Travel time statistical modeling with the Halphen distribution family

ABSTRACT

This article introduces the Halphen distribution family for modeling travel time distributions and their reliability on single road links. This probability family originally used in hydrology has a set of relevant characteristics. It is composed of three probability distribution functions for which the mathematical properties are described here. The article uses a graphical representation, the δ-Moment Ratio Diagram (δ-MRD). This tool allows characterizing travel time reliability as well as selecting best distribution candidates within the fitting processes, by considering empirical data sets. A systematic methodology is developed to take advantage of both aspects. From maximum log-likelihood estimation, it is shown that Halphen distributions are among the best state-of-the-art solutions for the travel time modeling purpose. This global framework is validated using two empirical data sets: an urban data set gathered in Portland, Oregon (USA), and a periurban data set from Lyon (France). The model calibration is eased through the use of the δ-MRD; this property opens new research directions about the mapping between traffic states and statistical modeling. It comes from all these considerations that the Halphen family is suitable to describe accurately the travel time dynamics on single links. Therefore, it could be part of a decision support system for practitioners interested in travel time variability.