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Lagrangian-based Hydrodynamic Model for Traffic Data Fusion on Freeways

Author

Listed:
  • Ke Han

    (Imperial College London)

  • Tao Yao

    (Pennsylvania State University)

  • Chaozhe Jiang

    (Southwest Jiaotong University)

  • Terry L. Friesz

    (Pennsylvania State University)

Abstract

This paper conducts a comprehensive study of the Lagrangian-based hydrodynamic model with application to highway state estimation. Our analysis is motivated by the practical problems of freeway traffic monitoring and estimation using multi-source data measured from mobile devices and fixed sensors. We conduct rigorous mathematical analysis on the Hamilton-Jacobi representation of the Lighthill-Whitham-Richards model in the transformed coordinates, and derive explicit and closed-form solutions with piecewise affine initial, boundary, and internal conditions, based on the variational principle. A numerical study of the Mobile Century field experiment demonstrates some unique features and the effectiveness in traffic estimation of the Lagrangian-based model.

Suggested Citation

  • Ke Han & Tao Yao & Chaozhe Jiang & Terry L. Friesz, 2017. "Lagrangian-based Hydrodynamic Model for Traffic Data Fusion on Freeways," Networks and Spatial Economics, Springer, vol. 17(4), pages 1071-1094, December.
    • Handle: RePEc:kap:netspa:v:17:y:2017:i:4:d:10.1007_s11067-017-9380-z
    DOI: 10.1007/s11067-017-9380-z
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    References listed on IDEAS

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    1. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    2. 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.
    3. Daganzo, Carlos F., 2006. "On the Variational Theory of Traffic Flow: Well-Posedness, Duality and Applications," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt61v1r1qq, Institute of Transportation Studies, UC Berkeley.
    4. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: basic theory and complex boundary conditions," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 187-196, February.
    5. 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.
    6. Mazaré, Pierre-Emmanuel & Dehwah, Ahmad H. & Claudel, Christian G. & Bayen, Alexandre M., 2011. "Analytical and grid-free solutions to the Lighthill–Whitham–Richards traffic flow model," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1727-1748.
    7. Herrera, Juan C. & Work, Daniel B. & Herring, Ryan & Ban, Xuegang Jeff & Bayen, Alexandre M, 2009. "Evaluation of Traffic Data Obtained via GPS-Enabled Mobile Phones: the Mobile Century Field Experiment," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt0sd42014, Institute of Transportation Studies, UC Berkeley.
    8. 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. Ke Han & Gabriel Eve & Terry L. Friesz, 2019. "Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation," Networks and Spatial Economics, Springer, vol. 19(3), pages 869-902, September.
    2. Hmaed Najafi Alamdarlo & Fariba Riyahi & Mohamad Hasan Vakilpoor, 2019. "Wheat Self-Sufficiency, Water Restriction and Virtual Water Trade in Iran," Networks and Spatial Economics, Springer, vol. 19(2), pages 503-520, June.

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