Development of Multiregime Speed–Density Relationships by Cluster Analysis

Abstract

Empirical speed–density relationships are important not only because of the central role that they play in macroscopic traffic flow theory but also because of their connection to car-following models, which are essential components of microscopic traffic simulation. Multiregime traffic speed– density relationships are more plausible than single-regime models for representing traffic flow over the entire range of density. However, a major difficulty associated with multiregime models is that the breakpoints of regimes are determined in an ad hoc and subjective manner. This paper proposes the use of cluster analysis as a natural tool for the segmentation of speed–density data. After data segmentation, regression analysis can be used to fit each data subset individually. Numerical examples with three real traffic data sets are presented to illustrate such an approach. Using cluster analysis, modelers have the flexibility to specify the number of regimes. It is shown that the K-means algorithm (where K represents the number of clusters) with original (nonstandardized) data works well for this purpose and can be conveniently used in practice.