This paper introduces the Halphen system as a toolbox for modeling travel time variability. We present the three distributions of the Halphen family and the Moment-Ratio Diagram (MRD), a graphical tool for selecting the best distribution given a specific data set. Then, we explore the mapping between the positions of travel time samples on the MRD and traffic conditions based on mesoscopic traffic simulation. A comprehensive supply-demand scenario enables the comparison between day-to-day and hour-by-hour travel time variability in terms of selection of the optimal distribution. The results highlight the capability of the Halphen system to model a wide range of traffic conditions. This flexible tool has the potential to be integrated into a practice-ready decision support system for modeling travel time variability at the network scale.