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On the numerical treatment of moving bottlenecks

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

Abstract

This paper shows how moving obstructions in (kinematic wave) traffic streams can be modeled with "off-the shelf" computer programs. It shows that if a moving obstruction is replaced by a sequence of fixed obstructions at nearby locations with the same "capacity", then the error in vehicle number converges uniformly to zero as the maximum separation between the moving and fixed bottlenecks is reduced. This result implies that average flows, densities, accumulations and delays can be predicted as accurately as desired with this method. Thus, any convergent finite difference scheme can be used to model moving bottlenecks. The approach can be used with non-concave fundamental diagrams and multiple bottlenecks, even if they pass each other. Examples are given. It is assumed that the bottleneck trajectories are exogenous to the model. However, by introducing suitable car-following laws and interaction rules, slow trucks and busses embedded in the traffic stream can be modeled endogenously.

Suggested Citation

  • Daganzo, Carlos F. & Laval, Jorge A., 2005. "On the numerical treatment of moving bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 39(1), pages 31-46, January.
    • Handle: RePEc:eee:transb:v:39:y:2005:i:1:p:31-46
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    References listed on IDEAS

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    1. Newell, G. F., 1998. "A moving bottleneck," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 531-537, November.
    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.
    3. Cassidy, Michael J. & Rudjanakanoknad, Jittichai, 2002. "Empirical Study of Ramp Metering and Capacity," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt41f4d25j, Institute of Transportation Studies, UC Berkeley.
    4. Daganzo, Carlos F. & Laval, Jorge A., 2003. "Moving Bottlenecks: A Numerical Method that Converges in Flows," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt1hp588xx, Institute of Transportation Studies, UC Berkeley.
    5. Yasuji Makigami & G. F. Newell & Richard Rothery, 1971. "Three-Dimensional Representation of Traffic Flow," Transportation Science, INFORMS, vol. 5(3), pages 302-313, August.
    6. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
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    Cited by:

    1. Shiomi, Yasuhiro & Yoshii, Toshio & Kitamura, Ryuichi, 2011. "Platoon-based traffic flow model for estimating breakdown probability at single-lane expressway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1314-1330.
    2. Xu Ouyang & Min Xu & Bojian Zhou, 2022. "An Elastic Demand Model for Locating Electric Vehicle Charging Stations," Networks and Spatial Economics, Springer, vol. 22(1), pages 1-31, March.
    3. Anderson, Paul & Geroliminis, Nikolas, 2020. "Dynamic lane restrictions on congested arterials," Transportation Research Part A: Policy and Practice, Elsevier, vol. 135(C), pages 224-243.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Rezaei, Danial & Aghayan, Iman & Hadadi, Farhad, 2021. "Studying perturbations and wave propagations by lane closures on traffic characteristics based on a dynamic approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    9. Leclercq, Ludovic, 2007. "Hybrid approaches to the solutions of the "Lighthill-Whitham-Richards" model," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 701-709, August.
    10. Leclercq, Ludovic, 2007. "Bounded acceleration close to fixed and moving bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 309-319, March.

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