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Strong Regularity and the Sensitivity Analysis of Traffic Equilibria: A Comment

Author

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  • Stephen M. Robinson

    (Department of Industrial and Systems Engineering, University of Wisconsin--Madison, 1513 University Avenue, Madison, Wisconsin 53706-1572)

Abstract

Patriksson (2004) analyzes the sensitivity of solutions of traffic equilibrium problems. One of his central results deals with directional differentiability in the elastic-demand case. Unfortunately, his proof contains crucial errors, and the purpose of this comment is to explain what they are and why they render the proof incorrect. The consequence is that Patriksson’s proof of his Theorem 5 is invalid, so the theorem must be regarded as unproven.

Suggested Citation

  • Stephen M. Robinson, 2006. "Strong Regularity and the Sensitivity Analysis of Traffic Equilibria: A Comment," Transportation Science, INFORMS, vol. 40(4), pages 540-542, November.
    • Handle: RePEc:inm:ortrsc:v:40:y:2006:i:4:p:540-542
    DOI: 10.1287/trsc.1060.0162
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    Citations

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    Cited by:

    1. Du, Muqing & Chen, Anthony, 2022. "Sensitivity analysis for transit equilibrium assignment and applications to uncertainty analysis," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 175-202.
    2. Byung Chung & Hsun-Jung Cho & Terry Friesz & Henh Huang & Tao Yao, 2014. "Sensitivity Analysis of User Equilibrium Flows Revisited," Networks and Spatial Economics, Springer, vol. 14(2), pages 183-207, June.
    3. Eikenbroek, Oskar A.L. & Still, Georg J. & van Berkum, Eric C., 2022. "Improving the performance of a traffic system by fair rerouting of travelers," European Journal of Operational Research, Elsevier, vol. 299(1), pages 195-207.
    4. S. Dempe & A. Zemkoho, 2012. "Bilevel road pricing: theoretical analysis and optimality conditions," Annals of Operations Research, Springer, vol. 196(1), pages 223-240, July.
    5. Connors, Richard D. & Sumalee, Agachai & Watling, David P., 2007. "Sensitivity analysis of the variable demand probit stochastic user equilibrium with multiple user-classes," Transportation Research Part B: Methodological, Elsevier, vol. 41(6), pages 593-615, July.
    6. Paramet Luathep & Agachai Sumalee & H. Ho & Fumitaka Kurauchi, 2011. "Large-scale road network vulnerability analysis: a sensitivity analysis based approach," Transportation, Springer, vol. 38(5), pages 799-817, September.
    7. Shu Lu, 2008. "Sensitivity of Static Traffic User Equilibria with Perturbations in Arc Cost Function and Travel Demand," Transportation Science, INFORMS, vol. 42(1), pages 105-123, February.

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