Mixture modeling of freeway speed and headway data using multivariate skew-t distributions

ABSTRACT The knowledge of vehicle speed and headway distributions is very useful for developing microscopic traffic simulation models. Traditionally, speed and headway distributions are often not studied jointly and some microscopic traffic simulation models consider vehicle speeds and arrival times as independent inputs to the traffic simulation process. However, the traditional approaches ignore the possible correlation between freeway vehicle speed and headway. Recently, a Farlie–Gumbel–Morgenstern (FGM) approach was used to construct bivariate distributions to describe the characteristics of speed and headway. The FGM approach only allows a weak statistical dependency and lacks the ability to consider the dynamic correlation structure for speed and headway data collected under different traffic conditions. The objective of this study is to explore the applicability of the finite mixtures of multivariate skew-t distributions to capture the heterogeneity in speed and headway data. The proposed bivariate mixture modeling approach is applied to the 24-hour traffic data collected on IH-35 in Austin, Texas. The results of this study show that the bivariate skew-t mixture model can provide an excellent fit to the multimodal speed and headway distribution. Moreover, the mixture modeling approach can naturally accommodate the varying correlation coefficient by assigning different covariance matrixes for each component in the finite mixture model. The findings in this study can also improve car-following models for simulation purposes.