Travel time functions define the relationship between travel time experienced at a road section and flow or density at that section. As such, they are an essential input to macroscopic dynamic assignment models as well as to some of the mesoscopic and microscopic assignment models. The fundamental diagram, of which various forms are known in the literature, is an example of such a relationship. The present paper considers the extension of travel time functions to multiple user classes (MUC). The user classes that are considered primarily are cars and trucks. To this end, a unique set of empirical data is analysed. After visualising iso-speed curves in the plane spanned by densities of car traffic and truck traffic, referred to as the MUC-density domain, a functional form is chosen for the MUC speed-flow curves and its parameters are calibrated. In a series of experiments, the predictive capabilities of the new MUC speed-flow relationship are compared to usage of a traditional speed-flow relationship. The traditional approach incorporates the MUC aspect only through the use of person-car equivalents and implies linear and parallel iso-speed curves in the above mentioned MUC-density domain. For practitioners, one of the interesting results that will follow from this analysis is the MUC-capacity. This capacity is defined by the iso-speed curve that is the most remote from the origin in the MUC-flow domain.
Abstract