IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v499y2018icp110-120.html
   My bibliography  Save this article

Modeling and simulation of driver’s anticipation effect in a two lane system on curved road with slope

Author

Listed:
  • Kaur, Ramanpreet
  • Sharma, Sapna

Abstract

The complexity of traffic flow phenomena on curved road with slope is investigated and a new lattice model is presented with the addition of driver’s anticipation effect for two lane system. The condition under which the free flow turns into the jammed one, is obtained theoretically by using stability analysis. The results obtained through linear analysis indicates that the stable region increases (decreases) corresponding to uphill (downhill) case due to increasing slope angle for fixed anticipation parameter. It is found that when the vehicular density becomes higher than a critical value, traffic jam appears in the form of kink antikink density waves. Analytically, the kink antikink density waves are described by the solution of mKdV equation obtained from non linear analysis. In addition, the theoretical results has been verified through numerical simulation, which confirm that the slope on a curved highway significantly influence the traffic dynamics and traffic jam can be suppressed efficiently by considering the anticipation parameter in a two lane lattice model when lane changing is allowed.

Suggested Citation

  • Kaur, Ramanpreet & Sharma, Sapna, 2018. "Modeling and simulation of driver’s anticipation effect in a two lane system on curved road with slope," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 110-120.
    • Handle: RePEc:eee:phsmap:v:499:y:2018:i:c:p:110-120
    DOI: 10.1016/j.physa.2017.12.101
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117313511
    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.2017.12.101?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. Nagatani, Takashi, 1998. "Modified KdV equation for jamming transition in the continuum models of traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 599-607.
    2. Tang, Tie-Qiao & He, Jia & Yang, Shi-Chun & Shang, Hua-Yan, 2014. "A car-following model accounting for the driver’s attribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 583-591.
    3. Jiang, Rui & Wu, Qing-Song & Zhu, Zuo-Jin, 2002. "A new continuum model for traffic flow and numerical tests," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 405-419, June.
    4. Komada, Kazuhito & Masukura, Shuichi & Nagatani, Takashi, 2009. "Effect of gravitational force upon traffic flow with gradients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2880-2894.
    5. Kaur, Ramanpreet & Sharma, Sapna, 2017. "Analysis of driver’s characteristics on a curved road in a lattice model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 59-67.
    6. Guanghan Peng, 2013. "A New Lattice Model Of Two-Lane Traffic Flow With The Consideration Of Multi-Anticipation Effect," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(07), pages 1-13.
    7. Denos C. Gazis & Robert Herman & Richard W. Rothery, 1961. "Nonlinear Follow-the-Leader Models of Traffic Flow," Operations Research, INFORMS, vol. 9(4), pages 545-567, August.
    8. Tang, Tie-Qiao & Luo, Xiao-Feng & Liu, Kai, 2016. "Impacts of the driver’s bounded rationality on the traffic running cost under the car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 316-321.
    9. Gupta, Arvind Kumar & Redhu, Poonam, 2013. "Analyses of driver’s anticipation effect in sensing relative flux in a new lattice model for two-lane traffic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5622-5632.
    10. Leslie C. Edie, 1961. "Car-Following and Steady-State Theory for Noncongested Traffic," Operations Research, INFORMS, vol. 9(1), pages 66-76, February.
    11. Jin-Liang Cao & Zhon-Ke Shi, 2015. "A novel lattice traffic flow model on a curved road," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 26(11), pages 1-18.
    12. Ge, Hong-Xia & Cheng, Rong-Jun, 2008. "The “backward looking” effect in the lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(28), pages 6952-6958.
    13. Nagatani, Takashi, 1999. "Jamming transition in traffic flow on triangular lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 271(1), pages 200-221.
    14. Zhu, Wen-Xing & Yu, Rui-Ling, 2012. "Nonlinear analysis of traffic flow on a gradient highway," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 954-965.
    15. Zhu, Wen-Xing & Zhang, Li-Dong, 2012. "Friction coefficient and radius of curvature effects upon traffic flow on a curved Road," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4597-4605.
    16. Shiyong Lan & Yiguang Liu & Bingbing Liu & Peng Sheng & Tao Wang & Xinsheng Li, 2011. "Effect Of Slopes In Highway On Traffic Flow," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 319-331.
    17. Nagatani, Takashi, 1999. "Jamming transitions and the modified Korteweg–de Vries equation in a two-lane traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(1), pages 297-310.
    18. Jianzhong Chen & Zhongke Shi & Yanmei Hu & Lei Yu & Yuan Fang, 2013. "An Extended Macroscopic Model For Traffic Flow On A Highway With Slopes," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(09), pages 1-14.
    19. G. F. Newell, 1961. "Nonlinear Effects in the Dynamics of Car Following," Operations Research, INFORMS, vol. 9(2), pages 209-229, April.
    20. Sharma, Sapna, 2015. "Lattice hydrodynamic modeling of two-lane traffic flow with timid and aggressive driving behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 401-411.
    21. Tang, Tie-Qiao & Luo, Xiao-Feng & Zhang, Jian & Chen, Liang, 2018. "Modeling electric bicycle’s lane-changing and retrograde behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1377-1386.
    22. Gupta, A.K. & Katiyar, V.K., 2006. "A new anisotropic continuum model for traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(2), pages 551-559.
    23. Redhu, Poonam & Gupta, Arvind Kumar, 2015. "Jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 249-260.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Lixiang & Cheng, Rongjun & Ge, Hongxia, 2021. "New feedback control for a novel two-dimensional lattice hydrodynamic model considering driver’s memory effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    2. Madaan, Nikita & Sharma, Sapna, 2021. "A lattice model accounting for multi-lane traffic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 564(C).
    3. Shuang Jin & Jianxi Yang & Zhongcheng Liu, 2022. "Modeling and Analysis of Car-Following for Intelligent Connected Vehicles Considering Expected Speed in Helical Ramps," Sustainability, MDPI, vol. 14(24), pages 1-20, December.
    4. Wang, Zihao & Zhu, Wen-Xing, 2022. "Modeling and stability analysis of traffic flow considering electronic throttle dynamics on a curved road with slope," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    5. Zhang, Jing & Xu, Keyu & Li, Shubin & Wang, Tao, 2020. "A new two-lane lattice hydrodynamic model with the introduction of driver’s predictive effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    6. Zhai, Cong & Wu, Weitiao & Xiao, Yingping, 2023. "The jamming transition of multi-lane lattice hydrodynamic model with passing effect," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    7. Huimin Liu & Yuhong Wang, 2021. "Impact of Strong Wind and Optimal Estimation of Flux Difference Integral in a Lattice Hydrodynamic Model," Mathematics, MDPI, vol. 9(22), pages 1-13, November.
    8. Wen Huan Ai & Ming Ming Wang & Da Wei Liu, 2023. "Analysis of macroscopic traffic flow model considering throttle dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(6), pages 1-18, June.

    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. Kaur, Ramanpreet & Sharma, Sapna, 2017. "Analysis of driver’s characteristics on a curved road in a lattice model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 59-67.
    2. Kaur, Daljeet & Sharma, Sapna & Gupta, Arvind Kumar, 2022. "Analyses of lattice hydrodynamic area occupancy model for heterogeneous disorder traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    3. Nikita Madaan & Sapna Sharma, 2022. "Influence of driver’s behavior with empirical lane changing on the traffic dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(1), pages 1-11, January.
    4. Kaur, Daljeet & Sharma, Sapna, 2020. "A new two-lane lattice model by considering predictive effect in traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    5. Kaur, Ramanpreet & Sharma, Sapna, 2018. "Analyses of lattice hydrodynamic model using delayed feedback control with passing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 446-455.
    6. Liu, Zhaoze & Ge, Hongxia & Cheng, Rongjun, 2018. "KdV–Burgers equation in the modified continuum model considering the effect of friction and radius on a curved road," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1218-1227.
    7. Madaan, Nikita & Sharma, Sapna, 2021. "A lattice model accounting for multi-lane traffic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 564(C).
    8. Junyan Han & Xiaoyuan Wang & Gang Wang, 2022. "Modeling the Car-Following Behavior with Consideration of Driver, Vehicle, and Environment Factors: A Historical Review," Sustainability, MDPI, vol. 14(13), pages 1-27, July.
    9. Zhai, Cong & Zhang, Ronghui & Peng, Tao & Zhong, Changfu & Xu, Hongguo, 2023. "Heterogeneous lattice hydrodynamic model and jamming transition mixed with connected vehicles and human-driven vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).
    10. Hou, Qinzhong & Meng, Xianghai & Leng, Junqiang & Yu, Lu, 2018. "Application of a random effects negative binomial model to examine crash frequency for freeways in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 937-944.
    11. Chang, Yinyin & He, Zhiting & Cheng, Rongjun, 2019. "Analysis of the historical time integral form of relative flux and feedback control in an extended lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 326-334.
    12. Sun, Fengxin & Chow, Andy H.F. & Lo, S.M. & Ge, Hongxia, 2018. "A two-lane lattice hydrodynamic model with heterogeneous lane changing rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 389-400.
    13. Wang, Jufeng & Sun, Fengxin & Ge, Hongxia, 2019. "An improved lattice hydrodynamic model considering the driver’s desire of driving smoothly," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 119-129.
    14. Zhang, Yicai & Zhao, Min & Sun, Dihua & Liu, Xiaoyu & Huang, Shuai & Chen, Dong, 2022. "Robust H-infinity control for connected vehicles in lattice hydrodynamic model at highway tunnel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    15. Madaan, Nikita & Sharma, Sapna, 2022. "Delayed-feedback control in multi-lane traffic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    16. Sun, Yuqing & Ge, Hongxia & Cheng, Rongjun, 2018. "An extended car-following model under V2V communication environment and its delayed-feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 349-358.
    17. Liu, Hui & Sun, Dihua & Liu, Weining, 2016. "Lattice hydrodynamic model based traffic control: A transportation cyber–physical system approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 795-801.
    18. Wang, Zihao & Ge, Hongxia & Cheng, Rongjun, 2018. "Nonlinear analysis for a modified continuum model considering driver’s memory and backward looking effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 18-27.
    19. Zhang, Jing & Xu, Keyu & Li, Shubin & Wang, Tao, 2020. "A new two-lane lattice hydrodynamic model with the introduction of driver’s predictive effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    20. Redhu, Poonam & Gupta, Arvind Kumar, 2015. "Jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 249-260.

    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:499:y:2018:i:c:p:110-120. 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.