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Network-Optimized Road Pricing: Part I: A Parable and a Model

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  • Robert B. Dial

    (Volpe National Transportation Systems Center, Cambridge, Massachusetts)

Abstract

Part I of a two-part series, this paper recites a parable and formulates a stochastic optimization model that determines optimal link tolls on a road network whose users' value of time is a random variable. The parable, introducing the problem, demonstrates the importance of the variability of the value of time. The model, cast as a variational inequality, becomes a specialized form of a bicriterion user-equilibrium traffic assignment. Its solution is a set of efficient tolls for all links in the network. These tolls induce an equilibrium traffic flow that is at once system-optimal and user-optimal—for all trips, regardless of their value of time. Part II develops a solution algorithm, gives examples, and provides performance statistics.

Suggested Citation

  • Robert B. Dial, 1999. "Network-Optimized Road Pricing: Part I: A Parable and a Model," Operations Research, INFORMS, vol. 47(1), pages 54-64, February.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:1:p:54-64
    DOI: 10.1287/opre.47.1.54
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    Cited by:

    1. Nagurney, Anna & Dong, June, 2002. "A multiclass, multicriteria traffic network equilibrium model with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 445-469, June.
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    3. Fabio Bagagiolo & Silvia Faggian & Rosario Maggistro & Raffaele Pesenti, 2022. "Optimal Control of the Mean Field Equilibrium for a Pedestrian Tourists’ Flow Model," Networks and Spatial Economics, Springer, vol. 22(2), pages 243-266, June.
    4. Chi Xie & Xing Wu & Stephen Boyles, 2019. "Traffic equilibrium with a continuously distributed bound on travel weights: the rise of range anxiety and mental account," Annals of Operations Research, Springer, vol. 273(1), pages 279-310, February.
    5. Andrea Raith & Judith Wang & Matthias Ehrgott & Stuart Mitchell, 2014. "Solving multi-objective traffic assignment," Annals of Operations Research, Springer, vol. 222(1), pages 483-516, November.
    6. Dao-Li Zhu & Hai Yang & Chang-Min Li & Xiao-Lei Wang, 2015. "Properties of the Multiclass Traffic Network Equilibria Under a Tradable Credit Scheme," Transportation Science, INFORMS, vol. 49(3), pages 519-534, August.
    7. Cipriani, Ernesto & Mannini, Livia & Montemarani, Barbara & Nigro, Marialisa & Petrelli, Marco, 2019. "Congestion pricing policies: Design and assessment for the city of Rome, Italy," Transport Policy, Elsevier, vol. 80(C), pages 127-135.
    8. Patrice Marcotte & Anne Mercier & Gilles Savard & Vedat Verter, 2009. "Toll Policies for Mitigating Hazardous Materials Transport Risk," Transportation Science, INFORMS, vol. 43(2), pages 228-243, May.
    9. Robert B. Dial, 1999. "Network-Optimized Road Pricing: Part II: Algorithms and Examples," Operations Research, INFORMS, vol. 47(2), pages 327-336, April.
    10. Feng Xiao & H. M. Zhang, 2014. "Pareto-Improving and Self-Sustainable Pricing for the Morning Commute with Nonidentical Commuters," Transportation Science, INFORMS, vol. 48(2), pages 159-169, May.
    11. Wang, Guangchao & Jia, Ning & Ma, Shoufeng & Qi, Hang, 2014. "A rank-dependent bi-criterion equilibrium model for stochastic transportation environment," European Journal of Operational Research, Elsevier, vol. 235(3), pages 511-529.
    12. Wang, Guangmin & Gao, Ziyou & Xu, Meng & Sun, Huijun, 2014. "Joint link-based credit charging and road capacity improvement in continuous network design problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 67(C), pages 1-14.
    13. Rambha, Tarun & Boyles, Stephen D. & Unnikrishnan, Avinash & Stone, Peter, 2018. "Marginal cost pricing for system optimal traffic assignment with recourse under supply-side uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 104-121.
    14. Guo, Xiaolei & Yang, Hai, 2009. "User heterogeneity and bi-criteria system optimum," Transportation Research Part B: Methodological, Elsevier, vol. 43(4), pages 379-390, May.
    15. Rouhani, Omid M. & Niemeier, Debbie, 2014. "Flat versus spatially variable tolling: A case study in Fresno, California," Journal of Transport Geography, Elsevier, vol. 37(C), pages 10-18.
    16. Wu, Wen-Xiang & Huang, Hai-Jun, 2014. "Finding anonymous tolls to realize target flow pattern in networks with continuously distributed value of time," Transportation Research Part B: Methodological, Elsevier, vol. 65(C), pages 31-46.
    17. Xu, Zhandong & Chen, Anthony & Liu, Xiaobo, 2023. "Time and toll trade-off with heterogeneous users: A continuous time surplus maximization bi-objective user equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 31-58.
    18. Wang, Xiaolei & Yang, Hai & Zhu, Daoli & Li, Changmin, 2012. "Tradable travel credits for congestion management with heterogeneous users," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(2), pages 426-437.
    19. Yang, Hai & Huang, Hai-Jun, 2004. "The multi-class, multi-criteria traffic network equilibrium and systems optimum problem," Transportation Research Part B: Methodological, Elsevier, vol. 38(1), pages 1-15, January.

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