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

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 and the other on Bayesian neural network. Both approaches use a recurrent neural network to predict multiple time steps into the future, but handle the time-dependent uncertainty estimation differently. We present a novel 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 protection application as a case study: An expert system to determine whether a bus driver should hold and wait for a connecting service, thus ensuring the connection, or break the connection and reduce its own delay. Our results show that the proposed quantile sampling method performs overall best for the 80%, 90% and 95% prediction intervals, both for a 15 min time horizon into the future (𝑡 + 1), but also for the 30 and 45 min 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 Bayesian 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 protection application.