The Complex Dynamical Behaviour of Congested Road Traffic

Abstract

The mathematical models used to describe the dynamical behaviour of a group of closely-spaced road vehicles travelling in a single lane without overtaking are known as car-following models. This paper presents a novel car-following model, which differs from the traditional models by having an equilibrium solution that corresponds to consecutive vehicles having not only zero relative velocity, but also travelling at a certain desired distance apart. This new model is investigated using both numerical and analytical techniques. For many parameter values the equilibrium solution is stable to a periodic perturbation but, for certain parameter values, chaotic motion results. This shows that in congested traffic, even drivers attempting to follow a safe driving strategy, may find themselves driving in an unpredictable fashion.

Citation

Low, D.J. and Addison, P.S. (1998), "The Complex Dynamical Behaviour of Congested Road Traffic", Griffiths, J.D. (Ed.) Mathematics in Transport Planning and Control, Emerald Group Publishing Limited, Leeds, pp. 341-350. https://doi.org/10.1108/9780585474182-033