Kullback-Leibler comparison framework for the evaluation of travel time distribution estimates

In the 1970s a framework was developed by Oppenlander for evaluation of travel time estimation studies. This framework is still recommended today. This paper develops a new framework to improve upon the ideas set forth by Oppenlander. This new framework is based upon the Kullback-Leibler divergence. It allows for travel time studies to be evaluated in a more comprehensive way. Travel time estimation methods can now be evaluated on their ability to estimate travel time distributions instead of only the mean travel time. Also, this framework can be used on any travel time distribution whereas the Oppenlander framework was only properly suited for Gaussian distributions. The Kullback-Leibler divergence also allows for both ID matching and signature matching travel time estimation algorithms to be evaluated, while the Oppenlander framework was best suited for the ID matching algorithms. In this paper the Kullback-Leibler comparison framework for travel time studies is developed. The framework is then used to provide a comparison of an example ID matching and an example signature matching algorithm to demonstrate how both can be evaluated in a single framework. Finally, conclusions are made about the usefulness of the Kullback-Leibler comparison framework.