Bayesian Mixture Model for Estimating Freeway Travel Time Distributions from Small Probe Samples from Multiple Days

This study formulates a hierarchical Bayesian mixture model for estimating travel time distributions along freeway sections by using small data samples from vehicle probes, which have been collected over multiple days. Two normal components are used to capture the heterogeneity in the experienced travel times and to model various distributional shapes generally known to be skewed or multimodal. Travel time data collected during different intervals under similar traffic conditions are used to construct the prior for model parameters via a hierarchical Bayesian formulation. The posterior distributions can be continuously updated as new data from probes become available, and are used for prediction under different levels of data availability. A simulation study shows that true travel time distribution for each section during each interval can be well-approximated with the use of this proposed model.