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Numerical simulation of macroscopic continuum traffic models

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  • Leo, Chin Jian
  • Pretty, Robert L.

Abstract

This paper presents the derived Roe's flux difference splitting method for Payne's formulation of the macroscopic model. In recent years, this finite difference method has generated much interest and been used successfully in gas dynamics. Payne's equations are actually those of the isentropic gas having constant speed of sound and in homogeneous terms on the right hand side. Our motivation for deriving Roe's flux difference splitting algorithm for Payne's model and also highlighting the scalar equivalent of Roe's method (the Murman scheme) for the Lighthill-Whitham (LW) model stems from the reports of numerical simulation difficulties pertaining to two models. The numerical schemes were used on Payne's and LW models to simulate three traffic scenarios with satisfactory results. We were able to simulate the propagation of congested density upstream in one freeway bottleneck scenario at a finer discretization. Another scenario did not manage to obtain realistic results with Payne's model, we did.

Suggested Citation

  • Leo, Chin Jian & Pretty, Robert L., 1992. "Numerical simulation of macroscopic continuum traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 26(3), pages 207-220, June.
    • Handle: RePEc:eee:transb:v:26:y:1992:i:3:p:207-220
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    Cited by:

    1. 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.
    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. 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. Kai Nagel & Peter Wagner & Richard Woesler, 2003. "Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling," Operations Research, INFORMS, vol. 51(5), pages 681-710, October.
    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. Nelson, Paul, 1995. "On deterministic developments of traffic stream models," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 297-302, August.
    7. Zhang, H. M., 1998. "A theory of nonequilibrium traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 32(7), pages 485-498, September.
    8. Maitra, B. & Azmi, M. & Kumar, N. & Sarkar, J. R., 2004. "Modeling traffic impact of flyover at an urban intersection under mixed traffic environment," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 27, pages 57-68.
    9. 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.
    10. Zhang, H. M. & Recker, W. W., 1999. "On optimal freeway ramp control policies for congested traffic corridors," Transportation Research Part B: Methodological, Elsevier, vol. 33(6), pages 417-436, August.
    11. Yi, Jingang & Lin, Hao & Alvarez, Luis & Horowitz, Roberto, 2003. "Stability of macroscopic traffic flow modeling through wavefront expansion," Transportation Research Part B: Methodological, Elsevier, vol. 37(7), pages 661-679, August.

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