Convective Instability and Structure Formation in Traffic Flow

Abstract

The effects of a localized perturbation in an initially uniform traffic flow are investigated with the optimal velocity model under an open boundary condition. The parameter region where the uniform solution is convectively unstable is determined by linear analysis. It is shown that the oscillatory flow, which is linearly unstable but convectively stabilized, is triggered out of a linearly unstable uniform flow by a localized perturbation, and in the upper stream it eventually breaks up into an alternating sequence of jams and free flows. This observation suggests that the real traffic flow pattern observed near an on-ramp [B. S. Kerner: Phys. Rev. Lett. 81 (1998) 3797] is a noise-sustained structure in an open flow system. We also find that, in a certain parameter region, the convectively stabilized uniform flow is destabilized by the non-linearly induced free flow.