Examining vehicular speed characteristics through divergences from prior distributions

Abstract

A variety of approaches, within literature, has been conducted to interpret vehicular speed characteristics. This study turns the attention to the entropy-based approaches, and thus focuses on the maximum entropy method of statistical mechanics and the Kullback–Leibler (KL) divergence approach to examining the vehicular speeds. The vehicle speeds at the selected highway are analyzed in order to find out the disparities among them. However, it is turned out that the speed dynamics could not be distinguished over the speed distributions; hence the maximization of Shannon entropy seems insufficient to compare the speed distributions of each data set. For this reason, the KL divergence approach was performed. This approach displays the comparison, among the speed distributions, based on two prior distribution models, i.e., uniform and Gauss. The examination of the trends of KL divergences obtained from both distributions was made. It was concluded that the KL divergence values for the highway speed data sets ranged between about 0.53 and 0.70 for the uniform case, while for the Gaussian case the obtained values are between 0.16 and 0.33. The KL divergence trends for the real speeds were obtained analogous for both cases, but they differed significantly when the synthetic data sets were employed. As a result, the KL divergence approach proves suitable as an appropriate indicator to compare the speed distributions.