Validating Numerically Consistent Macroscopic Traffic Models Using Microscopic Data

The work discussed in this paper consists of a statistical assessment of various finite difference schemes including the backward Euler, upwind, forward differencing, and Lax-Friedrichs methods. Each finite differencing method is consistent with hydrodynamic, macroscopic models of traffic flow. The authors fit the models to the data using least squares approximation for parameter estimation. The authors show that certain finite differencing methods for macroscopic models are a better fit for the simulated data by looking at the statistical value of the estimated parameters. The result of this work is the verification of consistency between the macroscopic and microscopic models of traffic flow. Further, the authors provide a basic method that allows for researchers to statistically compare finite differencing schemes of macroscopic models of traffic flow given their data set whether it be simulated or experimental.