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On the existence of pricing strategies in the discrete time heterogeneous single bottleneck model

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  • Doan, Kien
  • Ukkusuri, Satish
  • Han, Lanshan

Abstract

In this paper, we study the pricing strategies in the discrete time single bottleneck model with general heterogeneous commuters. We first prove that in the system optimal assignment, the queue time must be zero for all the departures. Based on this result, the system optimal problem is formulated as a linear program. The solution existence and uniqueness are discussed. Applying linear programming duality, we then prove that the optimal dual variable values provide an optimal toll with which the system optimal solution is also an equilibrium solution. Extensive computational results are reported to demonstrate the insights gained from the formulations in this paper. These results confirm that a system optimal equilibrium can be found using the proposed approach.

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  • Doan, Kien & Ukkusuri, Satish & Han, Lanshan, 2011. "On the existence of pricing strategies in the discrete time heterogeneous single bottleneck model," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1483-1500.
    • Handle: RePEc:eee:transb:v:45:y:2011:i:9:p:1483-1500
    DOI: 10.1016/j.trb.2011.05.019
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    Cited by:

    1. Ukkusuri, Satish V. & Han, Lanshan & Doan, Kien, 2012. "Dynamic user equilibrium with a path based cell transmission model for general traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1657-1684.
    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.
    3. 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.
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    7. Takayama, Yuki & Kuwahara, Masao, 2016. "Scheduling preferences, parking competition, and bottleneck congestion: A model of trip timing and parking location choices by heterogeneous commuters," MPRA Paper 68938, University Library of Munich, Germany.
    8. Yang, Hai & Liu, Wei & Wang, Xiaolei & Zhang, Xiaoning, 2013. "On the morning commute problem with bottleneck congestion and parking space constraints," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 106-118.
    9. 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.
    10. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Li, Xinwei, 2018. "Day-to-day departure time choice under bounded rationality in the bottleneck model," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 832-849.
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