Stability analysis of the classical car-following model

Stability analysis of the classical car-following model

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Article ID: iaor19982832
Country: United Kingdom
Volume: 31B
Issue: 6
Start Page Number: 441
End Page Number: 462
Publication Date: Nov 1997
Journal: Transportation Research. Part B: Methodological
Authors: ,
Abstract:

This paper investigates the stability of the classical car-following model. Conditions for local and asymptotic stability as defined in the references cited are established for the linear model. These differ from those in the literature in two ways. First, it will be shown that, in the autonomous model when the product of the coefficient of proportionality α and the reaction time τ is less than or equal to l/e, there exist oscillatory solutions with higher frequencies than 2π, although there are none with lower frequencies. Secondly, asymptotic stability is considered along with local stability. The derived condition for asymptotic stability is both necessary and sufficient. In addition, the condition depends on the frequency of the forcing term, with the sufficient condition ατ < 1/2 for the asymptotic stability found in the literature being included as a special case. The nonlinear model is considered by linearization and numerical integrations. Some practical values of parameters are tested for the stability of the model. The analyses in this paper are extended to consider different values of α and τ for different drivers in the line.

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