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The nonlinear analysis for a new continuum model considering anticipation and traffic jerk effect

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  • Rongjun, Cheng
  • Hongxia, Ge
  • Jufeng, Wang

Abstract

Considering the anticipation and traffic jerk simultaneously, a new macro model of traffic flow is put forwarded in this paper. By means of linear stability theory, the new model's linear stability with the effect of traffic jerk and anticipation term is obtained.

Suggested Citation

  • Rongjun, Cheng & Hongxia, Ge & Jufeng, Wang, 2018. "The nonlinear analysis for a new continuum model considering anticipation and traffic jerk effect," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 493-505.
    • Handle: RePEc:eee:apmaco:v:332:y:2018:i:c:p:493-505
    DOI: 10.1016/j.amc.2018.03.077
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    References listed on IDEAS

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    1. Tie-Qiao Tang & Qiang Yu, 2016. "Influences of vehicles’ fuel consumption and exhaust emissions on the trip cost without late arrival under car-following model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(01), pages 1-9, January.
    2. Peng, G.H., 2012. "A study of wide moving jams in a new lattice model of traffic flow with the consideration of the driver anticipation effect and numerical simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5971-5977.
    3. Zhu, H.B. & Dai, S.Q., 2008. "Numerical simulation of soliton and kink density waves in traffic flow with periodic boundaries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4367-4375.
    4. Qian, Y.S. & Shao, X.M. & Zeng, J.W. & Wang, M., 2013. "An improved cellular automaton model with the consideration of a multi-point tollbooth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5874-5878.
    5. Tian, Huan-huan & He, Hong-di & Wei, Yan-fang & Yu, Xue & Lu, Wei-zhen, 2009. "Lattice hydrodynamic model with bidirectional pedestrian flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2895-2902.
    6. D. Helbing, 2009. "Derivation of non-local macroscopic traffic equations and consistent traffic pressures from microscopic car-following models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 69(4), pages 539-548, June.
    7. Tang, Tie-Qiao & Yu, Qiang & Yang, Shi-Chun & Ding, Chuan, 2015. "Impacts of the vehicle’s fuel consumption and exhaust emissions on the trip cost allowing late arrival under car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 431(C), pages 52-62.
    8. Tang, T.Q. & He, J. & Wu, Y.H. & Caccetta, L., 2014. "Propagating properties of traffic flow on a ring road without ramp," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 164-172.
    9. 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.
    10. 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.
    11. 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.
    12. Tang, Tie-Qiao & Zhang, Jian & Liu, Kai, 2017. "A speed guidance model accounting for the driver’s bounded rationality at a signalized intersection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 45-52.
    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. 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.
    15. Zhu, Wen-Xing & Zhang, Li-Dong, 2016. "Analysis of car-following model with cascade compensation strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 265-274.
    16. 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.
    17. Peng, G.H. & Cai, X.H. & Cao, B.F. & Liu, C.Q., 2012. "A new lattice model of traffic flow with the consideration of the traffic interruption probability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 656-663.
    18. Herrmann, Matthias & Kerner, Boris S, 1998. "Local cluster effect in different traffic flow models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 255(1), pages 163-188.
    19. Peng, Guang-han & Cheng, Rong-jun, 2013. "A new car-following model with the consideration of anticipation optimal velocity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3563-3569.
    20. Peng, G.H. & Song, W. & Peng, Y.J. & Wang, S.H., 2014. "A novel macro model of traffic flow with the consideration of anticipation optimal velocity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 76-82.
    21. 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.
    22. 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.
    23. 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.
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