ArrivalNet: Predicting City-wide Bus/Tram Arrival Time with Two-dimensional Temporal Variation Modeling

Accurate arrival time prediction (ATP) of buses and trams plays a crucial role in public transport operations. Current methods focused on modeling one-dimensional temporal information but overlooked the latent periodic information within time series. Moreover, most studies developed algorithms for ATP based on a single or a few routes of public transport, which reduces the transferability of the prediction models and their applicability in public transport management systems. To this end, this paper proposes \textit{ArrivalNet}, a two-dimensional temporal variation-based multi-step ATP for buses and trams. It decomposes the one-dimensional temporal sequence into intra-periodic and inter-periodic variations, which can be recast into two-dimensional tensors (2D blocks). Each row of a tensor contains the time points within a period, and each column involves the time points at the same intra-periodic index across various periods. The transformed 2D blocks in different frequencies have an image-like feature representation that enables effective learning with computer vision backbones (e.g., convolutional neural network). Drawing on the concept of residual neural network, the 2D block module is designed as a basic module for flexible aggregation. Meanwhile, contextual factors like workdays, peak hours, and intersections, are also utilized in the augmented feature representation to improve the performance of prediction. 125 days of public transport data from Dresden were collected for model training and validation. Experimental results show that the root mean square error, mean absolute error, and mean absolute percentage error of the proposed predictor decrease by at least 6.1\%, 14.7\%, and 34.2\% compared with state-of-the-art baseline methods.