Evaluation of urban bus service reliability on variable time horizons using a hybrid deep learning method

•A LSTM deep learning method for transit arrival prediction is evaluated.•The VMD is adopted to model average bus link speed series into several sub-layers.•The LSTM network is adopted as the predictor of each sub-layer.•The VMD-LSTM model provides satisfactory bus speed forecasting results.•The method may be useful to improve transportation systems. Unreliable transit services can negatively impact transit ridership and discourage passengers from regularly choosing public transport. As the most important content of bus service reliability, accurate bus arrival prediction can improve travel efficiency for enabling a reliable and convenient transportation system. Accordingly, this paper proposes a novel deep learning method, i.e. variational mode decomposition long short-term memory (VMD-LSTM), for bus travel speed prediction in urban traffic networks using a forecast of bus arrival information on variable time horizons. The method uses the temporal and spatial patterns of the average bus speed series. The results show that the VMD-LSTM model outperforms other models on forecasting bus link speed series in future time intervals, whereas the artificial neural network model achieves the worst prediction. In conclusion, the VMD-LSTM method can detect irregular peaks of transit samples from a series of temporal or spatial variations and performs better on major and auxiliary corridors.