Reconstruction of traffic speed distributions from kinetic models with uncertainties

In this work we investigate the ability of a kinetic approach for traffic dynamics to predict speed distributions obtained through rough data. The present approach adopts the formalism of uncertainty quantification, since reaction strengths are uncertain and linked to different types of driver behaviour or different classes of vehicles present in the flow. Therefore, the calibration of the expected speed distribution has to face the reconstruction of the distribution of the uncertainty. We adopt experimental microscopic measurements recorded on a German motorway, whose speed distribution shows a multimodal trend. The calibration is performed by extrapolating the uncertainty parameters of the kinetic distribution via a constrained optimisation approach. The results confirm the validity of the theoretical set-up.