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Car-following models: fifty years of linear stability analysis -- a mathematical perspective

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  • R.E. Wilson
  • J.A. Ward

Abstract

A general framework for car-following models is developed and its linear stability properties are analysed. The concepts of uniform flow, platoon stability and string stability are introduced and criteria which test for them are developed. Finally, string instability is divided into absolute, convective upstream and convective downstream sub-classes, and a procedure is developed to distinguish between them.

Suggested Citation

  • R.E. Wilson & J.A. Ward, 2010. "Car-following models: fifty years of linear stability analysis -- a mathematical perspective," Transportation Planning and Technology, Taylor & Francis Journals, vol. 34(1), pages 3-18, July.
    • Handle: RePEc:taf:transp:v:34:y:2010:i:1:p:3-18
    DOI: 10.1080/03081060.2011.530826
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    References listed on IDEAS

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    1. Denos C. Gazis & Robert Herman & Richard W. Rothery, 1961. "Nonlinear Follow-the-Leader Models of Traffic Flow," Operations Research, INFORMS, vol. 9(4), pages 545-567, August.
    2. Robert Herman & Elliott W. Montroll & Renfrey B. Potts & Richard W. Rothery, 1959. "Traffic Dynamics: Analysis of Stability in Car Following," Operations Research, INFORMS, vol. 7(1), pages 86-106, February.
    3. Treiber, Martin & Kesting, Arne & Helbing, Dirk, 2010. "Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 983-1000, September.
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    Cited by:

    1. Talebpour, Alireza & Mahmassani, Hani S. & Hamdar, Samer H., 2018. "Effect of information availability on stability of traffic flow: Percolation theory approach," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 624-638.
    2. Li, Yongfu & Zhao, Hang & Zhang, Li & Zhang, Chao, 2018. "An extended car-following model incorporating the effects of lateral gap and gradient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 177-189.

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