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Accurate traffic congestion estimation and prediction are critical building blocks for smart trip planning and rerouting decisions in transportation systems. Over the decades, there have been many studies focusing on traffic congestion estimation and prediction with different statistical approaches (e.g., Markov chain) and machine learning models (e.g., clustering, Bayesian networks, and artificial neural networks). However, there is a lack of a unified framework to address the mechanisms of different models and integrate the advantages of different methods through combinations. This paper introduces the FD-Markov-LSTM model, a hybrid interpretable approach that combines the fundamental diagram (FD), Markov chain, and long short-term memory (LSTM). The aim is to estimate and predict traffic states by integrating statistical data in both congested and uncongested scenarios. The FD-Markov-LSTM model leverages the FD to identify hierarchical traffic states and utilizes the Markov process to capture the probabilistic transitions between these states. We employ the LSTM model to further capture the residual time series produced by the Markov chain model (assuming a memoryless property) to enhance the estimation and prediction performance. The proposed model's accuracy in estimating and predicting traffic flow is evaluated using empirical data from three case studies conducted in Beijing and Los Angeles. The results highlight a significant improvement in accuracy compared to classical benchmark models such as the Markov model, ARIMA model, k-Nearest Neighbor model, Random Forest model, and LSTM. Specifically, the FD-Markov-LSTM model achieves reductions of over 39% in mean absolute error, 35% in root mean squared error, and 7.4% in mean absolute percentage error. These results clearly demonstrate that the FD-Markov-LSTM model outperforms the benchmark models, enabling more precise predictions of traffic flow. [ABSTRACT FROM AUTHOR]

• Bayesian inference and deep learning is integrated for traffic congestion modeling; • A dynamic Bayesian graph convolutional network (DBGCN) is proposed. • The DBGCN outperforms the state-of-the-art prediction models. • The DBGCN can simulate congestion evolution via dynamic adjacency matrix. • The change of congestion source location leads to different congestion patterns. Congestion, whether recurrent or non-recurrent, propagates through the road network. The process of congestion propagation from a particular road to its neighbors can be regarded as a kind of message passing with a directed relationship. Existing methods have created a solid foundation for characterizing congestion propagation; however, they are either built upon simplified assumptions in traffic flow theory or predefined relationships among road sections, which would lead to downgraded accuracy in practice. This paper proposes a dynamic Bayesian graph convolutional network (DBGCN), which integrates Bayesian inference into a deep learning framework. Therefore, the rules of congestion propagation in the network can be actively learned from the observed data instead of predefining them based on prior knowledge. Experimental results on 971 testbeds in a regional road network in Beijing demonstrate that DBGCN outperforms the state-of-the-art models in inferring the congestion propagation spatiotemporal coverage and reveals variations in congestion propagation patterns according to the road network structure. Furthermore, the proposed model can simulate the congestion propagation process in customized scenarios by learning the latent congestion propagation rules. The results in different scenarios show that the change of congestion source location leads to distinct congestion magnitude, and the propagation of congestion will eventually stop at the road sections with strong shunting effect. [ABSTRACT FROM AUTHOR]