Bayesian Mixture Model to Estimate Freeway Travel Time under Low-Frequency Probe Data

This study develops a novel estimation method under low-frequency probe data using the Bayesian approach. Given the challenges in estimating travel time under low-frequency probe data and prior distribution of the parameters in a traditional Bayesian approach, the proposed algorithm adopts a historical data-based data-driven method according to the characteristics of travel time regularity. Due to the variability of travel times during peak periods, this paper adopts a mixture distribution of travel times in the Bayesian approach rather than traditional single distribution. The Gibbs sampling method with a burn-in period is used to generate a series of sampling sequences from an unknown joint posterior distribution for estimating the posterior distribution of the parameters. The proposed algorithm is tested using traffic data collected from the Korean freeway section from Giheung IC to Dongtan IC. Both MAPE and RMSE of the estimation results show that the proposed method has the smallest deviation from the ground truth travel time compared to the simple mean and moving average methods. Moreover, the proposed Bayesian estimation yields the smallest standard deviation of MAPE for all test days. The credible intervals for estimated travel times show that the proposed method provides good accuracy in estimating travel time reliability.