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Nonlinear analysis for an improved car-following model account for the optimal velocity changes with memory

Author

Listed:
  • Jin, Zhizhan
  • Li, Zhipeng
  • Cheng, Rongjun
  • Ge, Hongxia

Abstract

In this paper, an extended car-following model is developed basing on the full velocity difference model (FVDM) to investigate the effect of the optimal velocity changes with memory on traffic flow. The stability conditions of the improved model are obtained through linear stability analysis. Then the time-dependent Ginzburg–Landau (TDGL) equation and the modified Korteweg–de Vries (mKdV) equation are derived by using nonlinear analysis. The kink–antikink soliton can describe the traffic jams near the critical point. Moreover, the evolution of traffic jam and corresponding the change of energy consumption are discussed. Numerical simulations show that the extended model is found not only to enhance the stability of traffic flow but also to depress the energy consumption. The numerical results are in good agreement with the theoretical analysis.

Suggested Citation

  • Jin, Zhizhan & Li, Zhipeng & Cheng, Rongjun & Ge, Hongxia, 2018. "Nonlinear analysis for an improved car-following model account for the optimal velocity changes with memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 278-288.
    • Handle: RePEc:eee:phsmap:v:507:y:2018:i:c:p:278-288
    DOI: 10.1016/j.physa.2018.05.043
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    1. Ge, H.X. & Cheng, R.J. & Li, Z.P., 2008. "Two velocity difference model for a car following theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5239-5245.
    2. Ou, Hui & Tang, Tie-Qiao, 2018. "Impacts of moving bottlenecks on traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 131-138.
    3. Chen, Jing & Lin, Lan & Jiang, Rui, 2017. "Assigning on-ramp flows to maximize capacity of highway with two on-ramps and one off-ramp in between," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 347-357.
    4. Xue, Shuqi & Jia, Bin & Jiang, Rui & Li, Xingang & Shan, Jingjing, 2017. "An improved Burgers cellular automaton model for bicycle flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 487(C), pages 164-177.
    5. 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.
    6. Zhipeng Li & Chenjie Zhong & Lizhu Chen & Shangzhi Xu & Yeqing Qian, 2016. "Analytical studies on a new lattice hydrodynamic traffic flow model with consideration of traffic current cooperation among three consecutive sites," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(03), pages 1-16, March.
    7. Jiang, Rui & Wu, Qing-Song, 2007. "The night driving behavior in a car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 297-306.
    8. 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.
    9. 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.
    10. Ou, Hui & Tang, Tie-Qiao, 2018. "An extended two-lane car-following model accounting for inter-vehicle communication," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 260-268.
    11. Guo, Lantian & Zhao, Xiangmo & Yu, Shaowei & Li, Xiuhai & Shi, Zhongke, 2017. "An improved car-following model with multiple preceding cars’ velocity fluctuation feedback," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 436-444.
    12. Peng, Guanghan & He, Hongdi & Lu, Wei-Zhen, 2016. "A new car-following model with the consideration of incorporating timid and aggressive driving behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 197-202.
    13. Nagatani, Takashi, 1999. "TDGL and MKdV equations for jamming transition in the lattice models of traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(3), pages 581-592.
    14. Sun, Jie & Li, Zhipeng & Sun, Jian, 2015. "Study on traffic characteristics for a typical expressway on-ramp bottleneck considering various merging behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 440(C), pages 57-67.
    15. Wang, Yunong & Cheng, Rongjun & Ge, Hongxia, 2017. "A lattice hydrodynamic model based on delayed feedback control considering the effect of flow rate difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 478-484.
    16. Jiang, Rui & Hu, Mao-Bin & Zhang, H.M. & Gao, Zi-You & Jia, Bin & Wu, Qing-Song, 2015. "On some experimental features of car-following behavior and how to model them," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 338-354.
    17. Li, Xiaoqin & Fang, Kangling & Peng, Guanghan, 2017. "A new lattice model accounting for multiple optimal current differences’ anticipation effect in two-lane system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 814-826.
    18. 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.
    19. Zhipeng Li & Xun Xu & Shangzhi Xu & Yeqing Qian & Juan Xu, 2016. "Analytical studies on an extended car following model for mixed traffic flow with slow and fast vehicles," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(01), pages 1-20, January.
    20. Yu, Shaowei & Zhao, Xiangmo & Xu, Zhigang & Shi, Zhongke, 2016. "An improved car-following model considering the immediately ahead car’s velocity difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 446-455.
    21. 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.
    22. Yu, Shaowei & Shi, Zhongke, 2015. "The effects of vehicular gap changes with memory on traffic flow in cooperative adaptive cruise control strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 206-223.
    23. Tang, Tie-Qiao & Wang, Tao & Chen, Liang & Huang, Hai-Jun, 2018. "Analysis of the equilibrium trip cost accounting for the fuel cost in a single-lane traffic system without late arrival," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 451-457.
    24. Li, Xiaoqin & Fang, Kangling & Peng, Guanghan, 2017. "A new lattice model of traffic flow with the consideration of the drivers’ aggressive characteristics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 315-321.
    25. Yu, Shaowei & Huang, Mengxing & Ren, Jia & Shi, Zhongke, 2016. "An improved car-following model considering velocity fluctuation of the immediately ahead car," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 1-17.
    26. Xue, Yu & Kang, San-Jun & Lu, Wei-Zhen & He, Hong-Di, 2014. "Energy dissipation of traffic flow at an on-ramp," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 172-178.
    27. Tang, T.Q. & Li, P. & Yang, X.B., 2013. "An extended macro model for traffic flow with consideration of multi static bottlenecks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3537-3545.
    28. Cheng, Rongjun & Ge, Hongxia & Wang, Jufeng, 2017. "KdV–Burgers equation in a new continuum model based on full velocity difference model considering anticipation effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 52-59.
    29. Wen-Xing Zhu & Li-Dong Zhang, 2014. "An original traffic flow model with signal effect for energy dissipation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(07), pages 1-11.
    30. Tang, Tie-Qiao & Rui, Ying-Xu & Zhang, Jian & Shang, Hua-Yan, 2018. "A cellular automation model accounting for bicycle’s group behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1782-1797.
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