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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Leslie C. Edie, 1961. "Car-Following and Steady-State Theory for Noncongested Traffic," Operations Research, INFORMS, vol. 9(1), pages 66-76, February.
    19. 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.
    20. 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.
    21. G. F. Newell, 1961. "Nonlinear Effects in the Dynamics of Car Following," Operations Research, INFORMS, vol. 9(2), pages 209-229, April.
    22. 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.
    23. 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.
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