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A semi-discrete model and its approach to a solution for a wide moving jam in traffic flow

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  • Zhang, Peng
  • Wu, Chun-Xiu
  • Wong, S.C.

Abstract

This paper investigates the analytical and numerical solutions to wide moving jams in traffic flow. Under the framework of the Lagrange coordinates, a semi-discrete model and a continuum model correlate with each other, in which the former model approaches the latter as the increment ΔM in the former model vanishes. This implies that the solution to a wide moving jam in the latter model, which can be analytically derived using the known theory, can be conceivably taken as an approximation to that of the former model. These results were verified through numerical simulations. Because a detailed understanding of the traffic phase “wide moving jam” is very important for the further development of Kerner’s three-phase traffic theory, this study helps to explain the empirical features of traffic breakdown and resulting congested traffic patterns that are observed in real traffic.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:3:p:456-463
    DOI: 10.1016/j.physa.2011.08.035
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    References listed on IDEAS

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    1. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part III: Multi-destination flows," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 305-313, August.
    2. Zhang, Peng & Wong, S.C. & Dai, S.Q., 2009. "A conserved higher-order anisotropic traffic flow model: Description of equilibrium and non-equilibrium flows," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 562-574, June.
    3. H. M. Zhang, 2009. "Comment on “On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models" by D. Helbing and A.F. Johansson," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 69(4), pages 563-568, June.
    4. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: basic theory and complex boundary conditions," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 187-196, February.
    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.
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    Citations

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    Cited by:

    1. Meng, Y.C. & Lin, Z.Y. & Li, X.Y. & Qiao, D.L. & Guo, M.M. & Zhang, P., 2022. "A semi-discrete model of traffic flow in correspondence with a continuum model under Lagrange coordinate system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    2. Ai, Wen-Huan & Shi, Zhong-Ke & Liu, Da-Wei, 2015. "Bifurcation analysis of a speed gradient continuum traffic flow model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 418-429.
    3. Costeseque, Guillaume & Lebacque, Jean-Patrick, 2014. "A variational formulation for higher order macroscopic traffic flow models: Numerical investigation," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 112-133.
    4. Wu, Chun-Xiu & Zhang, Peng & Wong, S.C. & Choi, Keechoo, 2014. "Steady-state traffic flow on a ring road with up- and down-slopes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 85-93.

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