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Analysis of interrupted traffic flow by finite difference methods

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  • Michalopoulos, Panos G.
  • Beskos, Dimitrios E.
  • Lin, Jaw-Kuan

Abstract

Three numerical techniques for macroscopic analysis of traffic dynamics at signalized links (isolated or coordinated) are presented. The techniques are based on finite differences in time and space and assist in implementing continuum models at real situations. The general methodology presented allows treatment of any arrival and departure pattern, inclusion of sinks or sources, employment of any desired equilibrium flow-density relationship and arbitrary specified initial conditions. Implementation of the proposed method to a signalized intersection and a coordinated link suggests satisfactory agreement with field data and notable agreement with analytical results, respectively. Comparisons made under progressively realistic assumptions demonstrate substantial improvements in model performance as the complexity of the assumptions increases

Suggested Citation

  • Michalopoulos, Panos G. & Beskos, Dimitrios E. & Lin, Jaw-Kuan, 1984. "Analysis of interrupted traffic flow by finite difference methods," Transportation Research Part B: Methodological, Elsevier, vol. 18(4-5), pages 409-421.
    • Handle: RePEc:eee:transb:v:18:y:1984:i:4-5:p:409-421
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    Cited by:

    1. 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.
    2. Ho, H.W. & Wong, S.C. & Loo, Becky P.Y., 2006. "Combined distribution and assignment model for a continuum traffic equilibrium problem with multiple user classes," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 633-650, September.
    3. Yadong Lu & S. C. Wong & Mengping Zhang & Chi-Wang Shu, 2009. "The Entropy Solutions for the Lighthill-Whitham-Richards Traffic Flow Model with a Discontinuous Flow-Density Relationship," Transportation Science, INFORMS, vol. 43(4), pages 511-530, November.
    4. Daganzo, Carlos F., 1995. "A finite difference approximation of the kinematic wave model of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 261-276, August.
    5. Wu, Xinkai & Liu, Henry X., 2011. "A shockwave profile model for traffic flow on congested urban arterials," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1768-1786.
    6. Wong, S. C. & Wong, G. C. K., 2002. "An analytical shock-fitting algorithm for LWR kinematic wave model embedded with linear speed-density relationship," Transportation Research Part B: Methodological, Elsevier, vol. 36(8), pages 683-706, September.
    7. Sun, Lu & Jafaripournimchahi, Ammar & Kornhauser, Alain & Hu, Wushen, 2020. "A new higher-order viscous continuum traffic flow model considering driver memory in the era of autonomous and connected vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    8. Lu, Yadong & Wong, S.C. & Zhang, Mengping & Shu, Chi-Wang & Chen, Wenqin, 2008. "Explicit construction of entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a piecewise quadratic flow-density relationship," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 355-372, May.
    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. Klug, Florian, 2014. "Modelling and analysis of synchronised material flow with fluid dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 404-417.

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