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A Section Approach To A Traffic Flow Model On Networks

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  • ARVIND KUMAR GUPTA

    (Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140001, India)

Abstract

The development of real time traffic flow models for urban road networks is of paramount importance for the purposes of optimizing and control of traffic flow. Motivated by the modeling of road networks in last decade, this paper proposes a different and simplified approach, known as section approach to model road networks in the framework of macroscopic traffic flow models. For evaluation of the traffic states on a single road, an anisotropic continuum GK-model developed by [Gupta and Katiyar,J. Phys. A38, 4069 (2005)] is used as a single-section model. This model is applied to a two-section single lane road with points of entry and exits. In place of modeling the effect of off- and on-ramps in the continuity equation, a set of special boundary condition is taken into account to treat the points of entry and exit. A four-section road network comprised of two one-lane roads is also modeled using this methodology. The performances of the section approaches are investigated and obtained results are demonstrated over simulated data for different boundary conditions.

Suggested Citation

  • Arvind Kumar Gupta, 2013. "A Section Approach To A Traffic Flow Model On Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(05), pages 1-23.
    • Handle: RePEc:wsi:ijmpcx:v:24:y:2013:i:05:n:s0129183113500186
    DOI: 10.1142/S0129183113500186
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    1. ., 2006. "Physical and Social Indicators," Chapters, in: Middle East Oil Exporters, chapter 5, Edward Elgar Publishing.
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    Cited by:

    1. Liao, Peng & Tang, Tie-Qiao & Wang, Tao & Zhang, Jian, 2019. "A car-following model accounting for the driving habits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 108-118.
    2. Verma, Muskan & Sharma, Sapna, 2023. "The role of occupancy and transition rate on traffic flow in a percolation-backbone fractal," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Tang, Tie-Qiao & Yi, Zhi-Yan & Zhang, Jian & Wang, Tao & Leng, Jun-Qiang, 2018. "A speed guidance strategy for multiple signalized intersections based on car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 399-409.
    4. Ou, Hui & Tang, Tie-Qiao & Zhang, Jian & Zhou, Jie-Ming, 2018. "A car-following model accounting for probability distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 105-113.
    5. 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.
    6. Chen, Dong & Sun, Dihua & Zhao, Min & Zhou, Tong & Cheng, Senlin, 2018. "Modeling and analyses for an extended car-following model accounting for drivers’ situation awareness from cyber physical perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 52-68.
    7. Xiaomeng Wang & Ling Peng & Tianhe Chi & Mengzhu Li & Xiaojing Yao & Jing Shao, 2015. "A Hidden Markov Model for Urban-Scale Traffic Estimation Using Floating Car Data," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-20, December.
    8. Nagatani, Takashi, 2020. "Traffic flow on percolation-backbone fractal," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    9. Ou, Hui & Tang, Tie-Qiao, 2018. "Impacts of moving bottlenecks on traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 131-138.
    10. Tang, Tie-Qiao & Zhang, Jian & Chen, Liang & Shang, Hua-Yan, 2017. "Analysis of vehicle’s safety envelope under car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 127-133.
    11. Li, Chuan-Yao & Huang, Hai-Jun & Tang, Tie-Qiao, 2017. "Analysis of social optimum for staggered shifts in a single-entry traffic corridor with no late arrivals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 275-283.
    12. Zhang, Zhao-Ze & Huang, Hai-Jun & Tang, Tie-Qiao, 2018. "Impacts of preceding information on travelers’ departure time behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 523-529.
    13. Zhao, Jing & Li, Peng, 2016. "An extended car-following model with consideration of speed guidance at intersections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 1-8.
    14. Li, Chuan-Yao & Sun, Qi-Jia, 2019. "Influence of coarse toll on the dynamic properties of traffic flow in a single-entry traffic corridor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    15. Ou, Hui & Tang, Tie-Qiao & Rui, Ying-Xu & Zhou, Jie-Ming, 2018. "Electric bicycle management and control at a signalized intersection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1000-1008.
    16. Zhao, Jing & Li, Peng, 2017. "An extended car-following model with consideration of vehicle to vehicle communication of two conflicting streams," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 178-187.
    17. Li, Chuan-Yao & Huang, Hai-Jun & Tang, Tie-Qiao, 2017. "Analysis of user equilibrium for staggered shifts in a single-entry traffic corridor with no late arrivals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 8-18.
    18. Ou, Hui & Tang, Tie-Qiao & Rui, Ying-Xu & Zhou, Jie-Ming, 2018. "Modeling electric bicycle’s abnormal behavior at a signalized intersection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 218-231.
    19. Tang, Tie-Qiao & Yi, Zhi-Yan & Lin, Qing-Feng, 2017. "Effects of signal light on the fuel consumption and emissions under car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 200-205.
    20. Wang, Jing-Peng & Huang, Hai-Jun & (Jeff) Ban, Xuegang, 2019. "Optimal capacity allocation for high occupancy vehicle (HOV) lane in morning commute," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 354-361.
    21. Nagatani, Takashi, 2021. "Traffic flow on star graph: Nonlinear diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    22. 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).
    23. 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.
    24. Verma, Muskan & Sharma, Sapna, 2023. "Modeling heterogeneity in an open percolation backbone fractal traffic network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).

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