IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v201y2010i2p463-469.html
   My bibliography  Save this article

Bounding the inefficiency of logit-based stochastic user equilibrium

Author

Listed:
  • Guo, Xiaolei
  • Yang, Hai
  • Liu, Tian-Liang

Abstract

Bounding the inefficiency of selfish routing has become an emerging research subject. A central result obtained in the literature is that the inefficiency of deterministic User Equilibrium (UE) is bounded and the bound is independent of network topology. This paper makes a contribution to the literature by bounding the inefficiency of the logit-based Stochastic User Equilibrium (SUE). In a stochastic environment there are two different definitions of system optimization: one is the traditional System Optimum (SO) which minimizes the total actual system travel time, and the other is the Stochastic System Optimum (SSO) which minimizes the total perceived travel time of all users. Thus there are two ways to define the inefficiency of SUE, i.e. to compare SUE with SO in terms of total actual system travel time, or to compare SUE with SSO in terms of total perceived travel time. We establish upper bounds on the inefficiency of SUE in both situations.

Suggested Citation

  • Guo, Xiaolei & Yang, Hai & Liu, Tian-Liang, 2010. "Bounding the inefficiency of logit-based stochastic user equilibrium," European Journal of Operational Research, Elsevier, vol. 201(2), pages 463-469, March.
    • Handle: RePEc:eee:ejores:v:201:y:2010:i:2:p:463-469
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(09)00192-1
    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. Stewart, Kathryn, 2007. "Tolling traffic links under stochastic assignment: Modelling the relationship between the number and price level of tolled links and optimal traffic flows," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(7), pages 644-654, August.
    3. Roughgarden, Tim & Tardos, Eva, 2004. "Bounding the inefficiency of equilibria in nonatomic congestion games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 389-403, May.
    4. Han, Deren & Yang, Hai, 2008. "The multi-class, multi-criterion traffic equilibrium and the efficiency of congestion pricing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(5), pages 753-773, September.
    5. Han, Deren & Lo, Hong K. & Sun, Jie & Yang, Hai, 2008. "The toll effect on price of anarchy when costs are nonlinear and asymmetric," European Journal of Operational Research, Elsevier, vol. 186(1), pages 300-316, April.
    6. Maher, Mike & Stewart, Kathryn & Rosa, Andrea, 2005. "Stochastic social optimum traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 39(8), pages 753-767, September.
    7. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    8. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    9. Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
    10. Hai Yang, 1999. "System Optimum, Stochastic User Equilibrium, and Optimal Link Tolls," Transportation Science, INFORMS, vol. 33(4), pages 354-360, November.
    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. Liu, Tian-Liang & Chen, Jian & Huang, Hai-Jun, 2011. "Existence and efficiency of oligopoly equilibrium under toll and capacity competition," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 908-919.
    2. Hai-Jun Huang & Tian-Liang Liu & Xiaolei Guo & Hai Yang, 2011. "Inefficiency of Logit-Based Stochastic User Equilibrium in a Traffic Network Under ATIS," Networks and Spatial Economics, Springer, vol. 11(2), pages 255-269, June.
    3. Anny B. Wang & W. Y. Szeto, 2020. "Bounding the Inefficiency of the Reliability-Based Continuous Network Design Problem Under Cost Recovery," Networks and Spatial Economics, Springer, vol. 20(2), pages 395-422, June.
    4. 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.
    5. Jie Ma & Lin Cheng & Dawei Li & Qiang Tu, 2018. "Stochastic Electric Vehicle Network Considering Environmental Costs," Sustainability, MDPI, vol. 10(8), pages 1-16, August.
    6. 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.
    7. Qiang Tu & Lin Cheng & Dawei Li & Jie Ma & Chao Sun, 2018. "Stochastic Transportation Network Considering ATIS with the Information of Environmental Cost," Sustainability, MDPI, vol. 10(11), pages 1-16, October.
    8. 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.
    9. Qi, Jin & Sim, Melvyn & Sun, Defeng & Yuan, Xiaoming, 2016. "Preferences for travel time under risk and ambiguity: Implications in path selection and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 264-284.
    10. Wang, Chenlan & Doan, Xuan Vinh & Chen, Bo, 2014. "Price of anarchy for non-atomic congestion games with stochastic demands," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 90-111.
    11. Harks, Tobias & Schröder, Marc & Vermeulen, Dries, 2019. "Toll caps in privatized road networks," European Journal of Operational Research, Elsevier, vol. 276(3), pages 947-956.
    12. Yuxin He & Jin Qin & Jian Hong, 2017. "Comparative analysis of quantitative efficiency evaluation methods for transportation networks," PLOS ONE, Public Library of Science, vol. 12(4), pages 1-14, April.

    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. 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.
    2. Zijun Wu & Rolf H. Moehring & Chunying Ren & Dachuan Xu, 2020. "A convergence analysis of the price of anarchy in atomic congestion games," Papers 2007.14769, arXiv.org, revised Dec 2021.
    3. Hai-Jun Huang & Tian-Liang Liu & Xiaolei Guo & Hai Yang, 2011. "Inefficiency of Logit-Based Stochastic User Equilibrium in a Traffic Network Under ATIS," Networks and Spatial Economics, Springer, vol. 11(2), pages 255-269, June.
    4. 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.
    5. Knight, Vincent A. & Harper, Paul R., 2013. "Selfish routing in public services," European Journal of Operational Research, Elsevier, vol. 230(1), pages 122-132.
    6. Qi, Jin & Sim, Melvyn & Sun, Defeng & Yuan, Xiaoming, 2016. "Preferences for travel time under risk and ambiguity: Implications in path selection and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 264-284.
    7. Koster, Paul & Verhoef, Erik & Shepherd, Simon & Watling, David, 2018. "Preference heterogeneity and congestion pricing: The two route case revisited," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 137-157.
    8. 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.
    9. Georgia Perakis, 2007. "The “Price of Anarchy” Under Nonlinear and Asymmetric Costs," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 614-628, 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. Paul Koster & Erik T. Verhoef & Simon Shepherd & David Watling, 2014. "Probabilistic Choice and Congestion Pricing with Heterogeneous Travellers and Price-Sensitive Demand," Tinbergen Institute Discussion Papers 14-078/VIII, Tinbergen Institute, revised 13 Nov 2014.
    12. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    13. Zijun Wu & Rolf H. Möhring & Yanyan Chen & Dachuan Xu, 2021. "Selfishness Need Not Be Bad," Operations Research, INFORMS, vol. 69(2), pages 410-435, March.
    14. 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).
    15. Younes Hamdouch & Siriphong Lawphongpanich, 2010. "Congestion Pricing for Schedule-Based Transit Networks," Transportation Science, INFORMS, vol. 44(3), pages 350-366, August.
    16. Vincenzo Bonifaci & Tobias Harks & Guido Schäfer, 2010. "Stackelberg Routing in Arbitrary Networks," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 330-346, May.
    17. José R. Correa & Nicolás Figueroa & Nicolás E. Stier-Moses, 2008. "Pricing with markups in industries with increasing marginal costs," Documentos de Trabajo 256, Centro de Economía Aplicada, Universidad de Chile.
    18. Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Documents de travail du Centre d'Economie de la Sorbonne 14033, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    19. Jiang, Chenming & Bhat, Chandra R. & Lam, William H.K., 2020. "A bibliometric overview of Transportation Research Part B: Methodological in the past forty years (1979–2019)," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 268-291.
    20. 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.

    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:ejores:v:201:y:2010:i:2:p:463-469. 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/locate/eor .

    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.