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Constrained optimization for bottleneck coarse tolling

Author

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  • Xu, Da
  • Guo, Xiaolei
  • Zhang, Guoqing
Abstract
We study the optimal single-step coarse toll design problem for the bottleneck model where the toll level and tolling duration have maximum acceptable upper bounds and the unconstrained optimal solution exceeds the upper bounds. We consider proportional user heterogeneity where users’ values of time and schedule delay vary in fixed proportions. Three classic coarse tolling models are studied, the ADL, Laih and braking models. In the ADL model, untolled users form a mass arrival at the bottleneck following the last tolled user. In the Laih model, there is a separated waiting facility for untolled users to wait until the toll ends. In the braking model, untolled users can choose to defer their arrival at the bottleneck to avoid paying the toll. We find that, in the ADL and the Laih models, the optimal solution chooses the maximum acceptable toll level and tolling duration. The ADL model further requires the tolling period to be started as late as possible to eliminate the queue at the toll ending moment. In the braking model, if the upper bound of the tolling duration is too small, no toll should be charged. Otherwise the optimal solution chooses the maximum acceptable tolling duration and may choose a toll price less than the maximum acceptable level.

Suggested Citation

  • Xu, Da & Guo, Xiaolei & Zhang, Guoqing, 2019. "Constrained optimization for bottleneck coarse tolling," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 1-22.
    • Handle: RePEc:eee:transb:v:128:y:2019:i:c:p:1-22
    DOI: 10.1016/j.trb.2019.07.013
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    References listed on IDEAS

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    1. van den Berg, Vincent A.C., 2014. "Coarse tolling with heterogeneous preferences," Transportation Research Part B: Methodological, Elsevier, vol. 64(C), pages 1-23.
    2. Robin Lindsey, C. & van den Berg, Vincent A.C. & Verhoef, Erik T., 2012. "Step tolling with bottleneck queuing congestion," Journal of Urban Economics, Elsevier, vol. 72(1), pages 46-59.
    3. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand," American Economic Review, American Economic Association, vol. 83(1), pages 161-179, March.
    4. Xiao, Feng & Qian, Zhen (Sean) & Zhang, H. Michael, 2013. "Managing bottleneck congestion with tradable credits," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 1-14.
    5. Chen, Hongyu & Nie, Yu (Marco) & Yin, Yafeng, 2015. "Optimal multi-step toll design under general user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 775-793.
    6. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    7. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1990. "Economics of a bottleneck," Journal of Urban Economics, Elsevier, vol. 27(1), pages 111-130, January.
    8. Arnott Richard & Kraus Marvin, 1995. "Financing Capacity in the Bottleneck Model," Journal of Urban Economics, Elsevier, vol. 38(3), pages 272-290, November.
    9. Xiao, Feng & Shen, Wei & Michael Zhang, H., 2012. "The morning commute under flat toll and tactical waiting," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1346-1359.
    10. Fielding, Gordon J., 2001. "Private Toll Roads: Acceptability of Congestion Pricing in Southern California," University of California Transportation Center, Working Papers qt749118j3, University of California Transportation Center.
    11. van den Berg, Vincent & Verhoef, Erik T., 2011. "Congestion tolling in the bottleneck model with heterogeneous values of time," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 60-78, January.
    12. 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.
    13. Yang, Hai & Hai-Jun, Huang, 1997. "Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory," Transportation Research Part B: Methodological, Elsevier, vol. 31(6), pages 425-440, November.
    14. Knockaert, Jasper & Verhoef, Erik T. & Rouwendal, Jan, 2016. "Bottleneck congestion: Differentiating the coarse charge," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 59-73.
    15. Jia, Zehui & Wang, David Z.W. & Cai, Xingju, 2016. "Traffic managements for household travels in congested morning commute," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 91(C), pages 173-189.
    16. Feng Xiao & Zhen Qian & H. Zhang, 2011. "The Morning Commute Problem with Coarse Toll and Nonidentical Commuters," Networks and Spatial Economics, Springer, vol. 11(2), pages 343-369, June.
    17. Li, Zhi-Chun & Lam, William H.K. & Wong, S.C., 2017. "Step tolling in an activity-based bottleneck model," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 306-334.
    18. Yu Nie, 2015. "A New Tradable Credit Scheme for the Morning Commute Problem," Networks and Spatial Economics, Springer, vol. 15(3), pages 719-741, September.
    19. Chen-Hsiu Laih, 2004. "Effects of the optimal step toll scheme on equilibrium commuter behaviour," Applied Economics, Taylor & Francis Journals, vol. 36(1), pages 59-81.
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