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Some observations on stochastic user equilibrium and system optimum of traffic assignment

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  • Prashker, Joseph N.
  • Bekhor, Shlomo

Abstract

Traffic assignment models can be classified according to the behavioral assumption governing route choice. The deterministic user equilibrium (UE), stochastic user equilibrium (SUE) and system optimum (SO) models have been studied extensively in the literature. The relationship between the UE solution and the SO solution for a given network is well known, as is the relationship between UE and SUE. The question that arises concerns the relationship between SUE and (deterministic) SO. The flow pattern obtained from the SO solution serves as a yardstick for comparison with the flow patterns obtained from the UE and SUE solutions. The investigation examines whether the stochastic equilibrium is "closer" than the deterministic user equilibrium to the system optimum. This paper compares the performance of the different solutions for simple networks. The comparison is made by evaluating the relative difference in total system times for UE and SUE solutions with respect to the SO solution. This paper also presents an extension of previous results to show that the Braess' paradox can occur for certain ranges of demand volumes in the case of stochastic equilibrium and non-linear cost functions.

Suggested Citation

  • Prashker, Joseph N. & Bekhor, Shlomo, 2000. "Some observations on stochastic user equilibrium and system optimum of traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 34(4), pages 277-291, May.
    • Handle: RePEc:eee:transb:v:34:y:2000:i:4:p:277-291
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    References listed on IDEAS

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    1. 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.
    2. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    3. Pas, Eric I. & Principio, Shari L., 1997. "Braess' paradox: Some new insights," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 265-276, June.
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    Cited by:

    1. Konrad, Kai A., 2003. "Mobilität in mehrstufigen Ausbildungsturnieren [Mobility in Multi-Stage Education Systems]," Discussion Papers, Research Unit: Market Processes and Governance SP II 2003-30, WZB Berlin Social Science Center.
    2. Xiao Chen & Carolina Osorio & Bruno Filipe Santos, 2019. "Simulation-Based Travel Time Reliable Signal Control," Transportation Science, INFORMS, vol. 53(2), pages 523-544, March.
    3. 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.
    4. He, Zhidong & Navneet, Kumar & van Dam, Wirdmer & Van Mieghem, Piet, 2021. "Robustness assessment of multimodal freight transport networks," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    5. Caixia Li & Sreenatha Gopalarao Anavatti & Tapabrata Ray, 2017. "A Path-Based Solution Algorithm for Dynamic Traffic Assignment," Networks and Spatial Economics, Springer, vol. 17(3), pages 841-860, September.
    6. Di, Xuan & He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2014. "Braess paradox under the boundedly rational user equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 86-108.
    7. Castillo, Enrique & Menéndez, José María & Jiménez, Pilar & Rivas, Ana, 2008. "Closed form expressions for choice probabilities in the Weibull case," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 373-380, May.
    8. Yao, Jia & Huang, Wenhua & Chen, Anthony & Cheng, Zhanhong & An, Shi & Xu, Guangming, 2019. "Paradox links can improve system efficiency: An illustration in traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 35-49.
    9. 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.
    10. Haddad, Jack & Ramezani, Mohsen & Geroliminis, Nikolas, 2013. "Cooperative traffic control of a mixed network with two urban regions and a freeway," Transportation Research Part B: Methodological, Elsevier, vol. 54(C), pages 17-36.
    11. MacGregor Smith, J. & Cruz, F.R.B., 2014. "M/G/c/c state dependent travel time models and properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 560-579.
    12. Cruz, F.R.B. & van Woensel, T. & MacGregor Smith, J. & Lieckens, K., 2010. "On the system optimum of traffic assignment in M/G/c/c state-dependent queueing networks," European Journal of Operational Research, Elsevier, vol. 201(1), pages 183-193, February.
    13. Liu, Ke & Liu, Yanli, 2023. "Stochastic user equilibrium based spatial-temporal distribution prediction of electric vehicle charging load," Applied Energy, Elsevier, vol. 339(C).

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