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

Alan McKee and Mark McCartney

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 12, 2476-2482

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.

Keywords: Traffic flow; Time delay differential equations (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:12:p:2476-2482

DOI: 10.1016/j.physa.2009.02.019

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