This paper addresses the problem of traffic prediction in distributed backend systems and proposes a graph neural network based modeling approach to overcome the limitations of traditional models in capturing complex dependencies and dynamic features. The system is abstracted as a graph with nodes and edges, where node features represent traffic and resource states, and adjacency relations describe service interactions. A graph convolution mechanism enables multi order propagation and aggregation of node features, while a gated recurrent structure models historical sequences dynamically, thus integrating spatial structures with temporal evolution. A spatiotemporal joint modeling module further fuses graph representation with temporal dependency, and a decoder generates future traffic predictions. The model is trained with mean squared error to minimize deviations from actual values. Experiments based on public distributed system logs construct combined inputs of node features, topology, and sequences, and compare the proposed method with mainstream baselines using MSE, RMSE, MAE, and MAPE. Results show that the proposed method achieves stable performance and low error across different prediction horizons and model depths, significantly improving the accuracy and robustness of traffic forecasting in distributed backend systems and verifying the potential of graph neural networks in complex system modeling.