  In this work we present a two-dimensional kinetic traffic model which takes
into account speed changes both when vehicles interact along the road lanes and
when they change lane. Assuming that lane changes are less frequent than
interactions along the same lane and considering that their mathematical
description can be done up to some uncertainty in the model parameters, we
derive a hybrid stochastic Fokker-Planck-Boltzmann equation in the
quasi-invariant interaction limit. By means of suitable numerical methods,
precisely structure preserving and direct Monte Carlo schemes, we use this
equation to compute theoretical speed-density diagrams of traffic both along
and across the lanes, including estimates of the data dispersion, and validate
them against real data.
