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Learning marginal-cost pricing via a trial-and-error procedure with day-to-day flow dynamics

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  • Ye, Hongbo
  • Yang, Hai
  • Tan, Zhijia

Abstract

This paper investigates the convergence of the trial-and-error procedure to achieve the system optimum by incorporating the day-to-day evolution of traffic flows. The path flows are assumed to follow an ‘excess travel cost dynamics’ and evolve from disequilibrium states to the equilibrium day by day. This implies that the observed link flow pattern during the trial-and-error procedure is in disequilibrium. By making certain assumptions on the flow evolution dynamics, we prove that the trial-and-error procedure is capable of learning the system optimum link tolls without requiring explicit knowledge of the demand functions and flow evolution mechanism. A methodology is developed for updating the toll charges and choosing the inter-trial periods to ensure convergence of the iterative approach towards the system optimum. Numerical examples are given in support of the theoretical findings.

Suggested Citation

  • Ye, Hongbo & Yang, Hai & Tan, Zhijia, 2015. "Learning marginal-cost pricing via a trial-and-error procedure with day-to-day flow dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 794-807.
    • Handle: RePEc:eee:transb:v:81:y:2015:i:p3:p:794-807
    DOI: 10.1016/j.trb.2015.08.001
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    3. Ren-Yong Guo & Hai-Jun Huang & Hai Yang, 2019. "Tradable Credit Scheme for Control of Evolutionary Traffic Flows to System Optimum: Model and its Convergence," Networks and Spatial Economics, Springer, vol. 19(3), pages 833-868, September.
    4. Liu, Wei & Geroliminis, Nikolas, 2017. "Doubly dynamics for multi-modal networks with park-and-ride and adaptive pricing," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 162-179.
    5. 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.
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    7. Lie Han, 2022. "Proportional-Switch Adjustment Process with Elastic Demand and Congestion Toll in the Absence of Demand Functions," Networks and Spatial Economics, Springer, vol. 22(4), pages 709-735, December.
    8. Chen, Xinyuan & Zhang, Wei & Guo, Xiaomeng & Liu, Zhiyuan & Wang, Shuaian, 2021. "An improved learning-and-optimization train fare design method for addressing commuting congestion at CBD stations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 153(C).
    9. Ren-Yong Guo & Hai Yang & Hai-Jun Huang, 2018. "Are We Really Solving the Dynamic Traffic Equilibrium Problem with a Departure Time Choice?," Transportation Science, INFORMS, vol. 52(3), pages 603-620, June.
    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. 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.
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