Constructing a bivariate distribution for freeway speed and headway data

Abstract

Accurate description of speed and headway distributions is critical for developing microscopic traffic simulation models. A number of microscopic simulation models generate vehicle speeds and vehicle arrival times as independent inputs to the simulation process. However, this traditional approach ignores the possible correlation between speed and headway. This article proposes a Farlie–Gumbel–Morgenstern (FGM) approach to construct a bivariate distribution to simultaneously describe the characteristics of speed and headway. For the FGM approach, the distributions of speed and headway need to be specified separately before the construction of the bivariate distribution. While using conventional distributions for headway, this study uses normal, skew-normal and skew-t mixture distributions for speed. To examine the applicability of the FGM, the proposed approach is applied to a 24-hour speed and headway dataset collected on IH-35 in Austin, Texas. The results show the FGM approach has successfully constructed the bivariate distribution for speed and headway. Moreover, data analyses indicate that there is a weak correlation coefficient between speed and headway. The methodology in this research can be used in analysing the characteristics of speed and headway data. The findings can also be used in the development and validation of microscopic simulation models for freeway traffic.