The existing Intelligent Transportation System (ITS) achieves high success. As an essential component of ITS, Traffic Flow Prediction (TFP) has attracted tremendous attention. It is a critical but challenging task to improve the robust convergence and high accuracy of TFP in real-world scenarios. This study presents an optimized Federated Learning (FL)-based ChebNet model, FedproxChebNet, to realize the highly effective and accurate TFP. By selecting the best penalty constant in the proximal term to optimize the objective function, this model can achieve fast and stable convergence. Using the ChebNet model to aggregate neighbor nodes’ characteristics, more hidden information underlying the spatio-temporal traffic data can be taken into consideration for training the global and local models. All the superiority of the FedproxChebNet model makes it outperform other FL models with the Graph Convolutional Network (GCN), Graph Attention Network (GAT) and Spatio-Temporal Graph Convolutional Network (STGCN). We designed a series of experiments on various FL-based GNN model comparisons, parameter sensitivity tests, and on verifying the performance of FedproxChebNet with different heterogeneous systems with [Formula: see text], [Formula: see text] and [Formula: see text]. Based on four real-world data sets from the cognitive network, the experimental results demonstrate that the presented FedproxChebNet provides the best convergence and the highest accuracy in TFP, and achieves the best performance in a highly heterogeneous system ([Formula: see text]). Specifically, the accuracy of FedproxChebNet is at least improved by [Formula: see text] on PeMS07 than other FL-based GNN models. This proposed FedproxChebNet model may be preferable for different scenarios in ITS such as route planning, traffic congestion control and reversible lanes.
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