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Optimal joint distance and time toll for cordon-based congestion pricing

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  • Liu, Zhiyuan
  • Wang, Shuaian
  • Meng, Qiang

Abstract

This paper addresses the optimal toll design problem for the cordon-based congestion pricing scheme, where both a time-toll and a nonlinear distance-toll (i.e., joint distance and time toll) are levied for each network user’s trip in a pricing cordon. The users’ route choice behaviour is assumed to follow the Logit-based stochastic user equilibrium (SUE). We first propose a link-based convex programming model for the Logit-based SUE problem with a joint distance and time toll pattern. A mathematical program with equilibrium constraints (MPEC) is developed to formulate the optimal joint distance and time toll design problem. The developed MPEC model is equivalently transformed into a semi-infinite programming (SIP) model. A global optimization method named Incremental Constraint Method (ICM) is designed for solving the SIP model. Finally, two numerical examples are used to assess the proposed methodology.

Suggested Citation

  • Liu, Zhiyuan & Wang, Shuaian & Meng, Qiang, 2014. "Optimal joint distance and time toll for cordon-based congestion pricing," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 81-97.
    • Handle: RePEc:eee:transb:v:69:y:2014:i:c:p:81-97
    DOI: 10.1016/j.trb.2014.08.005
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    1. Eliasson, Jonas, 2009. "A cost-benefit analysis of the Stockholm congestion charging system," Transportation Research Part A: Policy and Practice, Elsevier, vol. 43(4), pages 468-480, May.
    2. Takashi Akamatsu, 1997. "Decomposition of Path Choice Entropy in General Transport Networks," Transportation Science, INFORMS, vol. 31(4), pages 349-362, November.
    3. Wang, Shuaian & Meng, Qiang & Yang, Hai, 2013. "Global optimization methods for the discrete network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 50(C), pages 42-60.
    4. Rotaris, Lucia & Danielis, Romeo & Marcucci, Edoardo & Massiani, Jérôme, 2010. "The urban road pricing scheme to curb pollution in Milan, Italy: Description, impacts and preliminary cost-benefit analysis assessment," Transportation Research Part A: Policy and Practice, Elsevier, vol. 44(5), pages 359-375, June.
    5. Mun, Se-il & Konishi, Ko-ji & Yoshikawa, Kazuhiro, 2003. "Optimal cordon pricing," Journal of Urban Economics, Elsevier, vol. 54(1), pages 21-38, July.
    6. Wang, Judith Y.T. & Lindsey, Robin & Yang, Hai, 2011. "Nonlinear pricing on private roads with congestion and toll collection costs," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 9-40, January.
    7. Meng, Qiang & Liu, Zhiyuan & Wang, Shuaian, 2012. "Optimal distance tolls under congestion pricing and continuously distributed value of time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(5), pages 937-957.
    8. Maruyama, Takuya & Sumalee, Agachai, 2007. "Efficiency and equity comparison of cordon- and area-based road pricing schemes using a trip-chain equilibrium model," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(7), pages 655-671, August.
    9. 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.
    10. Joakim Ekström & Leonid Engelson & Clas Rydergren, 2009. "Heuristic algorithms for a second-best congestion pricing problem," Netnomics, Springer, vol. 10(1), pages 85-102, April.
    11. Theodore Tsekeris & Stefan Voß, 2009. "Design and evaluation of road pricing: state-of-the-art and methodological advances," Netnomics, Springer, vol. 10(1), pages 5-52, April.
    12. Zhang, Xiaoning & Yang, Hai, 2004. "The optimal cordon-based network congestion pricing problem," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 517-537, July.
    13. Daskin, Mark S. & Schofer, Joseph L. & Haghani, Ali E., 1988. "A quadratic programming model for designing and evaluating distance-based and zone fares for urban transit," Transportation Research Part B: Methodological, Elsevier, vol. 22(1), pages 25-44, February.
    14. Yang, Hai & Zhang, Xiaoning & Meng, Qiang, 2004. "Modeling private highways in networks with entry-exit based toll charges," Transportation Research Part B: Methodological, Elsevier, vol. 38(3), pages 191-213, March.
    15. Xie, Chi & Travis Waller, S., 2012. "Stochastic traffic assignment, Lagrangian dual, and unconstrained convex optimization," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1023-1042.
    16. May, A. D. & Milne, D. S., 2000. "Effects of alternative road pricing systems on network performance," Transportation Research Part A: Policy and Practice, Elsevier, vol. 34(6), pages 407-436, August.
    17. Hai Yang, 1999. "System Optimum, Stochastic User Equilibrium, and Optimal Link Tolls," Transportation Science, INFORMS, vol. 33(4), pages 354-360, November.
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    9. Thi Ngoc Nguyen & Felix Muesgens, 2024. "Fuel tax loss in a world of electric mobility: A window of opportunity for congestion pricing," Papers 2409.20033, arXiv.org.
    10. Xinyuan Chen & Yiran Wang & Yuan Zhang, 2021. "A Trial-and-Error Toll Design Method for Traffic Congestion Mitigation on Large River-Crossing Channels in a Megacity," Sustainability, MDPI, vol. 13(5), pages 1-13, March.
    11. 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.
    12. Chen, Zhi & Wu, Wen-Xiang & Huang, Hai-Jun & Shang, Hua-Yan, 2022. "Modeling traffic dynamics in periphery-downtown urban networks combining Vickrey's theory with Macroscopic Fundamental Diagram: user equilibrium, system optimum, and cordon pricing," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 278-303.
    13. Li, Zhi-Chun & Cheng, Li & de Palma, André, 2024. "Ring road investment, cordon tolling, and urban spatial structure," Transportation Research Part B: Methodological, Elsevier, vol. 182(C).
    14. Qixiu Cheng & Jun Chen & Honggang Zhang & Zhiyuan Liu, 2021. "Optimal Congestion Pricing with Day-to-Day Evolutionary Flow Dynamics: A Mean–Variance Optimization Approach," Sustainability, MDPI, vol. 13(9), pages 1-15, April.
    15. Xijie Li & Ying Lv & Wei Sun & Li Zhou, 2019. "Cordon- or Link-Based Pricing: Environment-Oriented Toll Design Models Development and Application," Sustainability, MDPI, vol. 11(1), pages 1-16, January.
    16. David A. Hensher & Edward Wei & Wen Liu & Loan Ho & Chinh Ho, 2023. "Development of a practical aggregate spatial road freight modal demand model system for truck and commodity movements with an application of a distance-based charging regime," Transportation, Springer, vol. 50(3), pages 1031-1071, June.
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    19. Zhi-Chun Li & Li Cheng & André de Palma, 2023. "Ring road investment, cordon tolling, and urban spatial structure: Formulation and a case study," THEMA Working Papers 2023-07, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.

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