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Sensitivity Analysis for Stochastic User Equilibrium Network Flows—A Dual Approach

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  • Jiang Qian Ying

    (Faculty of Regional Studies, Gifu University, Yanagido, Gifu, 501, Japan)

  • Toshihiko Miyagi

    (Faculty of Regional Studies, Gifu University, Yanagido, Gifu, 501, Japan)

Abstract

Recently, extensive studies have been conducted on the computational methods of sensitivity analysis for the Wardropian equilibrium modeling of traffic networks and their applications. But the same problems in the context of the stochastic user equilibrium modeling seem not to have been addressed. In this paper, we present a method for sensitivity analysis for network flows at stochastic user equilibrium. Our method is developed from a dual formulation of the stochastic user equilibrium analysis. By adopting Dial's algorithm for stochastic traffic assignment, we are able to formulate a computationally efficient link-based algorithm for the sensitivity analysis. Since the Wardropian equilibrium in a traffic network is an extreme case of stochastic user equilibrium with θ → ∞, θ being a dispersion parameter in the expected utility function for stochastic route choice, the method presented here can also be used for sensitivity analysis of the Wardropian equilibrium by setting θ large enough.

Suggested Citation

  • Jiang Qian Ying & Toshihiko Miyagi, 2001. "Sensitivity Analysis for Stochastic User Equilibrium Network Flows—A Dual Approach," Transportation Science, INFORMS, vol. 35(2), pages 124-133, May.
    • Handle: RePEc:inm:ortrsc:v:35:y:2001:i:2:p:124-133
    DOI: 10.1287/trsc.35.2.124.10137
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    References listed on IDEAS

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    1. Yan, Hai & Lam, William H. K., 1996. "Optimal road tolls under conditions of queueing and congestion," Transportation Research Part A: Policy and Practice, Elsevier, vol. 30(5), pages 319-332, September.
    2. Yang, Hai & Bell, Michael G. H., 1997. "Traffic restraint, road pricing and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 303-314, August.
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    Cited by:

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    2. Rinaldi, Marco & Tampère, Chris M.J. & Viti, Francesco, 2018. "On characterizing the relationship between route choice behaviour and optimal traffic control solution space," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 892-906.
    3. 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.
    4. Ying, Jiang Qian, 2024. "Optimization of regulation and fiscal policies for urban residential land use and traffic network management," Regional Science and Urban Economics, Elsevier, vol. 105(C).
    5. Jiang Ying, 2005. "Sensitivity Analysis Based Method for Optimal Road Network Pricing," Annals of Operations Research, Springer, vol. 133(1), pages 303-317, January.
    6. François Gilbert & Patrice Marcotte & Gilles Savard, 2015. "A Numerical Study of the Logit Network Pricing Problem," Transportation Science, INFORMS, vol. 49(3), pages 706-719, August.
    7. Jiang Qian Ying, 2015. "Optimization for Multiclass Residential Location Models with Congestible Transportation Networks," Transportation Science, INFORMS, vol. 49(3), pages 452-471, August.
    8. Michael Patriksson, 2004. "Sensitivity Analysis of Traffic Equilibria," Transportation Science, INFORMS, vol. 38(3), pages 258-281, August.
    9. Sun, S. & Szeto, W.Y., 2019. "Optimal sectional fare and frequency settings for transit networks with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 147-177.
    10. Huo, Jinbiao & Liu, Zhiyuan & Chen, Jingxu & Cheng, Qixiu & Meng, Qiang, 2023. "Bayesian optimization for congestion pricing problems: A general framework and its instability," Transportation Research Part B: Methodological, Elsevier, vol. 169(C), pages 1-28.
    11. Ş. İlker Birbil & Gül Gürkan & Ovidiu Listeş, 2006. "Solving Stochastic Mathematical Programs with Complementarity Constraints Using Simulation," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 739-760, November.

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