Compound Gamma Representation for Modeling Vehicle-to-vehicle and Day-to-day Travel Time Variability in a Traffic Network

This paper proposes a compound probability distribution approach for capturing both vehicle-to-vehicle and day-to-day variability in modeling travel time reliability in a network. Starting from the observation that standard deviation and mean of distance-normalized travel time in a network are highly positively correlated and their relationship is well characterized by a linear function, this study assumes multiplicative error structures to describe data with such characteristics and derives a compound distribution to model travel delay per unit distance as a surrogate for travel time. The proposed Gamma-Gamma model arises when (within-day) vehicle-to-vehicle travel delay per unit distance is distributed according to a Gamma distribution, with mean that itself fluctuates from day to day following another Gamma distribution. The study calibrates the model parameters and validates the underlying assumptions using simulated vehicle trajectory data. The Gamma-Gamma distribution shows good fits to travel delay observations when compared to the (simple) Gamma and Log-normal distributions. The main advantage of the Gamma-Gamma model is its ability to recognize different variability dimensions reflected in travel time data, and a clear physical meaning of its parameters in connection with vehicle-to-vehicle and day-to-day variability. As such, the model provides a systematic way of quantifying, comparing and assessing different types of variability, which is important in understanding travel time characteristics and evaluating various transportation measures that affect reliability.