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Bounding the inefficiency of logit-based stochastic user equilibrium

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  • 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
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    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. 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.
    4. 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.
    5. 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.
    6. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    7. 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.
    8. Hai Yang, 1999. "System Optimum, Stochastic User Equilibrium, and Optimal Link Tolls," Transportation Science, INFORMS, vol. 33(4), pages 354-360, November.
    9. 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.
    10. 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.
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    Cited by:

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    2. 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.
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.

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