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A trial-and-error congestion pricing scheme for networks with elastic demand and link capacity constraints

Author

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  • Zhou, Bojian
  • Bliemer, Michiel
  • Yang, Hai
  • He, Jie

Abstract

This paper proposes a combination of trial-and-error congestion pricing schemes that have been studied in the literature. It not only considers the minimization of the total system cost but also addresses the capacity constraints. A two-level iteration method is proposed for solving the hybrid problem, in which the approximate subgradient projection method is used for the outer level iteration phase, and the partial linearization method is used for the inner level iteration phase. We prove the convergence of the two-level iteration method, under the condition that the subproblem for the inner level iteration is only solved approximately, which makes the method efficient and practical. A numerical example is presented to illustrate the application of the two-level iteration method to the trial-and-error congestion pricing scheme.

Suggested Citation

  • Zhou, Bojian & Bliemer, Michiel & Yang, Hai & He, Jie, 2015. "A trial-and-error congestion pricing scheme for networks with elastic demand and link capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 77-92.
    • Handle: RePEc:eee:transb:v:72:y:2015:i:c:p:77-92
    DOI: 10.1016/j.trb.2014.11.009
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    1. B. S. He & H. Yang & Q. Meng & D. R. Han, 2002. "Modified Goldstein–Levitin–Polyak Projection Method for Asymmetric Strongly Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 129-143, January.
    2. Yang, Hai & Meng, Qiang & Lee, Der-Horng, 2004. "Trial-and-error implementation of marginal-cost pricing on networks in the absence of demand functions," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 477-493, July.
    3. Larsson, Torbjörn & Patriksson, Michael, 1995. "An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 433-455, December.
    4. Ferrari, Paolo, 1997. "Capacity constraints in urban transport networks," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 291-301, August.
    5. Correa Romar, 2014. "Mathematical Foci," Mathematical Economics Letters, De Gruyter, vol. 2(1-2), pages 1-7, August.
    6. Han, Deren & Yang, Hai, 2009. "Congestion pricing in the absence of demand functions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 45(1), pages 159-171, January.
    7. Henry Liu & Xiaozheng He & Bingsheng He, 2009. "Method of Successive Weighted Averages (MSWA) and Self-Regulated Averaging Schemes for Solving Stochastic User Equilibrium Problem," Networks and Spatial Economics, Springer, vol. 9(4), pages 485-503, December.
    8. Deren Han & Wei Xu & Hai Yang, 2010. "Solving a class of variational inequalities with inexact oracle operators," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 427-452, June.
    9. 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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