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

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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.
Original languageEnglish
Article number120751
JournalExpert Systems with Applications
Number of pages12
Publication statusPublished - 2023


  • Connection protection
  • Deep uncertainty estimation
  • Public transport transfer synchronization
  • Travel time uncertainty prediction


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