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A new continuum traffic flow model with two delays

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  • Yu, Lei

Abstract

A new continuum version of the car following FVD-Ds model is developed by using a series expansion of the headway in terms of the density. FVD-Ds model is the extension of the full velocity difference (FVD) model with two delays. The stability condition of the new continuum model is derived using the linear stability theory. The Korteweg–de Vries (KdV) equation is derived to describe traffic behavior near the neutral stability line by applying the reductive perturbation method. The corresponding soliton solution of the KdV equation is also obtained. The numerical simulations show that the local clusters appear. It agrees with the theoretical analysis.

Suggested Citation

  • Yu, Lei, 2020. "A new continuum traffic flow model with two delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s037843711932093x
    DOI: 10.1016/j.physa.2019.123757
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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. Li, Xiangchen & Luo, Xia & He, Mengchen & Chen, Siwei, 2018. "An improved car-following model considering the influence of space gap to the response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 536-545.
    3. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    4. Zhang, Yicai & Xue, Yu & Zhang, Peng & Fan, Deli & di He, Hong, 2019. "Bifurcation analysis of traffic flow through an improved car-following model considering the time-delayed velocity difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 133-140.
    5. Tang, Tie-Qiao & Chen, Liang & Wu, Yong-Hong & Caccetta, Lou, 2015. "A macro traffic flow model accounting for real-time traffic state," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 55-67.
    6. 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.
    7. Ou, Zhong-Hui, 2008. "Density waves in the continuum analog of the full velocity difference model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 1799-1806.
    8. Malenje, Jairus Odawa & Zhao, Jing & Li, Peng & Han, Yin, 2018. "An extended car-following model with the consideration of the illegal pedestrian crossing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 650-661.
    9. 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.
    10. Lei Yu & Zhong-Ke Shi, 2009. "Density Wave In A New Anisotropic Continuum Model For Traffic Flow," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(11), pages 1849-1859.
    11. 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.
    12. Wang, Xiao & Jiang, Rui & Li, Li & Lin, Yi-Lun & Wang, Fei-Yue, 2019. "Long memory is important: A test study on deep-learning based car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 786-795.
    13. Jin, Sheng & Qu, Xiaobo & Xu, Cheng & Wang, Dian-Hai, 2013. "Dynamic characteristics of traffic flow with consideration of pedestrians’ road-crossing behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 3881-3890.
    14. Jian-Xun Ding & Hai-Jun Huang, 2010. "A Cellular Automata Model Of Traffic Flow With Consideration Of The Inertial Driving Behavior," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 549-557.
    15. L. Yu & Z.-K. Shi, 2007. "Density waves in traffic flow model with relative velocity," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(1), pages 115-120, May.
    16. Wang, Jufeng & Sun, Fengxin & Ge, Hongxia, 2018. "Effect of the driver’s desire for smooth driving on the car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 96-108.
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