Characterizing travel time variability in vehicular traffic networks

Modeling travel time reliability requires characterizing travel time distributions. Two key statistics commonly used to describe a distribution are the mean deviation and the standard deviation, with one depicting the central tendency and the other describing the dispersion. Although the mean travel time is easier to measure and predict, the corresponding standard deviation is usually hard to obtain because of the insufficiency of individual trip data. Building on seminal insight that goes back to Herman and Prigogine's kinetic theory, this study explores a robust characterization of travel time variability that provides for a near-linear relation between the standard deviation of travel time per unit distance and the corresponding mean value. Simulation-generated vehicle trajectory data from three road networks are used to explore this relationship. On the basis of multiscale and multilevel analysis, large amounts of data show that these two quantities are highly positively correlated; that is, the dispersion of the distribution of individual travel time per unit distance increases with increasing value of the mean travel time per unit distance. Furthermore, regression models and statistical testing indicate that this relation is linear or near-linear. The relation is also validated by Global Positioning System probe data from the Seattle, Washington, area. This relation provides a robust basis for predicting the standard deviation per unit distance when the mean value is known and thus for characterizing the reliability of travel in a network in strategic and operational studies.