IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i22p2897-d678832.html
   My bibliography  Save this article

Impact of Strong Wind and Optimal Estimation of Flux Difference Integral in a Lattice Hydrodynamic Model

Author

Listed:
  • Huimin Liu

    (Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China)

  • Yuhong Wang

    (Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China)

Abstract

A modified lattice hydrodynamic model is proposed, in which the impact of strong wind and the optimal estimation of flux difference integral are simultaneously analyzed. Based on the control theory, the stability condition is acquired through linear analysis. The modified Korteweg-de Vries (mKdV) equation is derived via nonlinear analysis, in order to express a description of the evolution of density waves. Then, numerical simulation is conducted. From the simulation results, strong wind can largely influence the traffic flow stability. The stronger the wind becomes, the more stable the traffic flow is, to some extent. Similarly, the optimal estimation of flux difference integral also contributes to stabilizing traffic flow. The simulation results show no difference compared with the theoretical findings. In conclusion, the new model is able to make the traffic flow more stable.

Suggested Citation

  • Huimin Liu & Yuhong Wang, 2021. "Impact of Strong Wind and Optimal Estimation of Flux Difference Integral in a Lattice Hydrodynamic Model," Mathematics, MDPI, vol. 9(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2897-:d:678832
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/22/2897/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/22/2897/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sun, Yuqing & Ge, Hongxia & Cheng, Rongjun, 2018. "An extended car-following model under V2V communication environment and its delayed-feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 349-358.
    2. Yang, Shu-hong & Li, Chun-gui & Tang, Xin-lai & Tian, Chuan, 2016. "Effect of optimal estimation of flux difference information on the lattice traffic flow model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 394-399.
    3. Kaur, Ramanpreet & Sharma, Sapna, 2018. "Modeling and simulation of driver’s anticipation effect in a two lane system on curved road with slope," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 110-120.
    4. Tang, Tie-Qiao & Shi, Wei-Fang & Huang, Hai-Jun & Wu, Wen-Xiang & Song, Ziqi, 2019. "A route-based traffic flow model accounting for interruption factors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 767-785.
    5. Changxi Ma & Wei Hao & Ruichun He & Xiaoyan Jia & Fuquan Pan & Jing Fan & Ruiqi Xiong, 2018. "Distribution path robust optimization of electric vehicle with multiple distribution centers," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-16, March.
    6. Peng, Guanghan & Kuang, Hua & Qing, Li, 2018. "A new lattice model of traffic flow considering driver’s anticipation effect of the traffic interruption probability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 374-380.
    7. Wang, Jufeng & Sun, Fengxin & Ge, Hongxia, 2019. "An improved lattice hydrodynamic model considering the driver’s desire of driving smoothly," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 119-129.
    8. Wang, Ting & Cheng, Rongjun & Ge, Hongxia, 2019. "An extended two-lane lattice hydrodynamic model for traffic flow on curved road with passing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    9. Zhu, Wen-Xing & Zhang, H.M., 2018. "Analysis of mixed traffic flow with human-driving and autonomous cars based on car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 274-285.
    10. 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.
    11. Wu, Xia & Zhao, Xiangmo & Song, Huansheng & Xin, Qi & Yu, Shaowei, 2019. "Effects of the prevision relative velocity on traffic dynamics in the ACC strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 192-198.
    12. 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.
    13. Xin, Qi & Yang, Nan & Fu, Rui & Yu, Shaowei & Shi, Zhongke, 2018. "Impacts analysis of car following models considering variable vehicular gap policies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 338-355.
    14. 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.
    15. 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.
    16. Ou, Hui & Tang, Tie-Qiao, 2018. "An extended two-lane car-following model accounting for inter-vehicle communication," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 260-268.
    17. Dawei Liu & Zhongke Shi & Wenhuan Ai, 2017. "An Improved Car-Following Model Accounting for Impact of Strong Wind," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-12, October.
    18. 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.
    19. 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.
    20. 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.
    21. Peng, Guanghan & Yang, Shuhong & Xia, Dongxue & Li, Xiaoqin, 2018. "A novel lattice hydrodynamic model considering the optimal estimation of flux difference effect on two-lane highway," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 929-937.
    22. 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.
    23. Wang, Qingying & Ge, Hongxia, 2019. "An improved lattice hydrodynamic model accounting for the effect of “backward looking” and flow integral," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 438-446.
    24. 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.
    25. 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.
    26. Changxi Ma & Ruichun He & Wei Zhang, 2018. "Path optimization of taxi carpooling," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-15, August.
    27. Peng, Guanghan & Zhao, Hongzhuan & Li, Xiaoqin, 2019. "The impact of self-stabilization on traffic stability considering the current lattice’s historic flux for two-lane freeway," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 31-37.
    28. Changtao-Jiang, & Rongjun-Cheng, & Hongxia-Ge,, 2019. "Mean-field flow difference model with consideration of on-ramp and off-ramp," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 465-476.
    29. Tang, Tie-Qiao & Rui, Ying-Xu & Zhang, Jian & Shang, Hua-Yan, 2018. "A cellular automation model accounting for bicycle’s group behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1782-1797.
    30. Changxi Ma & Wei Hao & Fuquan Pan & Wang Xiang, 2018. "Road screening and distribution route multi-objective robust optimization for hazardous materials based on neural network and genetic algorithm," PLOS ONE, Public Library of Science, vol. 13(6), pages 1-22, June.
    31. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yumin Cheng, 2022. "Preface to the Special Issue on “Numerical Computation, Data Analysis and Software in Mathematics and Engineering”," Mathematics, MDPI, vol. 10(13), pages 1-5, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Lixiang & Cheng, Rongjun & Ge, Hongxia, 2021. "New feedback control for a novel two-dimensional lattice hydrodynamic model considering driver’s memory effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    2. Yan, Chunyue & Ge, Hongxia & Cheng, Rongjun, 2019. "An extended car-following model by considering the optimal velocity difference and electronic throttle angle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Qi, Xinyue & Ge, Hongxia & Cheng, Rongjun, 2019. "Analysis of a novel lattice hydrodynamic model considering density integral and “backward looking” effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 714-723.
    4. Chang, Yinyin & He, Zhiting & Cheng, Rongjun, 2019. "Analysis of the historical time integral form of relative flux and feedback control in an extended lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 326-334.
    5. Chen, Can & Ge, Hongxia & Cheng, Rongjun, 2019. "Self-stabilizing analysis of an extended car-following model with consideration of expected effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    6. Ma, Xinjuan & Ge, Hongxia & Cheng, Rongjun, 2019. "Influences of acceleration with memory on stability of traffic flow and vehicle’s fuel consumption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 143-154.
    7. Jiao, Yulei & Ge, Hongxia & Cheng, Rongjun, 2019. "Nonlinear analysis for a modified continuum model considering electronic throttle (ET) and backward looking effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    8. Li, Shihao & Cheng, Rongjun & Ge, Hongxia, 2020. "An improved car-following model considering electronic throttle dynamics and delayed velocity difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    9. Zhaoze, Liu & Rongjun, Cheng & Hongxia, Ge, 2019. "Research on preceding vehicle’s taillight effect and energy consumption in an extended macro traffic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 304-314.
    10. Chen, Can & Cheng, Rongjun & Ge, Hongxia, 2019. "An extended car-following model considering driver’s sensory memory and the backward looking effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 278-289.
    11. Wang, Zihao & Ge, Hongxia & Cheng, Rongjun, 2020. "An extended macro model accounting for the driver’s timid and aggressive attributions and bounded rationality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    12. Ren, Weilin & Cheng, Rongjun & Ge, Hongxia, 2021. "Bifurcation analysis for a novel heterogeneous continuum model considering electronic throttle angle changes with memory," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    13. Sun, Yuqing & Ge, Hongxia & Cheng, Rongjun, 2019. "A car-following model considering the effect of electronic throttle opening angle over the curved road," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    14. Huimin Liu & Rongjun Cheng & Tingliu Xu, 2021. "Analysis of a Novel Two-Dimensional Lattice Hydrodynamic Model Considering Predictive Effect," Mathematics, MDPI, vol. 9(19), pages 1-13, October.
    15. Hongxia Ge & Siteng Li & Chunyue Yan, 2021. "An Extended Car-Following Model Based on Visual Angle and Electronic Throttle Effect," Mathematics, MDPI, vol. 9(22), pages 1-17, November.
    16. Peng, Guanghan & Jia, Teti & Kuang, Hua & Tan, Huili, 2022. "Energy consumption in a new lattice hydrodynamic model based on the delayed effect of collaborative information transmission under V2X environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    17. Wang, Jufeng & Sun, Fengxin & Ge, Hongxia, 2019. "An improved lattice hydrodynamic model considering the driver’s desire of driving smoothly," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 119-129.
    18. 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.
    19. Wang, Zihao & Zhu, Wen-Xing, 2022. "Modeling and stability analysis of traffic flow considering electronic throttle dynamics on a curved road with slope," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    20. Zhai, Cong & Wu, Weitiao & Xiao, Yingping & Luo, Qiang & Zhang, Yusong, 2022. "Modeling bidirectional pedestrian flow with the perceived uncertainty of preceding pedestrian information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2897-:d:678832. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.