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Steady-state traffic flow on a ring road with up- and down-slopes

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

Abstract

Steady-state traffic flow on a ring road with up- and down-slopes is investigated using a semi-discrete model. By exploiting the relations between the semi-discrete and continuum models, a steady-state solution is uniquely determined for a given total number of vehicles on a ring road. The solution is exact and always stable with respect to the first-order continuum model, whereas it is a good approximation with respect to the semi-discrete model provided that the involved equilibrium constant states are linearly stable. In other cases, the instability of one or more equilibria could trigger stop-and-go waves propagating in certain sections of road or throughout the ring road. The indicated results are reasonable and thus physically significant for better understanding of real-world traffic flow on inhomogeneous roads, such as those with junctions or bottlenecks.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:403:y:2014:i:c:p:85-93
    DOI: 10.1016/j.physa.2014.02.016
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    References listed on IDEAS

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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. Qiao, Dianliang & Lin, Zhiyang & Guo, Mingmin & Yang, Xiaoxia & Li, Xiaoyang & Zhang, Peng & Zhang, Xiaoning, 2022. "Riemann solvers of a conserved high-order traffic flow model with discontinuous fluxes," Applied Mathematics and Computation, Elsevier, vol. 413(C).

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