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A multi-commodity Lighthill–Whitham–Richards model of lane-changing traffic flow

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  • Jin, Wen-Long

Abstract

Systematic lane changes can seriously deteriorate traffic safety and efficiency inside lane-drop, merge, and other bottleneck areas. In our previous studies (Jin, 2010a,b), a phenomenological model of lane-changing traffic flow was proposed, calibrated, and analyzed based on a new concept of lane-changing intensity. In this study, we further consider weaving and non-weaving vehicles as two commodities and develop a multi-commodity, behavioral Lighthill–Whitham–Richards (LWR) model of lane-changing traffic flow. Based on a macroscopic model of lane-changing behaviors, we derive a fundamental diagram with parameters determined by car-following and lane-changing characteristics as well as road geometry and traffic composition. We further calibrate and validate fundamental diagrams corresponding to a triangular car-following fundamental diagram with NGSIM data. We introduce an entropy condition for the multi-commodity LWR model and solve the Riemann problem inside a homogeneous lane-changing area. From the Riemann solutions, we derive a flux function in terms of traffic demand and supply. Then we apply the model to study lane-changing traffic dynamics inside a lane-drop area and show that the smoothing effect of HOV lanes is consistent with observations in existing studies. The new theory of lane-changing traffic flow can be readily incorporated into Cell Transmission Model, and this study could lead to better strategies for mitigating bottleneck effects of lane-changing traffic flow.

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  • Jin, Wen-Long, 2013. "A multi-commodity Lighthill–Whitham–Richards model of lane-changing traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 361-377.
    • Handle: RePEc:eee:transb:v:57:y:2013:i:c:p:361-377
    DOI: 10.1016/j.trb.2013.06.002
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    Cited by:

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    2. He, Jia & Yang, Hai & Huang, Hai-Jun & Tang, Tie-Qiao, 2018. "Impacts of wireless charging lanes on travel time and energy consumption in a two-lane road system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 1-10.
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    5. Khelfa, Basma & Ba, Ibrahima & Tordeux, Antoine, 2023. "Predicting highway lane-changing maneuvers: A benchmark analysis of machine and ensemble learning algorithms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 612(C).
    6. Gong, Siyuan & Du, Lili, 2016. "Optimal location of advance warning for mandatory lane change near a two-lane highway off-ramp," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 1-30.
    7. Zheng, Zuduo, 2014. "Recent developments and research needs in modeling lane changing," Transportation Research Part B: Methodological, Elsevier, vol. 60(C), pages 16-32.
    8. Jin, Zuan & Ma, Minghui & Liang, Shidong & Yao, Hongguang, 2024. "Differential variable speed limit control strategy consider lane assignment at the freeway lane drop bottleneck," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    9. Li, Zhengming & Smirnova, M.N. & Zhang, Yongliang & Smirnov, N.N. & Zhu, Zuojin, 2022. "Tunnel speed limit effects on traffic flow explored with a three lane model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 185-197.
    10. Mingmin Guo & Zheng Wu & Huibing Zhu, 2018. "Empirical study of lane-changing behavior on three Chinese freeways," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-22, January.
    11. Oh, Simon & Yeo, Hwasoo, 2015. "Impact of stop-and-go waves and lane changes on discharge rate in recovery flow," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 88-102.
    12. Jin, Wen-Long, 2018. "Unifiable multi-commodity kinematic wave model," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 639-659.
    13. Nima Dadashzadeh & Murat Ergun, 2019. "An Integrated Variable Speed Limit and ALINEA Ramp Metering Model in the Presence of High Bus Volume," Sustainability, MDPI, vol. 11(22), pages 1-26, November.
    14. Jin, Wen-Long & Gan, Qi-Jian & Lebacque, Jean-Patrick, 2015. "A kinematic wave theory of capacity drop," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 316-329.
    15. He, Jia & He, Zhengbing & Fan, Bo & Chen, Yanyan, 2020. "Optimal location of lane-changing warning point in a two-lane road considering different traffic flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    16. Feng, Shumin & Li, Jinyang & Ding, Ning & Nie, Cen, 2015. "Traffic paradox on a road segment based on a cellular automaton: Impact of lane-changing behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 90-102.
    17. Chauhan, Prajwal & Kanagaraj, Venkatesan & Asaithambi, Gowri, 2022. "Understanding the mechanism of lane changing process and dynamics using microscopic traffic data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    18. Zhou, Hao & Toth, Christopher & Guensler, Randall & Laval, Jorge, 2022. "Hybrid modeling of lane changes near freeway diverges," Transportation Research Part B: Methodological, Elsevier, vol. 165(C), pages 1-14.

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