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The stability analysis of the full velocity and acceleration velocity model

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  • Xiaomei, Zhao
  • Ziyou, Gao

Abstract

The stability analysis is one of the important problems in the traffic flow theory, since the congestion phenomena can be regarded as the instability and the phase transition of a dynamical system. Theoretically, we analyze the stable conditions of the full velocity and acceleration difference model (FVADM), which is proposed by introducing the acceleration difference term based on the previous car-following models (the optimal velocity model and the full velocity difference model, OVM and FVDM). By numerical simulations, it is found that when the traffic flow is unstable, the traffic jam in the FVADM is weaker than that in the FVDM. Also it is observed that the spreading speed of the jam is slower in the FVADM than that in the FVDM and the fluctuations of vehicles in the FVADM are smaller than those in the FVDM. Therefore, the acceleration difference term has strong effects on traffic dynamics and plays an important role in stabilizing the traffic flow.

Suggested Citation

  • Xiaomei, Zhao & Ziyou, Gao, 2007. "The stability analysis of the full velocity and acceleration velocity model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 679-686.
    • Handle: RePEc:eee:phsmap:v:375:y:2007:i:2:p:679-686
    DOI: 10.1016/j.physa.2006.10.033
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    References listed on IDEAS

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    1. X. Zhao & Z. Gao, 2005. "A new car-following model: full velocity and acceleration difference model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 47(1), pages 145-150, September.
    2. Davis, L.C., 2003. "Modifications of the optimal velocity traffic model to include delay due to driver reaction time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 557-567.
    3. 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.
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    Cited by:

    1. Junyan Han & Xiaoyuan Wang & Gang Wang, 2022. "Modeling the Car-Following Behavior with Consideration of Driver, Vehicle, and Environment Factors: A Historical Review," Sustainability, MDPI, vol. 14(13), pages 1-27, July.

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