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A conserved higher-order anisotropic traffic flow model: Description of equilibrium and non-equilibrium flows

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  • Zhang, Peng
  • Wong, S.C.
  • Dai, S.Q.
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    Abstract

    This paper takes into account three regimes for the description of traffic dynamics, which include the introduction of a pseudo-density transformed from the velocity, the pressure as a function of the pseudo-density and the relaxation of velocity to equilibrium. The resultant characteristic variables can be used to measure the deviation of the phase state to a desired state and derive physically bounded solutions. Taking the pseudo-density as a conserved variable, the approach is able to describe both equilibrium and non-equilibrium flows in a systematic and unified manner, and thus complex traffic phenomena. The theoretical properties of the model are thoroughly investigated, and numerical examples are used to demonstrate the ability of the model to reproduce some notable traffic phenomena.

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    Bibliographic Info

    Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

    Volume (Year): 43 (2009)
    Issue (Month): 5 (June)
    Pages: 562-574

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    Handle: RePEc:eee:transb:v:43:y:2009:i:5:p:562-574

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    Keywords: Hyperbolic conservation laws Physically bounded solution Unstable equilibrium Stop-and-go waves;

    References

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    1. Wong, G. C. K. & Wong, S. C., 2002. "A multi-class traffic flow model - an extension of LWR model with heterogeneous drivers," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(9), pages 827-841, November.
    2. Lebacque, Jean-Patrick & Mammar, Salim & Haj-Salem, Habib, 2007. "The Aw-Rascle and Zhang's model: Vacuum problems, existence and regularity of the solutions of the Riemann problem," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 710-721, August.
    3. 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.
    4. Lu, Yadong & Wong, S.C. & Zhang, Mengping & Shu, Chi-Wang & Chen, Wenqin, 2008. "Explicit construction of entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a piecewise quadratic flow-density relationship," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 355-372, May.
    5. 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.
    6. Castillo, J. M. Del & Benítez, F. G., 1995. "On the functional form of the speed-density relationship--I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 373-389, October.
    7. Castillo, J. M. Del & Benítez, F. G., 1995. "On the functional form of the speed-density relationship--II: Empirical investigation," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 391-406, October.
    8. Jiang, Rui & Wu, Qing-Song & Zhu, Zuo-Jin, 2002. "A new continuum model for traffic flow and numerical tests," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 405-419, June.
    9. Beskos, Dimitrios E. & Okutani, Iwao & Michalopoulos, Panos, 1984. "Testing of dynamic models for signal controlled intersections," Transportation Research Part B: Methodological, Elsevier, vol. 18(4-5), pages 397-408.
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    Cited by:
    1. Zhang, Peng & Wu, Chun-Xiu & Wong, S.C., 2012. "A semi-discrete model and its approach to a solution for a wide moving jam in traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 456-463.

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