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Traffic dynamics

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  • Ross, Paul

Abstract

Previous descriptions of traffic flow under changing conditions are shown to be untenable. Deterministic relationships between traffic speed and density do not allow for observed scatter and imply that traffic can lock up spontaneously. Equilibrium relationships between speed and density allow impossibly high traffic densities and provide unrealistically slow responses to changes in roadway and traffic conditions. A qualitatively superior representation of traffic flow is developed. Traffic is described as a fluid that cannot be compressed beyond a certain density, kjam. The equations of state are: (1) Volume = speed x density. (2) Continuity of vehicles. (3) Traffic speed "relaxes" to the free-flow speed of the roadway, independent of density except that volume cannot exceed roadway capacity and flow is incompressible when traffic density is equal to the jam density. The representation is innovative in two respects: (1) Traffic flowing with DENSITY = kjam is explicitly recognized as being incompressible. (2) No speed-density relationship is contained in or implied by the traffic formulation. The new traffic formulation models both interrupted and uninterrupted traffic flow. It has been tested by simulating several traffic flow situations. The reproductions of light to moderate flows are equal to those of the best previous traffic formulation, and the representations of congested and bottleneck flow are superior. The new traffic formulation also reproduces the general qualities of observed speed/ volume curves and provides interpretation of those curves in terms of upstream and downstream bottlenecks.

Suggested Citation

  • Ross, Paul, 1988. "Traffic dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 22(6), pages 421-435, December.
    • Handle: RePEc:eee:transb:v:22:y:1988:i:6:p:421-435
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    Cited by:

    1. 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.
    2. 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.
    3. Zheng, Liang & Jin, Peter J. & Huang, Helai, 2015. "An anisotropic continuum model considering bi-directional information impact," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 36-57.
    4. Jiang, Rui & Wu, Qing-Song, 2003. "Study on propagation speed of small disturbance from a car-following approach," Transportation Research Part B: Methodological, Elsevier, vol. 37(1), pages 85-99, January.
    5. Hurdle, V. F. & Son, Bongsoo, 2000. "Road test of a freeway model," Transportation Research Part A: Policy and Practice, Elsevier, vol. 34(7), pages 537-564, September.
    6. Nam, Do H. & Drew, Donald R., 1999. "Automatic measurement of traffic variables for intelligent transportation systems applications," Transportation Research Part B: Methodological, Elsevier, vol. 33(6), pages 437-457, August.
    7. Hilliges, Martin & Weidlich, Wolfgang, 1995. "A phenomenological model for dynamic traffic flow in networks," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 407-431, December.
    8. Jin, Wen-Long, 2016. "On the equivalence between continuum and car-following models of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 543-559.
    9. Zhong, R.X. & Sumalee, A. & Friesz, T.L. & Lam, William H.K., 2011. "Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 1035-1061, August.
    10. Nelson, Paul & Sopasakis, Alexandros, 1998. "The prigogine-herman kinetic model predicts widely scattered traffic flow data at high concentrations," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 589-604, November.
    11. Zhang, H. M., 1998. "A theory of nonequilibrium traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 32(7), pages 485-498, September.
    12. Dell'Orco, Mauro, 2006. "A dynamic network loading model for mesosimulation in transportation systems," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1447-1454, December.
    13. Zhang, H. M., 2001. "A finite difference approximation of a non-equilibrium traffic flow model," Transportation Research Part B: Methodological, Elsevier, vol. 35(4), pages 337-365, May.

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