Speed or spacing? Cumulative variables, and convolution of model errors and time in traffic flow models validation and calibration

This paper proves that in traffic flow model calibration and validation the cumulative sum of a variable has to be preferred to the variable itself as a measure of performance. As shown through analytical relationships, model residuals dynamics are preserved if discrep- ancy measures of a model against reality are calculated on a cumulative variable, rather than on the variable itself. Keeping memory of model residuals occurrence times is es- sential in traffic flow modelling where the ability of reproducing the dynamics of a phe- nomenon –as a bottleneck evolution or a vehicle deceleration profile –may count as much as the ability of reproducing its order of magnitude. According to the aforesaid finding, in a car-following models context, calibration on travelled space is more robust than calibra- tion on speed or acceleration. Similarly in case of macroscopic traffic flow models valida- tion and calibration, cumulative flows are to be preferred to flows. Actually, the findings above hold for any dynamic model.