The OSFM used in this research was introduced in previous spot speed studies by the authors [7, 8] to address some limitations of the widespread percentile-specific models .
The OSFM [7, 8], albeit using the entire speed distribution, follows a completely different approach based on stochastic frontier models from the econometric analysis [34, 35].
The new segment speed model is developed from the previous spot speed model, not only because both models adopt an OSFM formulation, but also because the aggregated effect produced by the segment characteristics on the operating speed is assumed identical in both models except for a scale factor.
The OSFM considers two disturbance terms: the noise term and the asymmetric disturbance term.
Thus, the OSFM is estimated through the maximization of the log-likelihood function shown in
To comply with the OSFM formulation, the speed predictors are transformed in log terms, which implies that the model is not applicable when ELC, B, DI, or SWPD is null.
Based on this approach, a speed profile approach was used to estimate segment speeds at the nine calibration segments, CS1 to CS9, and compare the results with the OSFM estimations.
In seven out of nine cases, the differences between the OSFM estimations and the observed values are smaller than 4 km/h, outperforming the speed profile method.
The OSFM estimations resulted in a MAD of 3.4 and a MSE of 32.1.
The model evolves from the authors' previous research on spot speed modelling, retaining the OSFM formulation presented in Lobo et al.
The OSFM was compared against a speed profile method with positive results.