From heterogeneous drivers to macroscopic patterns in congestion

This paper first presents a method to estimate Newell's car-following model parameters in congestion at a microscopic scale. I-80 NGSim data analysis shows that at this scale driving behaviors vary from one vehicle to the another. Then, relations between stochastic Newell's model with heterogeneous drivers and its associated macroscopic pattern are established. This proves that the mean jam spacing is the arithmetic mean of individual jam spacings whereas the mean wave speed is the harmonic mean of individual wave speeds. These new insights are valuable for (i) calibrating a macroscopic model from individual observations and (ii) establishing the equivalence between the stochastic and the well-calibrated deterministic versions of Newell's model for a sufficiently large number of vehicles.