Travelling Waves in a Linearly Stable, Optimal-Velocity Model of Road Traffic

Abstract

We investigate wave types which occur in the stable regime of a car-following model of road traffic based on a relaxation term. Numerical results show that several types of transitions from an upstream to a downstream headway exist, e.g. monotonic, oscillatory and dispersive. Moreover for specific upstream headways there is a travelling wave of maximum speed that is different from the theoretical maximum speed being deduced from the fundamental diagram. This wave occurs together with a second shock wave of different speed matching the downstream headway and a growing region of congested traffic in between. The different transitions are classified in a phase diagram whose structure depends on the sensitivity parameter of the model. It shows that the waves of maximum speed are analogous to jam fronts in the unstable regime. The qualitative behaviour of an autocade of different vehicles can be better understood with these phase diagrams.