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Symmetries in the kinematic wave model and a parameter-free representation of traffic flow

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  • Laval, Jorge A.
  • Chilukuri, Bhargava R.

Abstract

This paper identifies a family of linear transformations where conservation laws are invariant. In the case of a triangular fundamental diagram, it is shown that for a subset of these transformations, flow, total distance traveled and total delay are invariant. This means that for capacity or delay computations one may choose the transformation—i.e., the shape of the triangular diagram—that simplifies the problem the most, which does not require knowing the actual fundamental diagram. This is appealing also for delay-optimizing control problems since they may be solved using an isosceles fundamental diagram, which provides the most efficient numerical methods. Examples are given.

Suggested Citation

  • Laval, Jorge A. & Chilukuri, Bhargava R., 2016. "Symmetries in the kinematic wave model and a parameter-free representation of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 168-177.
    • Handle: RePEc:eee:transb:v:89:y:2016:i:c:p:168-177
    DOI: 10.1016/j.trb.2016.02.009
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    References listed on IDEAS

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    1. 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.
    2. Laval, Jorge A. & Castrillón, Felipe, 2015. "Stochastic approximations for the macroscopic fundamental diagram of urban networks," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 904-916.
    3. Jorge A. Laval & Ludovic Leclercq, 2010. "Continuum Approximation for Congestion Dynamics Along Freeway Corridors," Transportation Science, INFORMS, vol. 44(1), pages 87-97, February.
    4. Laval, Jorge A. & Leclercq, Ludovic, 2013. "The Hamilton–Jacobi partial differential equation and the three representations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 52(C), pages 17-30.
    5. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 281-287, August.
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    Cited by:

    1. Ludovic Leclercq & Mahendra Paipuri, 2019. "Macroscopic Traffic Dynamics Under Fast-Varying Demand," Transportation Science, INFORMS, vol. 53(6), pages 1526-1545, November.
    2. Maiti, Nandan & Laval, Jorge A. & Chilukuri, Bhargava Rama, 2024. "Universality of area occupancy-based fundamental diagrams in mixed traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 640(C).
    3. Laval, Jorge A. & Leclercq, Ludovic & Chiabaut, Nicolas, 2018. "Minimal parameter formulations of the dynamic user equilibrium using macroscopic urban models: Freeway vs city streets revisited," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 676-686.
    4. (Sean) Qian, Zhen & Li, Jia & Li, Xiaopeng & Zhang, Michael & Wang, Haizhong, 2017. "Modeling heterogeneous traffic flow: A pragmatic approach," Transportation Research Part B: Methodological, Elsevier, vol. 99(C), pages 183-204.
    5. Aghamohammadi, Rafegh & Laval, Jorge A., 2020. "Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models," Transportation Research Part B: Methodological, Elsevier, vol. 137(C), pages 99-118.
    6. Mariotte, Guilhem & Leclercq, Ludovic & Laval, Jorge A., 2017. "Macroscopic urban dynamics: Analytical and numerical comparisons of existing models," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 245-267.

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