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

arXiv: https://arxiv.org/abs/2104.06819 · HTML: https://mlsanity.com/paper/2104.06819/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 27 references that are in the map.
- First posted on arXiv 14 Apr 2021.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Bayesian Recurrent Neural Networks](https://mlsanity.com/paper/1704.02798/) (2017)
- [Beyond expectation: Deep joint mean and quantile regression for spatio-temporal problems](https://mlsanity.com/paper/1808.08798/) (2018)
- [Multi-output Bus Travel Time Prediction with Convolutional LSTM Neural Network](https://mlsanity.com/paper/1903.02791/) (2019)

## Built on by (most cited first, 3 of 3)

- [Measuring the Confidence of Traffic Forecasting Models: Techniques, Experimental Comparison and Guidelines towards Their Actionability](https://mlsanity.com/paper/2210.16049/) (2022)
- [Large Scale Passenger Detection with Smartphone/Bus Implicit Interaction and Multisensory Unsupervised Cause-effect Learning](https://mlsanity.com/paper/2202.11962/) (2022)
- [A Large-Scale Analysis on the Use of Arrival Time Prediction for Automated Shuttle Services in the Real World](https://mlsanity.com/paper/2401.05322/) (2024)

## Abstract (arXiv)

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.