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Generalization Second Order Macroscopic Traffic Models via Relative Velocity of the Congestion Propagation

Author

Listed:
  • Yaroslav Kholodov

    (Division of Applied Mathematics, Moscow Institute of Physics and Technology, Innopolis University, 420500 Innopolis, Russia)

  • Andrey Alekseenko

    (Institute for Computer Aided Design of RAS, 123056 Moscow, Russia)

  • Viktor Kazorin

    (Lab of Data Analysis and Bioinformatics, Innopolis University, 420500 Innopolis, Russia)

  • Alexander Kurzhanskiy

    (California Partners for Advanced Transportation Technology, University of California, Berkeley, CA 94720, USA)

Abstract

This paper presents a generalized second-order hydrodynamic traffic model. Its central piece is the expression for the relative velocity of the congestion (compression wave) propagation. We show that the well-known second-order models of Payne–Whitham, Aw–Rascal and Zhang are all special cases of the featured generalized model, and their properties are fully defined by how the relative velocity of the congestion is expressed. The proposed model is verified with traffic data from a segment of the Interstate 580 freeway in California, USA, collected by the California DOT’s Performance Measurement System (PeMS).

Suggested Citation

  • Yaroslav Kholodov & Andrey Alekseenko & Viktor Kazorin & Alexander Kurzhanskiy, 2021. "Generalization Second Order Macroscopic Traffic Models via Relative Velocity of the Congestion Propagation," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:2001-:d:618820
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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. Daganzo, Carlos F., 1995. "Requiem for second-order fluid approximations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 277-286, August.
    3. Papageorgiou, Markos, 1998. "Some remarks on macroscopic traffic flow modelling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(5), pages 323-329, September.
    4. Zhang, H. M., 2003. "Anisotropic property revisited--does it hold in multi-lane traffic?," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 561-577, July.
    5. Zhang, H. M., 2002. "A non-equilibrium traffic model devoid of gas-like behavior," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 275-290, March.
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    2. Zeyuan Song & Zuoren Sun, 2022. "Representing Functions in H 2 on the Kepler Manifold via WPOAFD Based on the Rational Approximation of Holomorphic Functions," Mathematics, MDPI, vol. 10(15), pages 1-15, August.

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