Resampling Methods for Estimating Travel Time Uncertainty: Application of the Gap Bootstrap

Abstract

To a large extent, methods of forecasting travel time have placed emphasis on the quality of the forecasted value—how close is the forecast point estimate of the mean travel time to its respective field value? However, understanding the reliability or uncertainty margin that exists around the forecasted point estimate is also important. Uncertainty about travel time is a fundamental factor as it leads end-users to change their routes and schedules even when the average travel time is low. Statistical resampling methods have been used previously for uncertainty modeling within the travel time prediction environment. This paper applies a recently developed nonparametric resampling method, the gap bootstrap, to the travel time uncertainty estimation problem, especially as it pertains to large (probe) data sets for which common resampling methods may not be practical because of the possible computational burden and complex patterns of inhomogeneity. The gap bootstrap partitions the original data into smaller groups of approximately uniform data sets and recombines individual group uncertainty estimates into a single estimate of uncertainty. Results of the gap bootstrap uncertainty estimates are compared with those of two popular resampling methods—the traditional bootstrap and the block bootstrap. The results suggest that, for the datasets used in this research, the gap bootstrap adequately captures the dependent structure when compared with the traditional and block bootstrap methods and may thus yield more credible estimates of uncertainty than either the block bootstrap method or the traditional bootstrap method.