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Structural properties of solutions arising from a nonequilibrium traffic flow theory

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  • Zhang, H. M.

Abstract

This paper analyzes the structural properties of the shock and rarefaction wave solutions of a nonequilibrium theory of vehicular traffic flow. It shows that this nonequilibrium theory has two families of characteristics: one is slower and the other is faster than vehicular speed. Corresponding to the slower characteristic arise 1-shock and 1-rarefaction waves, whose behavior is similar to that of the shock and rarefaction waves in the LWR theory; corresponding to the faster characteristic there are 2-shocks (and 2-rarefaction waves) that behave as bores in rivers. The latter behavior does not accord with the generally held view that traffic is an anisotropic fluid. It is shown, however, those 2-shocks and 2-rarefactions in the studied nonequilibrium theory are transitory and their influence on traffic flow decays exponentially. It is further argued that as long as the 2-shocks and 2-rarefactions do not persist, they can be allowed in a nonequilibrium theory. Apart from the behavioral aspects, the paper also derives the formulae for solving the Riemann problem associated with the nonequilibrium theory. Most of the results carry over directly to other nonequilibrium theories of the same kind, including the PW theory.

Suggested Citation

  • Zhang, H. M., 2000. "Structural properties of solutions arising from a nonequilibrium traffic flow theory," Transportation Research Part B: Methodological, Elsevier, vol. 34(7), pages 583-603, September.
    • Handle: RePEc:eee:transb:v:34:y:2000:i:7:p:583-603
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    References listed on IDEAS

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    1. Zhang, H. M., 1998. "A theory of nonequilibrium traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 32(7), pages 485-498, September.
    2. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    3. 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.
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    Cited by:

    1. Mohammadian, Saeed & Zheng, Zuduo & Haque, Mazharul & Bhaskar, Ashish, 2023. "NET-RAT: Non-equilibrium traffic model based on risk allostasis theory," Transportation Research Part A: Policy and Practice, Elsevier, vol. 174(C).
    2. Zhang, H. M., 2003. "Driver memory, traffic viscosity and a viscous vehicular traffic flow model," Transportation Research Part B: Methodological, Elsevier, vol. 37(1), pages 27-41, January.
    3. 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.
    4. Michael Z. F. Li, 2008. "A Generic Characterization of Equilibrium Speed-Flow Curves," Transportation Science, INFORMS, vol. 42(2), pages 220-235, May.
    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.
    6. W.-L. Jin & H. M. Zhang, 2003. "The Inhomogeneous Kinematic Wave Traffic Flow Model as a Resonant Nonlinear System," Transportation Science, INFORMS, vol. 37(3), pages 294-311, August.
    7. Li, Jia & Zhang, H.M., 2013. "The variational formulation of a non-equilibrium traffic flow model: Theory and implications," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 314-325.
    8. Zhang, H. M., 2003. "On the consistency of a class of traffic flow models," Transportation Research Part B: Methodological, Elsevier, vol. 37(1), pages 101-105, January.

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