. Cascetta, Ennio, 1989. "A stochastic process approach to the analysis of temporal dynamics in transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 23(1), pages 1-17, 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. Hazelton, Martin L., 2000. "Estimation of origin-destination matrices from link flows on uncongested networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(7), pages 549-566, September.
    2. Wei, Chong & Asakura, Yasuo & Iryo, Takamasa, 2014. "Formulating the within-day dynamic stochastic traffic assignment problem from a Bayesian perspective," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 45-57.
    3. Henn, Vincent & Ottomanelli, Michele, 2006. "Handling uncertainty in route choice models: From probabilistic to possibilistic approaches," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1526-1538, December.
    4. C. Robin Lindsey & Erik T. Verhoef, 1999. "Congestion Modelling," Tinbergen Institute Discussion Papers 99-091/3, Tinbergen Institute.
    5. Clark, Stephen & Watling, David, 2005. "Modelling network travel time reliability under stochastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 119-140, February.
    6. Martin L. Hazelton & David P. Watling, 2004. "Computation of Equilibrium Distributions of Markov Traffic-Assignment Models," Transportation Science, INFORMS, vol. 38(3), pages 331-342, August.
    7. Hazelton, Martin L., 2010. "Bayesian inference for network-based models with a linear inverse structure," Transportation Research Part B: Methodological, Elsevier, vol. 44(5), pages 674-685, June.
    8. Yin, Yafeng & Yang, Hai, 2003. "Simultaneous determination of the equilibrium market penetration and compliance rate of advanced traveler information systems," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(2), pages 165-181, February.
    9. Xie, Chi & Liu, Zugang, 2014. "On the stochastic network equilibrium with heterogeneous choice inertia," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 90-109.

    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. Paolo Delle Site, 2017. "On the Equivalence Between SUE and Fixed-Point States of Day-to-Day Assignment Processes with Serially-Correlated Route Choice," Networks and Spatial Economics, Springer, vol. 17(3), pages 935-962, September.
    2. He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2010. "A link-based day-to-day traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 597-608, May.
    3. Watling, David P. & Hazelton, Martin L., 2018. "Asymptotic approximations of transient behaviour for day-to-day traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 90-105.
    4. Katharina Parry & David P. Watling & Martin L. Hazelton, 2016. "A new class of doubly stochastic day-to-day dynamic traffic assignment models," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 5-23, March.
    5. Zhu, Zheng & Mardan, Atabak & Zhu, Shanjiang & Yang, Hai, 2021. "Capturing the interaction between travel time reliability and route choice behavior based on the generalized Bayesian traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 143(C), pages 48-64.
    6. Martin L. Hazelton & David P. Watling, 2004. "Computation of Equilibrium Distributions of Markov Traffic-Assignment Models," Transportation Science, INFORMS, vol. 38(3), pages 331-342, August.
    7. Xie, Chi & Liu, Zugang, 2014. "On the stochastic network equilibrium with heterogeneous choice inertia," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 90-109.
    8. Hazelton, Martin L., 2022. "The emergence of stochastic user equilibria in day-to-day traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 102-112.
    9. Hazelton, Martin L., 2002. "Day-to-day variation in Markovian traffic assignment models," Transportation Research Part B: Methodological, Elsevier, vol. 36(7), pages 637-648, August.
    10. David Watling & Giulio Cantarella, 2015. "Model Representation & Decision-Making in an Ever-Changing World: The Role of Stochastic Process Models of Transportation Systems," Networks and Spatial Economics, Springer, vol. 15(3), pages 843-882, September.
    11. David Watling, 2002. "A Second Order Stochastic Network Equilibrium Model, I: Theoretical Foundation," Transportation Science, INFORMS, vol. 36(2), pages 149-166, May.
    12. Rambha, Tarun & Boyles, Stephen D., 2016. "Dynamic pricing in discrete time stochastic day-to-day route choice models," Transportation Research Part B: Methodological, Elsevier, vol. 92(PA), pages 104-118.
    13. Wei Nai & Zan Yang & Dan Li & Lu Liu & Yuting Fu & Yuao Guo, 2024. "Urban Day-to-Day Travel and Its Development in an Information Environment: A Review," Sustainability, MDPI, vol. 16(6), pages 1-29, March.
    14. Wei, Chong & Asakura, Yasuo & Iryo, Takamasa, 2014. "Formulating the within-day dynamic stochastic traffic assignment problem from a Bayesian perspective," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 45-57.
    15. David Watling, 2002. "A Second Order Stochastic Network Equilibrium Model, II: Solution Method and Numerical Experiments," Transportation Science, INFORMS, vol. 36(2), pages 167-183, May.
    16. Sun, Mingmei, 2023. "A day-to-day dynamic model for mixed traffic flow of autonomous vehicles and inertial human-driven vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 173(C).
    17. 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.
    18. Kumar, Amit & Peeta, Srinivas, 2015. "A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 235-256.
    19. Xiaomei Zhao & Chunhua Wan & Jun Bi, 2019. "Day-to-Day Assignment Models and Traffic Dynamics Under Information Provision," Networks and Spatial Economics, Springer, vol. 19(2), pages 473-502, June.
    20. Bie, Jing & Lo, Hong K., 2010. "Stability and attraction domains of traffic equilibria in a day-to-day dynamical system formulation," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 90-107, January.

    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:2:p:101-108. 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.