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Moving bottlenecks: A numerical method that converges in flows

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  • Daganzo, Carlos F.
  • Laval, Jorge A.

Abstract

This paper presents a numerical method to model kinematic wave (KW) traffic streams containing slow vehicles. The slow vehicles are modeled discretely as moving boundaries that can affect the traffic stream. The proposed scheme converges in flows, densities and speeds without oscillations, and therefore can be readily used in situations where one wishes to model the effect of the traffic stream on the bottlenecks too.

Suggested Citation

  • Daganzo, Carlos F. & Laval, Jorge A., 2005. "Moving bottlenecks: A numerical method that converges in flows," Transportation Research Part B: Methodological, Elsevier, vol. 39(9), pages 855-863, November.
    • Handle: RePEc:eee:transb:v:39:y:2005:i:9:p:855-863
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    1. Daganzo, Carlos F., 2003. "A Variational Formulation for a Class of First Order PDE's," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt5p54n38q, Institute of Transportation Studies, UC Berkeley.
    2. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part III: Multi-destination flows," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 305-313, August.
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    Cited by:

    1. Lv, Wei & Song, Wei-guo & Liu, Xiao-dong & Ma, Jian, 2013. "A microscopic lane changing process model for multilane traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1142-1152.
    2. Xiaoxu Dai & Minghua Hu & Wen Tian & Daoyi Xie & Bin Hu, 2016. "Application of Epidemiology Model on Complex Networks in Propagation Dynamics of Airspace Congestion," PLOS ONE, Public Library of Science, vol. 11(6), pages 1-11, June.
    3. Chow, Andy H.F. & Li, Shuai & Zhong, Renxin, 2017. "Multi-objective optimal control formulations for bus service reliability with traffic signals," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 248-268.
    4. Shu-bin Li & Bai-bai Fu & Jian-feng Zheng, 2013. "Dynamic Analysis of Traffic State and Congestion Propagation on Bidirectional Grid Network," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-7, November.
    5. Laval, Jorge A. & Daganzo, Carlos F., 2006. "Lane-changing in traffic streams," Transportation Research Part B: Methodological, Elsevier, vol. 40(3), pages 251-264, March.
    6. Chubo Xu & Jianxiao Ma & Xiang Tang, 2022. "A Simulation-Based Study of the Influence of Low-Speed Vehicles on Expressway Traffic Safety," Sustainability, MDPI, vol. 14(19), pages 1-19, September.
    7. Laval, Jorge A., 2009. "Effects of geometric design on freeway capacity: Impacts of truck lane restrictions," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 720-728, July.
    8. 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.
    9. Wen Huan Ai & Ming Ming Wang & Da Wei Liu, 2024. "Saddle-node bifurcation control of macroscopic traffic flow model considering vehicle braking effect," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(5), pages 1-13, May.
    10. Xueyan Wei & Chengcheng Xu & Wei Wang & Menglin Yang & Xiaoma Ren, 2017. "Evaluation of average travel delay caused by moving bottlenecks on highways," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-25, August.
    11. Jiancheng Long & Ziyou Gao & Xiaomei Zhao & Aiping Lian & Penina Orenstein, 2011. "Urban Traffic Jam Simulation Based on the Cell Transmission Model," Networks and Spatial Economics, Springer, vol. 11(1), pages 43-64, March.
    12. He, Yifan & Zeng, An, 2024. "Expanding bottlenecks reveals hidden bottlenecks and leads to more congested city centers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 640(C).
    13. Li, Jia & Zhang, H.M., 2013. "The variational formulation of a non-equilibrium traffic flow model: Theory and implications," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 314-325.
    14. Simoni, Michele D. & Claudel, Christian G., 2017. "A fast simulation algorithm for multiple moving bottlenecks and applications in urban freight traffic management," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 238-255.

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