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A feedback control method with consideration of the next-nearest-neighbor interactions in a lattice hydrodynamic model

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  • Cen, Bing-ling
  • Xue, Yu
  • Zhang, Yi-cai
  • Wang, Xue
  • He, Hong-di

Abstract

A feedback control method with consideration of the next-nearest-neighbor interactions is investigated in the lattice hydrodynamic traffic model. The stability condition is obtained by discussing the first-order transfer function G1 and the second-order transfer function G2. The solution of mKdV equation which describe the density wave are yielded by nonlinear analysis. Theoretical analysis result indicates that the feedback gain λ, the weight coefficient of the nearest-neighbor interaction and the next-nearest-neighbor interaction have a great impact on the improvement of the stability of traffic flow. Numerical simulations by analyzing the short-term, long-term behaviors and hysteresis loop of traffic flow verify that the impacts of the feedback gain λ, the nearest-neighbor weight and the next-nearest-neighbor weight on traffic control. The feedback control method considering the next-nearest-neighbor interactions displays the nonlocal characteristics in the implementation of local control process.

Suggested Citation

  • Cen, Bing-ling & Xue, Yu & Zhang, Yi-cai & Wang, Xue & He, Hong-di, 2020. "A feedback control method with consideration of the next-nearest-neighbor interactions in a lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    • Handle: RePEc:eee:phsmap:v:559:y:2020:i:c:s0378437120305537
    DOI: 10.1016/j.physa.2020.125055
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    1. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    2. 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.
    3. Chang, Yinyin & He, Zhiting & Cheng, Rongjun, 2019. "An extended lattice hydrodynamic model considering the driver’s sensory memory and delayed-feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 522-532.
    4. 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.
    5. Sun, Yuqing & Ge, Hongxia & Cheng, Rongjun, 2019. "An extended car-following model considering driver’s memory and average speed of preceding vehicles with control strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 752-761.
    6. 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.
    7. 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.
    8. Zhao, Xiaomei & Gao, Ziyou, 2006. "A control method for congested traffic induced by bottlenecks in the coupled map car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 513-522.
    9. 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.
    10. 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.
    11. 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.
    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. 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.
    14. Cheng, Rongjun & Wang, Yunong, 2019. "An extended lattice hydrodynamic model considering the delayed feedback control on a curved road," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 510-517.
    15. Tian, Jun-fang & Yuan, Zhen-zhou & Jia, Bin & Li, Ming-hua & Jiang, Guo-jun, 2012. "The stabilization effect of the density difference in the modified lattice hydrodynamic model of traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(19), pages 4476-4482.
    16. 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.
    17. Nagatani, Takashi, 1999. "Jamming transition of high-dimensional traffic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(3), pages 592-611.
    18. Guanghan Peng & Xinhua Cai & Changqing Liu & Binfang Cao, 2011. "A New Lattice Model Of Traffic Flow With The Consideration Of The Honk Effect," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(09), pages 967-976.
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