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A kinematic wave model in Lagrangian coordinates incorporating capacity drop: Application to homogeneous road stretches and discontinuities

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  • Yuan, Kai
  • Knoop, Victor L.
  • Hoogendoorn, Serge P.

Abstract

On freeways, congestion always leads to capacity drop. This means the queue discharge rate is lower than the pre-queue capacity. Our recent research findings indicate that the queue discharge rate increases with the speed in congestion, that is the capacity drop is strongly correlated with the congestion state. Incorporating this varying capacity drop into a kinematic wave model is essential for assessing consequences of control strategies. However, to the best of authors’ knowledge, no such a model exists. This paper fills the research gap by presenting a Lagrangian kinematic wave model. “Lagrangian” denotes that the new model is solved in Lagrangian coordinates. The new model can give capacity drops accompanying both of stop-and-go waves (on homogeneous freeway section) and standing queues (at nodes) in a network. The new model can be applied in a network operation. In this Lagrangian kinematic wave model, the queue discharge rate (or the capacity drop) is a function of vehicular speed in traffic jams. Four case studies on links as well as at lane-drop and on-ramp nodes show that the Lagrangian kinematic wave model can give capacity drops well, consistent with empirical observations.

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  • Yuan, Kai & Knoop, Victor L. & Hoogendoorn, Serge P., 2017. "A kinematic wave model in Lagrangian coordinates incorporating capacity drop: Application to homogeneous road stretches and discontinuities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 472-485.
    • Handle: RePEc:eee:phsmap:v:465:y:2017:i:c:p:472-485
    DOI: 10.1016/j.physa.2016.08.060
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    References listed on IDEAS

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    Cited by:

    1. Kai Yuan & Hong K. Lo, 2021. "Multiclass Traffic Flow Dynamics: An Endogenous Model," Transportation Science, INFORMS, vol. 55(2), pages 456-474, March.
    2. Fu, Ding-Jun & Zhang, Cun-Bao & Liu, Jun & Li, Tao & Li, Qi-Lang, 2024. "Research of the left-turn vehicles lane-changing behaviors at signalized intersections with contraflow lane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    3. Wang, Jiawen & Zou, Linzhi & Zhao, Jing & Wang, Xinwei, 2024. "Dynamic capacity drop propagation in incident-affected networks: Traffic state modeling with SIS-CTM," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    4. Huang, Wei & Hu, Yang, 2022. "A modified cell transmission model considering queuing characteristics for channelized zone at signalized intersections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    5. van der Gun, Jeroen P.T. & Pel, Adam J. & van Arem, Bart, 2017. "Extending the Link Transmission Model with non-triangular fundamental diagrams and capacity drops," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 154-178.
    6. Schmitt, Marius & Ramesh, Chithrupa & Lygeros, John, 2017. "Sufficient optimality conditions for distributed, non-predictive ramp metering in the monotonic cell transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 401-422.
    7. Li, Zhen-Hua & Zheng, Shi-Teng & Jiang, Rui & Tian, Jun-Fang & Zhu, Kai-Xuan & Di Pace, Roberta, 2022. "Empirical and simulation study on traffic oscillation characteristic using floating car data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).

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