Developing a volume delay function (VDF) for the urban roads of the city of Alexandria

The Volume Delay Function (VDF) is crucial in trip assignment for calculating congested travel time on road networks. The BPR equation, widely used for VDF, requires calibration of parameters to accurately estimate travel time. Inaccurate travel time estimation leads to unreliable trip assignments and travel demand forecasting. Thus, calibrating BPR parameters (α, β and c) for local conditions is essential. This research used Alexandria as a case study, collecting data of link travel times and traffic volumes were collected. The calibration process utilizes nonlinear optimization techniques to optimize the BPR parameters. Data collection covers 66 sites with a total of 198 h of video taping which comprise 632 observatoins (15 min intervals). Three steps were used to calibrate the parameters, visual fitting helped getting rid of outliers. Later, relaxed linearized parameter estimation was performed. The resulted parameters (without capacity) were less roboust, yet, with better goodness of fit due to the relaxation conditions. The final calibration incorporated the capacity resulted in a more comparable parameter values with lowers goodness of fit. The values of parameters (α, β, c) were estimated for different road types and all types combined. The parameter values showed excellent trending confirming the estimation validity.