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Empirical evidence and stability analysis of the linear car-following model with gamma-distributed memory effect

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  • Pei, Xin
  • Pan, Yan
  • Wang, Haixin
  • Wong, S.C.
  • Choi, Keechoo

Abstract

Car-following models, which describe the reactions of the driver of a following car to the changes of the leading car, are essential for the development of traffic flow theory. A car-following model with a stochastic memory effect is considered to be more realistic in modeling drivers’ behavior. Because a gamma-distributed memory function has been shown to outperform other forms according to empirical data, in this study, we thus focus on a car-following model with a gamma-distributed memory effect; analytical and numerical studies are then conducted for stability analysis. Accordingly, the general expression of undamped and stability points is achieved by analytical study. The numerical results show great agreement with the analytical results: introducing the effect of the driver’s memory causes the stable regions to weaken slightly, but the metastable region is obviously enlarged. In addition, a numerical study is performed to further analyze the variation of the stable and unstable regions with respect to the different profiles of gamma distribution.

Suggested Citation

  • Pei, Xin & Pan, Yan & Wang, Haixin & Wong, S.C. & Choi, Keechoo, 2016. "Empirical evidence and stability analysis of the linear car-following model with gamma-distributed memory effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 311-323.
    • Handle: RePEc:eee:phsmap:v:449:y:2016:i:c:p:311-323
    DOI: 10.1016/j.physa.2015.12.104
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    References listed on IDEAS

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    1. Treiber, Martin & Kesting, Arne & Helbing, Dirk, 2006. "Delays, inaccuracies and anticipation in microscopic traffic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(1), pages 71-88.
    2. Robert E. Chandler & Robert Herman & Elliott W. Montroll, 1958. "Traffic Dynamics: Studies in Car Following," Operations Research, INFORMS, vol. 6(2), pages 165-184, April.
    3. Cao, Bao-gui, 2015. "A new car-following model considering driver’s sensory memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 218-225.
    4. Gentry Lee, 1966. "A Generalization of Linear Car-Following Theory," Operations Research, INFORMS, vol. 14(4), pages 595-606, August.
    5. 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.
    6. Yu, Shaowei & Shi, Zhongke, 2015. "The effects of vehicular gap changes with memory on traffic flow in cooperative adaptive cruise control strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 206-223.
    7. Yu, Shaowei & Shi, Zhongke, 2015. "An improved car-following model considering headway changes with memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 1-14.
    8. G. F. Newell, 1961. "Nonlinear Effects in the Dynamics of Car Following," Operations Research, INFORMS, vol. 9(2), pages 209-229, April.
    9. 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.
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    Cited by:

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    3. Zhai, Cong & Li, Kening & Zhang, Ronghui & Peng, Tao & Zong, Changfu, 2024. "Phase diagram in multi-phase heterogeneous traffic flow model integrating the perceptual range difference under human-driven and connected vehicles environment," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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