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Stability and instability in a class of car following model on a closed loop

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  • McKee, Alan
  • McCartney, Mark

Abstract

A velocity-matching car following model is modified to represent the motion of n vehicles travelling on a closed loop. Each vehicle is given a preferred velocity profile, which it attempts to achieve while also attempting to maintain a zero relative velocity between itself and the vehicle in front. The crucial distinctive of the looped model, as opposed to ‘non-looped’ models, is that the last vehicle in the stream is itself being followed by the lead (first) vehicle. The model gives rise to a system of n coupled time delay differential equations which are solved approximately (using a Taylor series expansion in time delay) and numerically using a fourth-order Runge–Kutta routine.

Suggested Citation

  • McKee, Alan & McCartney, Mark, 2009. "Stability and instability in a class of car following model on a closed loop," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(12), pages 2476-2482.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:12:p:2476-2482
    DOI: 10.1016/j.physa.2009.02.019
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    Cited by:

    1. Chen, Chen & Chen, Jianqiao & Guo, Xiwei, 2010. "Influences of overtaking on two-lane traffic with signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 141-148.

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