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Solving the step-tolled bottleneck model with general user heterogeneity

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  • Chen, Hongyu
  • Liu, Yang
  • Nie, Yu (Marco)

Abstract

Two new numerical methods, a semi-analytical method and an exact method, are proposed in this paper for solving the step-tolled user equilibrium problem for the bottleneck model with general user heterogeneity. The semi-analytical method transforms the step-tolled user equilibrium problem into a static traffic assignment problem with side constraints, which is formulated and solved as a variational inequality problem (VIP). Existence and uniqueness results are obtained by examining the properties of the VIP. The exact method, on the other hand, locates the equilibrium solution by enumerating all possible combinations of user departure orders. To improve the computational efficiency of the exact method, a simple heuristic is developed to reduce the number of solutions to be enumerated. Examples of up to 1000 classes are tested. The results confirm that ignoring user heterogeneity may lead to sub-optimal design of step tolls. In all experiments, the semi-analytical method is found to be more efficient than the heuristic version of the exact method by an order of magnitude, albeit they consistently produce nearly identical equilibrium solutions.

Suggested Citation

  • Chen, Hongyu & Liu, Yang & Nie, Yu (Marco), 2015. "Solving the step-tolled bottleneck model with general user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 210-229.
    • Handle: RePEc:eee:transb:v:81:y:2015:i:p1:p:210-229
    DOI: 10.1016/j.trb.2015.09.005
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    References listed on IDEAS

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    2. Akamatsu, Takashi & Wada, Kentaro & Iryo, Takamasa & Hayashi, Shunsuke, 2021. "A new look at departure time choice equilibrium models with heterogeneous users," Transportation Research Part B: Methodological, Elsevier, vol. 148(C), pages 152-182.
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    5. Xiao, Ling-Ling & Liu, Tian-Liang & Huang, Hai-Jun & Liu, Ronghui, 2021. "Temporal-spatial allocation of bottleneck capacity for managing morning commute with carpool," Transportation Research Part B: Methodological, Elsevier, vol. 143(C), pages 177-200.
    6. Hu, Lu & Zhao, Bin & Zhu, Juanxiu & Jiang, Yangsheng, 2019. "Two time-varying and state-dependent fluid queuing models for traffic circulation systems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 997-1019.
    7. Liu, Yang & Li, Yuanyuan & Hu, Lu, 2018. "Departure time and route choices in bottleneck equilibrium under risk and ambiguity," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 774-793.
    8. Liu, Peng & Liu, Jielun & Ong, Ghim Ping & Tian, Qiong, 2020. "Flow pattern and optimal capacity in a bi-modal traffic corridor with heterogeneous users," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 133(C).
    9. Khan, Zaid & Amin, Saurabh, 2018. "Bottleneck model with heterogeneous information," Transportation Research Part B: Methodological, Elsevier, vol. 112(C), pages 157-190.
    10. Li, Chuan-Yao & Sun, Qi-Jia, 2019. "Influence of coarse toll on the dynamic properties of traffic flow in a single-entry traffic corridor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    11. Fu, Xinying & van den Berg, Vincent A.C. & Verhoef, Erik T., 2018. "Private road supply in networks with heterogeneous users," Transportation Research Part A: Policy and Practice, Elsevier, vol. 118(C), pages 430-443.
    12. Vincent van den Berg, "undated". "Self-financing roads under coarse tolling and heterogeneous preferences," Tinbergen Institute Discussion Papers 22-045/VIII, Tinbergen Institute.
    13. Tian, Qiong & Liu, Peng & Ong, Ghim Ping & Huang, Hai-Jun, 2021. "Morning commuting pattern and crowding pricing in a many-to-one public transit system with heterogeneous users," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    14. An, Qinhe & Fu, Xiao & Huang, Di & Cheng, Qixiu & Liu, Zhiyuan, 2020. "Analysis of adding-runs strategy for peak-hour regular bus services," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    15. Li, Zhi-Chun & Huang, Hai-Jun & Yang, Hai, 2020. "Fifty years of the bottleneck model: A bibliometric review and future research directions," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 311-342.
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