Long-term multi-section traffic flow forecasting using the CNN–RNLSTM–MLR neural network

Nowadays, traffic congestion significantly contributes to severe economic and environmental problems in cities. Anticipating traffic flow is a highly effective strategy for mitigating congestion, and accurate predictions are vital for practical traffic guidance, management, and control. However, many existing approaches either treat spatial correlations and temporal dependencies separately or rely on single-architecture models, which limits their ability to capture complex spatiotemporal patterns in real-world networks. Even in cases where these factors have been considered in a combined manner, our proposed model is showed lower error rates compared to them. To address these limitations, this paper proposes a novel hybrid deep learning framework that integrates a Convolutional Neural Network (CNN) with a Long Short-Term Memory (LSTM) network enhanced by Multiple Linear Regression (MLR). The proposed model utilizes CNN to extract meaningful latent features from input data while also taking advantage of LSTM-MLR's ability to capture temporal context. In the first stage, a CNN–RNLSTM model is employed to forecast traffic conditions on four highways in the United Kingdom that are closely associated with a target road, jointly modeling spatial interactions and nonlinear temporal dynamics. In the second stage, the CNN–RNLSTM–MLR model leverages these intermediate forecasts, together with explanatory variables, to estimate traffic conditions on the target roadway through a regression-based fusion layer. This two-stage design allows the model to combine the representation power of deep learning with the interpretability and correction capability of linear regression. Experimental results demonstrate that the proposed hybrid approach consistently outperforms conventional baselines, including standalone MLR, LSTM, and MLR–LSTM models, as measured by Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). Notably, the RMSE exhibits a 22.96% improvement compared to the RNLSTM–MLR model. Overall, the proposed framework achieves the lowest error rate among state-of-the-art methods, indicating its superior ability to capture complex spatiotemporal dependencies in traffic flow forecasting.