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Delayed-feedback control in multi-lane traffic system

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  • Madaan, Nikita
  • Sharma, Sapna

Abstract

In this paper, we investigate the effect of delayed feedback control on a multi-lane system. An extended lattice hydrodynamic model is derived on a multi-lane road which includes more comprehensive information. The stability condition is obtained via control method (based on the Hurwitz criteria and the H∞- norm). The Bode-plot of transfer function shows that the stability region enhances when delayed-feedback controller on multi-lane system is considered. To describe the propagating behavior of traffic density wave near the critical point, the modified Korteweg–de Vries (mKdV) equation is formulated through nonlinear analysis. It is concluded that considering the delayed-feedback control in the multi-lane system contributes to mitigating traffic jams. All the theoretical results are verified in both transient and steady state with numerical simulations on a hypothetical circular road.

Suggested Citation

  • Madaan, Nikita & Sharma, Sapna, 2022. "Delayed-feedback control in multi-lane traffic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    • Handle: RePEc:eee:phsmap:v:599:y:2022:i:c:s0378437122002990
    DOI: 10.1016/j.physa.2022.127393
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    as
    1. Zhang, Jing & Xu, Keyu & Li, Shubin & Wang, Tao, 2020. "A new two-lane lattice hydrodynamic model with the introduction of driver’s predictive effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    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. Zhao, Hongzhuan & Xia, Dongxue & Yang, Shuhong & Peng, Guanghan, 2020. "The delayed-time effect of traffic flux on traffic stability for two-lane freeway," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. 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.
    5. 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.
    6. 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.
    7. Zeng, Jiao-Yan & Ou, Hui & Tang, Tie-Qiao, 2019. "Feedback strategy with delay in a two-route traffic network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    8. 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.
    9. 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.
    10. 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).
    11. Zhao, Hongzhuan & Chen, Qiguang & Shi, Wei & Gu, Tianlong & Li, Wenyong, 2019. "Stability analysis of an improved car-following model accounting for the driver’s characteristics and automation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    12. Peng, Guanghan & Yang, Shuhong & Xia, Dongxue & Li, Xiaoqin, 2019. "Delayed-feedback control in a car-following model with the combination of V2V communication," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    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. Peng, Guanghan & Yang, Shuhong & Zhao, Hongzhuan, 2018. "A delayed-feedback control method for the lattice hydrodynamic model caused by the historic density difference effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 855-860.
    15. Kaur, Daljeet & Sharma, Sapna, 2020. "A new two-lane lattice model by considering predictive effect in traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    16. Xinyue Qi & Hongxia Ge & Rongjun Cheng, 2020. "Analysis of a Novel Two-Lane Hydrodynamic Lattice Model Accounting for Driver’s Aggressive Effect and Flow Difference Integral," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-13, May.
    17. Wang, Tao & Tang, Tie-Qiao & Chen, Liang & Huang, Hai-Jun, 2019. "Analysis of trip cost allowing late arrival in a traffic corridor with one entry and one exit under car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 387-398.
    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.
    19. Zhang, Geng & Sun, Di-hua & Liu, Wei-ning & Zhao, Min & Cheng, Sen-lin, 2015. "Analysis of two-lane lattice hydrodynamic model with consideration of drivers’ characteristics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 16-24.
    20. Madaan, Nikita & Sharma, Sapna, 2021. "A lattice model accounting for multi-lane traffic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 564(C).
    21. 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.
    22. 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.
    23. Daljeet Kaur & Sapna Sharma, 2020. "The impact of the predictive effect on traffic dynamics in a lattice model with passing," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(3), pages 1-10, March.
    24. Kaur, Ramanpreet & Sharma, Sapna, 2018. "Analyses of lattice hydrodynamic model using delayed feedback control with passing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 446-455.
    25. Peng, Guanghan & Bai, Kezhao & Kuang, Hua, 2019. "Feedback control caused by honk effect incorporating the driver’s characteristics in lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    26. Sharma, Sapna, 2015. "Lattice hydrodynamic modeling of two-lane traffic flow with timid and aggressive driving behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 401-411.
    27. 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.
    28. Peng, Guanghan & Kuang, Hua & Zhao, Hongzhuan & Qing, Li, 2019. "Nonlinear analysis of a new lattice hydrodynamic model with the consideration of honk effect on flux for two-lane highway," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 93-101.
    29. Daljeet Kaur & Sapna Sharma, 2021. "Prior information affecting traffic dynamics in a two dimensional (2D) network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(9), pages 1-12, September.
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