Physical structure embedded model for bus arrival time prediction

Accurate prediction of bus arrival time is of great significance for the reliable operation and management of urban bus systems. However, this prediction task remains highly challenging due to the difficulty of obtaining spatially varying information on road and traffic conditions. Additionally, given the prevalence of the bus bunching problem, the lead–follow relationship between buses may dynamically change, adding extra complexity. To address these challenges, this study explicitly models dynamic inter-vehicle interactions and develops a Physical Structure Embedded (PSE) model for predicting the arrival time of the next bus to a stop, formulated within the spatio-temporal domain. This model not only predicts the remaining travel time but also forecasts an indicator representing potential bus overtaking situations. The input features are specifically designed to capture the operational characteristics and relative positions of buses. With a dual attention mechanism, our model is capable of extracting nuanced correlations between features, thereby enabling a more accurate approximation of the actual arrival time. The developed model is evaluated using multi-route field GPS datasets collected in Yancheng and Kunshan, China. Numerical results show that the developed model outperforms a diverse set of statistical and deep learning baselines, achieving an MAE of 14.41±1.43 s and an RMSE of 20.45±1.58 s, while providing accurate predictions under bus bunching and overtaking conditions.