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This paper presents two novel approaches for uncertainty estimation adaptedand extended for the multi-link bus travel time problem. The uncertainty ismodeled directly as part of recurrent artificial neural networks, but using twofundamentally different approaches: one based on Deep Quantile Regression (DQR)and the other on Bayesian Recurrent Neural Networks (BRNN). Both models predictmultiple time steps into the future, but handle the time-dependent uncertaintyestimation differently. We present a sampling technique in order to aggregatequantile estimates for link level travel time to yield the multi-link traveltime distribution needed for a vehicle to travel from its current position to aspecific downstream stop point or transfer site.  To motivate the relevance of uncertainty-aware models in the domain, we focuson the connection assurance application as a case study: An expert system todetermine 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 theDQR-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 30and 45 minutes time horizon (t + 2 and t + 3), with a constant, but very smallunderestimation of the uncertainty interval (1-4 pp.). However, we also show,that the BRNN model still can outperform the DQR for specific cases. Lastly, wedemonstrate how a simple decision support system can take advantage of ouruncertainty-aware travel time models to prioritize the difference in traveltime uncertainty for bus holding at strategic points, thus reducing theintroduced delay for the connection assurance application.

Short-term bus travel time prediction for transfer synchronization with intelligent uncertainty handling