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A continuum model for the dispersion of traffic on two-lane roads

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  • Holland, Edward N.
  • Woods, Andrew W.

Abstract

A continuum model for two-lane traffic flow is developed using the theory of kinematic waves in which the wavespeeds in the two lanes are assumed constant but unequal. The transient behaviour is found exactly using Riemann's method of characteristics and an asymptotic model of the long time flow is described. It is shown, that for large times, the traffic concentration moves with a weighted mean wavespeed of the two lanes and disperses about this mean speed as a result of interlane concentration differences generated by the relative wavespeeds. The dispersion can be described by a virtual coefficient of diffusion proportional to the square of the differences of the two wavespeeds and inversely proportional to the rate of lane changing. The technique is extended to describe three-lane traffic flow and to include the dependence of wavespeed upon concentration.

Suggested Citation

  • Holland, Edward N. & Woods, Andrew W., 1997. "A continuum model for the dispersion of traffic on two-lane roads," Transportation Research Part B: Methodological, Elsevier, vol. 31(6), pages 473-485, November.
    • Handle: RePEc:eee:transb:v:31:y:1997:i:6:p:473-485
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    References listed on IDEAS

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    1. P. K. Munjal & L. A. Pipes, 1971. "Propagation of On-Ramp Density Waves on Uniform Unidirectional Multilane Freeways," Transportation Science, INFORMS, vol. 5(4), pages 390-402, November.
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    Cited by:

    1. Logghe, S. & Immers, L.H., 2008. "Multi-class kinematic wave theory of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 42(6), pages 523-541, July.
    2. Mohan, Ranju & Ramadurai, Gitakrishnan, 2021. "Multi-class traffic flow model based on three dimensional flow–concentration surface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).
    3. Jin, Wen-Long, 2010. "A kinematic wave theory of lane-changing traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1001-1021, September.
    4. Xingliang Liu & Jian Wang & Tangzhi Liu & Jin Xu, 2021. "Forecasting Spatiotemporal Boundary of Emergency-Event-Based Traffic Congestion in Expressway Network Considering Highway Node Acceptance Capacity," Sustainability, MDPI, vol. 13(21), pages 1-17, November.
    5. Helbing, Dirk & Hennecke, Ansgar & Shvetsov, Vladimir & Treiber, Martin, 2001. "MASTER: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 35(2), pages 183-211, February.

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