Quantification of variability of valid travel times with FMMs for buses, passenger cars, and taxis

Abstract

Quantifying travel time variability (TTV) of buses, passenger cars, and taxis helps individuals understand the reliability of their trips. However, invalid travel time data compromises the accuracy of quantifying the variability of valid travel times. In this study, a clustering methodology, the K−2 finite mixture model (K−2FMM) based on a log-normal distribution, is presented to address the problems of identifying invalid travel times and quantifying the variability of valid travel times in the distribution. The K−2FMM approach can dynamically find an exact K value to cluster travel time data into K log-normal components to best classify the invalid and valid travel times. As a result, invalid travel times represented by component K are filtered out. Other K−1 components are used to measure the degree of variability of valid travel times and to determine some TTV indices such as mean, variance, and 90th percentile travel time. Two real cases illustrate the characteristics of period-to-period TTV for three travel modes. TTV of three travel modes are analysed and distinct taxi TTV is revealed by means of optimal K−1 components. Hence, the proposed K−2FMM approach is appropriate for researchers to more accurately quantify the variability of valid travel times.