Noise-induced instability of a class of stochastic higher order continuum traffic models

Traffic flow dynamics are complex and nonlinear, and depend on the interactions of many vehicles moving together. Especially, the stochastic driving behavior is a significant reason for many complex traffic phenomena such as the capacity drop or traffic instabilities without lane changing. To date, there has not been a satisfactory general theory that can be consistently applied to represent such traffic flow conditions. While there have been efforts to introduce stochastic behavior in deterministic traffic flow models, these attempts have mainly focused on the small stochastic fluctuations around the theoretical equilibrium fundamental diagram or model parameters. Little attention has been given to the physical relevance of the stochastic component, and the existing models do not consider large deviations from the equilibrium fundamental diagram that occur in the transient phases of traffic flow (i.e acceleration and/or deceleration). The goal of this paper is thus to improve current continuum traffic models, with the primary focus on the stochastic behavior arising in the acceleration and/or deceleration process. Our analytical results show noise-induced (long-wave length) stop-and-go waves in the low speed regime, which conform to the recent empirical findings. In addition, it is found that the stochasticity can lead to situations in which a bottleneck sometimes is activated and at other times is not activated under identical traffic demand.