Summary. The aim of this paper is to present recent progress in calibrating ten microscopic traffic flow models. The models have been tested using data collected via DGPS-equipped cars (Differential Global Positioning System) on a test track in Japan. To calibrate the models, the data of a leading car are fed into the model under consideration and the model is used to compute the headway time series of the following car. The deviations between the measured and the simulated headways are then used to calibrate and validate the models. The calibration results agree with earlier studies as there are errors of 12 % to 17 % for all models and no model can be denoted to be the best. The differences between individual drivers are larger than the differences between different models. The validation process leads to errors from 17 % to 22 %. But for special data sets with validation errors up to 60 % the calibration process has reached what is known as "overfitting": because of the adaptation to a particular situation, the models are not capable of generalizing to other situations.

We analyze the characteristic features of traffic breakdown. To describe this phenomenon we apply to the probabilistic model regarding the jam emergence as the formation of a large car cluster on highway. In these terms the breakdown occurs through the formation of a certain critical nucleus in the metastable vehicle flow, which enables us to confine ourselves to one cluster model. We assume that, first, the growth of the car cluster is governed by attachment of cars to the cluster whose rate is mainly determined by the mean headway distance between the car in the vehicle flow and, may be, also by the headway distance in the cluster. Second, the cluster dissolution is determined by the car escape from the cluster whose rate depends on the cluster size directly. The latter is justified using the available experimental data for the correlation properties of the synchronized mode. We write the appropriate master equation converted then into the Fokker-Plank equation for the cluster distribution function and analyze the formation of the critical car cluster due to the climb over a certain potential barrier. The further cluster growth irreversibly gives rise to the jam formation. Numerical estimates of the obtained characteristics and the experimental data of the traffic breakdown are compared. In particular, we draw a conclusion that the characteristic intrinsic time scale of the breakdown phenomenon should be about one minute and explain the case why the traffic volume interval inside which traffic breakdown is observed is sufficiently wide.

Several microscopic traffic flow models were tested with a publicly available data set. The task was to predict the travel times between several observers along a one-lane rural road, given as boundary conditions the flow into this road and the flow out of it. By using nonlinear optimization, the best matching set of parameters for each of the models was estimated. For this particular data set, the models that performed best were the ones with the smallest number of parameters. The average error rate of the best models is about 16%; however, this value is not very reliable: the error rate fluctuates between 2.5% and 25% for different parts of the data set.

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