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Lattice hydrodynamic model with bidirectional pedestrian flow

Author

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  • Tian, Huan-huan
  • He, Hong-di
  • Wei, Yan-fang
  • Yu, Xue
  • Lu, Wei-zhen

Abstract

The two-dimensional lattice hydrodynamic model of traffic is extended to the two-dimensional bidirectional pedestrian flow via taking four types of pedestrians into account. The stability condition and the mKdV equation to describe the density wave of pedestrian congestion are obtained by linear stability and nonlinear analysis, respectively. In addition, there exist three phase transitions among the freely moving phase, the coexisting phase and the uniformly congested phase in the phase diagram. It can also be found that the critical point ac refers to not only the fraction c1 of the eastbound and westbound pedestrians, but also the fraction c2 of the northbound and southbound pedestrians. However, the critical point ac could not appear in the phase diagram and congested crowd at any time when two fractions are equal to same value of 0.5 (c1=c2=0.5). Furthermore, numerical simulation is carried out to examine the performance of such a model and the results show coincidence with the theory analysis results.

Suggested Citation

  • Tian, Huan-huan & He, Hong-di & Wei, Yan-fang & Yu, Xue & Lu, Wei-zhen, 2009. "Lattice hydrodynamic model with bidirectional pedestrian flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2895-2902.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:14:p:2895-2902
    DOI: 10.1016/j.physa.2009.02.047
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    Cited by:

    1. 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).
    2. Ran Zhang & Zhonghua Wei & Heng Gu & Shi Qiu, 2021. "Behavior Evolution of Multi-Group in the Process of Pedestrian Crossing Based on Evolutionary Game Theory," Sustainability, MDPI, vol. 13(4), pages 1-17, February.
    3. Wang, Jufeng & Sun, Fengxin & Cheng, Rongjun & Ge, Hongxia, 2018. "An extended heterogeneous car-following model with the consideration of the drivers’ different psychological headways," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 1113-1125.
    4. 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.
    5. Saberi, Meead & Aghabayk, Kayvan & Sobhani, Amir, 2015. "Spatial fluctuations of pedestrian velocities in bidirectional streams: Exploring the effects of self-organization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 120-128.
    6. Tu, Lihua & Zhou, Jie, 2019. "Memory’s effect on bidirectional pedestrian flow based on lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    7. Rongjun, Cheng & Hongxia, Ge & Jufeng, Wang, 2018. "The nonlinear analysis for a new continuum model considering anticipation and traffic jerk effect," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 493-505.
    8. Lili Lu & Gang Ren & Wei Wang & Chen Yu & Chenzi Ding, 2013. "Exploring the Effects of Different Walking Strategies on Bi-Directional Pedestrian Flow," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-9, November.
    9. Henein, Colin Marc & White, Tony, 2010. "Microscopic information processing and communication in crowd dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4636-4653.
    10. Yuan Tang & Yu Xue & Muyang Huang & Qiyun Wen & Bingling Cen & Dong Chen, 2023. "A Lattice Hydrodynamic Model for Four-Way Pedestrian Traffic with Turning Capacity," Sustainability, MDPI, vol. 15(3), pages 1-17, January.
    11. 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.
    12. Wang, Jufeng & Sun, Fengxin & Cheng, Rongjun & Ge, Hongxia, 2018. "An extended car-following model considering the self-stabilizing driving behavior of headway," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 347-357.
    13. Cheng, Rongjun & Ge, Hongxia & Sun, Fengxin & Wang, Jufeng, 2018. "An extended macro model accounting for acceleration changes with memory and numerical tests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 270-283.
    14. Zhou, Jibiao & Chen, Siyuan & Ma, Changxi & Dong, Sheng, 2022. "Stability analysis of pedestrian traffic flow in horizontal channels: A numerical simulation method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    15. Yuan, Zijian & Wang, Tao & Zhang, Jing & Li, Shubin, 2022. "Influences of dynamic safe headway on car-following behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    16. Wang, Tao & Li, Guangyao & Zhang, Jing & Li, Shubin & Sun, Tao, 2019. "The effect of Headway Variation Tendency on traffic flow: Modeling and stabilization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 566-575.
    17. Zhai, Cong & Wu, Weitiao & Xiao, Yingping, 2023. "The jamming transition of multi-lane lattice hydrodynamic model with passing effect," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    18. 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.
    19. Jiang, Changtao & Cheng, Rongjun & Ge, Hongxia, 2018. "Effects of speed deviation and density difference in traffic lattice hydrodynamic model with interruption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 900-908.
    20. 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.
    21. Qingtao, Zhai & Hongxia, Ge & Rongjun, Cheng, 2018. "An extended continuum model considering optimal velocity change with memory and numerical tests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 774-785.

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