Uncertainty quantification in travel time estimation (TTE) aims to estimate the confidence interval for travel time, given the origin (O), destination (D), and departure time (T). Accurately quantifying this uncertainty requires generating the most likely path and assessing travel time uncertainty along the path. This involves two main challenges: 1) Predicting a path that aligns with the ground truth, and 2) modeling the impact of travel time in each segment on overall uncertainty under varying conditions. We propose DutyTTE to address these challenges. For the first challenge, we introduce a deep reinforcement learning method to improve alignment between the predicted path and the ground truth, providing more accurate travel time information from road segments to improve TTE. For the second challenge, we propose a mixture of experts guided uncertainty quantification mechanism to better capture travel time uncertainty for each segment under varying contexts. Additionally, we calibrate our results using Hoeffding's upper-confidence bound to provide statistical guarantees for the estimated confidence intervals. Extensive experiments on two real-world datasets demonstrate the superiority of our proposed method.

This paper presents two novel approaches for uncertainty estimation adapted and extended for the multi-link bus travel time problem. The uncertainty is modeled directly as part of recurrent artificial neural networks, but using two fundamentally different approaches: one based on Deep Quantile Regression (DQR) and the other on Bayesian Recurrent Neural Networks (BRNN). Both models predict multiple time steps into the future, but handle the time-dependent uncertainty estimation differently. We present a sampling technique in order to aggregate quantile estimates for link level travel time to yield the multi-link travel time distribution needed for a vehicle to travel from its current position to a specific downstream stop point or transfer site. To motivate the relevance of uncertainty-aware models in the domain, we focus on the connection assurance application as a case study: An expert system to determine whether a bus driver should hold and wait for a connecting service, or break the connection and reduce its own delay. Our results show that the DQR-model performs overall best for the 80%, 90% and 95% prediction intervals, both for a 15 minute time horizon into the future (t + 1), but also for the 30 and 45 minutes time horizon (t + 2 and t + 3), with a constant, but very small underestimation of the uncertainty interval (1-4 pp.). However, we also show, that the BRNN model still can outperform the DQR for specific cases. Lastly, we demonstrate how a simple decision support system can take advantage of our uncertainty-aware travel time models to prioritize the difference in travel time uncertainty for bus holding at strategic points, thus reducing the introduced delay for the connection assurance application.