  We consider kinetic vehicular traffic flow models of BGK type. Considering
different spatial and temporal scales, those models allow to derive a hierarchy
of traffic models including a hydrodynamic description. In this paper, the
kinetic BGK-model is extended by introducing a parametric stochastic variable
to describe possible uncertainty in traffic. The interplay of uncertainty with
the given model hierarchy is studied in detail. Theoretical results on
consistent formulations of the stochastic differential equations on the
hydrodynamic level are given. The effect of the possibly negative diffusion in
the stochastic hydrodynamic model is studied and numerical simulations of
uncertain traffic situations are presented.
