Smart traffic management is the cornerstone of Intelligent Transport Systems (ITS). To achieve smooth travel in urban road networks, ITS provide software-based traffic management based on traffic forecasts. Recently, spatial-temporal graph neural networks (STGNNs) have achieved significant improvements in traffic forecasting by taking into account spatial and temporal dependencies in traffic data. However, in spite of being an indispensable statistic in traffic management in urban areas, the length of congestion queues has not been a prediction target. In addition, existing methods have not considered the use of multimodal traffic data for forecasting. Moreover, given the significant impact of ITS on the real world, black-box predictions with less explainability are unreliable. In this paper, we propose aQueueing-theory-based Neural Network (QTNet), which combines data-driven STGNN methods with queueing-theory-based domain knowledge of traffic engineering in order to achieve accurate and explainable predictions. In our queue length prediction experiments using a real-world dataset collected in urban areas of Tokyo, QTNet outperformed the baseline methods including the state-of-the-art STGNNs by 12.6% in RMSE and 9.9% MAE, and particularly for severe congestion, by 8.1% and 8.4%.