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Delay-independent traffic flux control for a discrete-time lattice hydrodynamic model with time-delay

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  • Pan, Dong-Bo
  • Zhang, Geng
  • Jiang, Shan
  • Zhang, Yu
  • Cui, Bo-Yuan

Abstract

A discrete-time lattice hydrodynamic model with time-delay and delay-independent traffic flux control signal is introduced. The new model is analyzed with the discrete-time Lyapunov stability theorem and a sufficient stable condition of the model is presented in the form of linear matrix inequality. Through numerical simulation, the traffic flow evolution rules under different conditions of time-delay and control gain are demonstrated and compared. All the results show that the traffic system with time-delay can easily evolve into traffic congestion comparing to the traffic system without time-delay. Also the discrete-time traffic flux control signal can improve the stable level of traffic flow.

Suggested Citation

  • Pan, Dong-Bo & Zhang, Geng & Jiang, Shan & Zhang, Yu & Cui, Bo-Yuan, 2021. "Delay-independent traffic flux control for a discrete-time lattice hydrodynamic model with time-delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    • Handle: RePEc:eee:phsmap:v:563:y:2021:i:c:s0378437120307640
    DOI: 10.1016/j.physa.2020.125440
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    1. 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.
    2. Peng, Guanghan & Kuang, Hua & Qing, Li, 2018. "Feedback control method in lattice hydrodynamic model under honk environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 651-656.
    3. Zhang, Yu & Wang, Sha & Pan, Dong-bo & Zhang, Geng, 2021. "Stability analysis for a new lattice hydrodynamic model with time-varying delay in sensing traffic flux," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    4. 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.
    5. 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.
    6. Sun, Fengxin & Chow, Andy H.F. & Lo, S.M. & Ge, Hongxia, 2018. "A two-lane lattice hydrodynamic model with heterogeneous lane changing rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 389-400.
    7. Zhu, Chenqiang & Zhong, Shiquan & Li, Guangyu & Ma, Shoufeng, 2017. "New control strategy for the lattice hydrodynamic model of traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 445-453.
    8. Zhang, Yi-cai & Xue, Yu & Shi, Yin & Guo, Yan & Wei, Fang-ping, 2018. "Congested traffic patterns of two-lane lattice hydrodynamic model with partial reduced lane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 135-147.
    9. Zhipeng Li & Xingli Li & Fuqiang Liu, 2008. "STABILIZATION ANALYSIS AND MODIFIED KdV EQUATION OF LATTICE MODELS WITH CONSIDERATION OF RELATIVE CURRENT," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1163-1173.
    10. Zhao, Hongzhuan & Zhang, Geng & Li, Wenyong & Gu, Tianlong & Zhou, Dan, 2018. "Lattice hydrodynamic modeling of traffic flow with consideration of historical current integration effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1204-1211.
    11. Zhang, Geng & Zhang, Yu & Pan, Dong-Bo & Huang, Ren-Jie, 2019. "Study on the continuous delayed optimal flow on traffic stability in a new macro traffic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    12. Redhu, Poonam & Gupta, Arvind Kumar, 2016. "Effect of forward looking sites on a multi-phase lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 150-160.
    13. 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.
    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.
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