Mansurova A., Adamova A., Rakhymzhanov D., Yedilkhan D.
Mathematical Modeling of Transit Network Spatiotemporal Dynamics: A Data-Efficient Graph-BiLSTM Architecture for Segment-Level Travel Time Forecasting // Mathematics. — 2026. — Vol. 14, No. 9. — Article No. 1503. — DOI: 10.3390/math14091503.

Abstract: This study addresses the challenge of accurate short-term bus travel time prediction in data-constrained urban environments. Unlike many existing approaches that rely on extensive external data, the proposed framework is data-efficient and uses only standard operational transit data. The model integrates sequential deep learning with multi-relational graph modeling through a multi-relational graph spatio-temporal bidirectional LSTM (MRG-ST-BiLSTM), capturing temporal dependencies while preserving road network topology. A real-world case study using GTFS-based data from bus operations in the Greater Sydney Area (over four million stop-level records across five routes) demonstrates the effectiveness of the approach. Experimental results show improved prediction accuracy compared to baseline models, achieving MAE of 15.82 seconds and RMSE of 31.38 seconds, outperforming conventional LSTM, Hybrid-BiLSTM, and GCN-LSTM models. The framework provides a scalable and interpretable solution for intelligent transportation systems and transit agency planning.

Link / DOI: https://doi.org/10.3390/math14091503