Mixture models for fitting freeway travel time distributions and measuring travel time reliability

Travel time reliability has attracted increasing attention in recent years and is often listed as a major roadway performance and service quality measure for traffic engineers and travelers. Measuring travel time reliability is the first step toward improving it, ensuring on-time arrivals, and reducing travel costs. Most measures of travel time reliability derive from continuous probability distributions and apply to traffic data directly. However, little previous research shows a consensus for selection of a probability distribution family for travel time reliability. Different probability distribution families could yield different values for the same measure of travel time reliability (e.g., standard deviation). The authors believe that specific selection of probability distribution families has few effects on measuring travel time reliability. Therefore, they proposed two hypotheses for accurately measuring travel time reliability and designed an experiment to prove the two hypotheses. The first hypothesis was proved by (a) conducting the Kolmogorov-Smirnov test and (b) checking log likelihoods and the convergences of the corrected Akaike information criterion and of the Bayesian information criterion. The second hypothesis was proved by examining both moment- and percentile-based measures of travel time reliability. The results from testing the two hypotheses suggest that (a) underfitting may cause disagreement in distribution selection, (b) travel time can be precisely fitted by using mixture models with a higher value of K (regardless of distribution family), and (c) measures of travel time reliability are insensitive to the selection of the distribution family. These findings allow researchers and practitioners to avoid testing of various distributions, and travel time reliability can be more accurately measured by using mixture models because of the higher values of log likelihoods.