Estimating Required Probe Vehicle Re-identification Requirements for Characterizing Link Travel Times

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In the 1970s a framework was developed by Oppenlander to determine the sample size required for 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 comparing both ID matching (i.e., small sample sizes with no erroneous travel times) and signature matching (i.e., large sample sizes mixed with some erroneous travel times) 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.