Analytic Relationships Between Travel Time Reliability Measures

Travel time reliability is measured in various ways. Measures used in the transportation engineering field include the 90th or 95th percentile travel time, standard deviation, coefficient of variation, percent of variation, buffer index, planning time index, travel time index, skew statistic, misery index, frequency of congestion, and on-time arrival. Correlations and inconsistencies between these measures were observed on a case-by-case basis in past studies, without a full explanation or examination of the fundamental causes of such differing relationships. This paper analytically examines a number of reliability measures and explores their mathematical relationships and interdependencies. With the assumption of lognormal distributed travel times and the use of percent point function, a subset of reliability measures is expressed in relation to the shape parameter or the scale parameter of the lognormal distribution or to both. This process enables a clear understanding of the quantitative relationships and variation tendencies of different measures. Contrary to some previous studies and recommendations, this paper finds that the coefficient of variation, instead of the standard deviation, is a good proxy for several other reliability measures. The use of the average-based buffer index or average-based failure rate is not always appropriate, especially when travel time distributions are heavily skewed, in which case the median-based buffer index or failure rate is recommended.