A Multivariate Analysis of Freeway Speed and Headway Data
Yajie Zou, December 2013
The knowledge of speed and headway distributions is essential in microscopic traffic flow studies because speed and headway are both fundamental microscopic characteristics of traffic flow. For microscopic simulation models, one key process is the generation of entry vehicle speeds and vehicle arrival times. It is helpful to find desirable mathematical distributions to model individual speed and headway values, because the individual vehicle speed and arrival time in microscopic simulations are usually generated based on some form of mathematical models. Traditionally, distributions for speed and headway are investigated separately and independent of each other. However, this traditional approach ignores the possible dependence between speed and headway. To address this issue, the research presents a methodology to construct bivariate distributions to describe the characteristics of speed and headway. Based on the investigation of freeway speed and headway data measured from the loop detector data on IH-35 in Austin, it is shown that there exists a weak dependence between speed and headway.
The research first proposes skew-t mixture models to capture the heterogeneity in speed distribution. Finite mixture of skew-t distributions can significantly improve the goodness of fit of speed data. To develop a bivariate distribution to capture the dependence and describe the characteristics of speed and headway, this study proposes a Farlie-Gumbel Morgenstern (FGM) approach to construct a bivariate distribution to simultaneously describe the characteristics of speed and headway. The bivariate model can provide a satisfactory fit to the multimodal speed and headway distribution. Overall, the proposed methodologies in this research can be used to generate more accurate vehicle speeds and vehicle arrival times by considering their dependence on each other when developing microscopic traffic simulation models.
Keywords: Speed, Headway Correlation, Heterogeneity
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