IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v534y2019ics0378437119313330.html
   My bibliography  Save this article

Influence of coarse toll on the dynamic properties of traffic flow in a single-entry traffic corridor

Author

Listed:
  • Li, Chuan-Yao
  • Sun, Qi-Jia

Abstract

In this paper, we investigate the effects of coarse toll on the user equilibrium (UE) state in a single-entry traffic corridor with early and late arrivals from analytical and numerical perspective. Unlike previous studies on traffic tolls, the flow congestion model is used to take into account the dynamic propagation of traffic flow. The LWR (Lighthill–Whitham–Richards) model and the Greenshields’ velocity–density function are used to describe the dynamic properties of traffic flow. The quasi-analytic solutions of the three possible cases in UE due to different charges are derived. Both analytical and numerical results indicate that rarefaction waves and shock waves appear in the corridor under the coarse toll. The three-dimensional evolution diagrams of traffic flow and space–time diagrams illustrate that the introduction of course toll lets flow patterns more complicated. This extends the knowledge given by the classical bottleneck model.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:534:y:2019:i:c:s0378437119313330
    DOI: 10.1016/j.physa.2019.122316
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119313330
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.122316?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhu, Wen-Xing & Li, Shuo, 2019. "Study on discrete boundary-feedback-control strategy for traffic flow based on Macroscopic Fundamental Diagram," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1237-1247.
    2. Nagatani, Takashi, 2017. "Complex motion of a vehicle through a series of signals controlled by power-law phase," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 1-10.
    3. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1990. "Economics of a bottleneck," Journal of Urban Economics, Elsevier, vol. 27(1), pages 111-130, January.
    4. 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.
    5. Arvind Kumar Gupta, 2013. "A Section Approach To A Traffic Flow Model On Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(05), pages 1-23.
    6. 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.
    7. Tang, Tie-Qiao & Yi, Zhi-Yan & Zhang, Jian & Wang, Tao & Leng, Jun-Qiang, 2018. "A speed guidance strategy for multiple signalized intersections based on car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 399-409.
    8. Peng, Guanghan & Kuang, Hua & Qing, Li, 2018. "Feedback control method in lattice hydrodynamic model under honk environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 651-656.
    9. Nagatani, Takashi, 2014. "Jam formation with line changing at two tollgates on a highway," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 596-603.
    10. Nagatani, Takashi, 2015. "Effect of perception irregularity on chain-reaction crash in low visibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 92-99.
    11. Nagatani, Takashi, 2017. "Effect of periodic inflow on speed-controlled shuttle bus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 224-231.
    12. Li, Chuan-Yao & Huang, Hai-Jun & Tang, Tie-Qiao, 2017. "Analysis of social optimum for staggered shifts in a single-entry traffic corridor with no late arrivals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 275-283.
    13. Ge, Hong-Xia & Zheng, Peng-jun & Wang, Wei & Cheng, Rong-Jun, 2015. "The car following model considering traffic jerk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 274-278.
    14. Nagatani, Takashi, 2018. "Effect of bypasses on vehicular traffic through a series of signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 229-236.
    15. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    16. Tang, Tie-Qiao & Shi, Wei-Fang & Huang, Hai-Jun & Wu, Wen-Xiang & Song, Ziqi, 2019. "A route-based traffic flow model accounting for interruption factors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 767-785.
    17. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-479, June.
    18. G. F. Newell, 1988. "Traffic Flow for the Morning Commute," Transportation Science, INFORMS, vol. 22(1), pages 47-58, February.
    19. 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.
    20. Peng, Guanghan & Kuang, Hua & Qing, Li, 2018. "A new lattice model of traffic flow considering driver’s anticipation effect of the traffic interruption probability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 374-380.
    21. Peng, Guanghan & Yang, Shuhong & Xia, Dongxue & Li, Xiaoqin, 2018. "A novel lattice hydrodynamic model considering the optimal estimation of flux difference effect on two-lane highway," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 929-937.
    22. Nagatani, Takashi, 2017. "Effect of velocity-dependent friction on multiple-vehicle collisions in traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 636-643.
    23. Tang, Tie-Qiao & Huang, Hai-Jun & Shang, Hua-Yan, 2017. "An extended macro traffic flow model accounting for the driver’s bounded rationality and numerical tests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 322-333.
    24. Li, Chuan-Yao & Huang, Hai-Jun & Tang, Tie-Qiao, 2017. "Analysis of user equilibrium for staggered shifts in a single-entry traffic corridor with no late arrivals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 8-18.
    25. Li, Chuan-Yao & Huang, Hai-Jun, 2017. "Morning commute in a single-entry traffic corridor with early and late arrivals," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 23-49.
    26. Tang, Tie-Qiao & Yi, Zhi-Yan & Lin, Qing-Feng, 2017. "Effects of signal light on the fuel consumption and emissions under car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 200-205.
    27. 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.
    28. Arvind Kumar Gupta & Isha Dhiman, 2014. "Analyses of a continuum traffic flow model for a nonlane-based system," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(10), pages 1-24.
    29. Zhu, Wen-Xing & Zhang, H.M., 2018. "Analysis of feedback control scheme on discrete car-following system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 322-330.
    30. 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.
    31. Peng, Guanghan & Bai, Kezhao & Kuang, Hua, 2019. "Feedback control caused by honk effect incorporating the driver’s characteristics in lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    32. Zhu, Wen-Xing & Zhang, H.M., 2018. "Analysis of mixed traffic flow with human-driving and autonomous cars based on car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 274-285.
    33. Peng, Guanghan & Kuang, Hua & Zhao, Hongzhuan & Qing, Li, 2019. "Nonlinear analysis of a new lattice hydrodynamic model with the consideration of honk effect on flux for two-lane highway," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 93-101.
    34. Peng, Guanghan & Kuang, Hua & Bai, Kezhao, 2019. "The impact of the individual difference on traffic flow under honk environment in lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Li, Chuan-Yao & Xu, Guang-Ming & Tang, Tie-Qiao, 2018. "Social optimum for evening commute in a single-entry traffic corridor with no early departures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 236-247.
    3. Li, Chuan-Yao & Huang, Hai-Jun & Tang, Tie-Qiao, 2017. "Analysis of user equilibrium for staggered shifts in a single-entry traffic corridor with no late arrivals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 8-18.
    4. Song, Tao & Zhu, Wen-Xing, 2020. "Study on state feedback control strategy for car-following system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    5. van den Berg, Vincent A.C., 2024. "Self-financing roads under coarse tolling and preference heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 182(C).
    6. Vincent A.C. van den Berg & Erik T. Verhoef, 2015. "Robot Cars and Dynamic Bottleneck Congestion: The Effects on Capacity, Value of Time and Preference Heterogeneity," Tinbergen Institute Discussion Papers 15-062/VIII, Tinbergen Institute, revised 11 Jul 2016.
    7. 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.
    8. 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.
    9. Takayama, Yuki, 2020. "Who gains and who loses from congestion pricing in a monocentric city with a bottleneck?," Economics of Transportation, Elsevier, vol. 24(C).
    10. Wang, Zihao & Ge, Hongxia & Cheng, Rongjun, 2020. "An extended macro model accounting for the driver’s timid and aggressive attributions and bounded rationality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    11. Li, Chuan-Yao & Huang, Hai-Jun & Tang, Tie-Qiao, 2017. "Analysis of social optimum for staggered shifts in a single-entry traffic corridor with no late arrivals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 275-283.
    12. Wang, Jing-Peng & Huang, Hai-Jun & (Jeff) Ban, Xuegang, 2019. "Optimal capacity allocation for high occupancy vehicle (HOV) lane in morning commute," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 354-361.
    13. Li, Zhi-Chun & Lam, William H.K. & Wong, S.C., 2014. "Bottleneck model revisited: An activity-based perspective," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 262-287.
    14. 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.
    15. 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.
    16. Vincent van den Berg, "undated". "Self-financing roads under coarse tolling and heterogeneous preferences," Tinbergen Institute Discussion Papers 22-045/VIII, Tinbergen Institute.
    17. Ou, Hui & Tang, Tie-Qiao & Rui, Ying-Xu & Zhou, Jie-Ming, 2018. "Modeling electric bicycle’s abnormal behavior at a signalized intersection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 218-231.
    18. 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.
    19. Jiang, Changmin & Zhang, Anming, 2015. "Airport congestion pricing and terminal investment: Effects of terminal congestion, passenger types, and concessionsAuthor-Name: Wan, Yulai," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 91-113.
    20. van den Berg, Vincent A.C., 2014. "Coarse tolling with heterogeneous preferences," Transportation Research Part B: Methodological, Elsevier, vol. 64(C), pages 1-23.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:534:y:2019:i:c:s0378437119313330. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.