In the field of transportation, there are significant differences in traffic patterns across different regions and time periods, which poses challenges to the accuracy and generalization ability of predictive models. To account for the periodicity of traffic data, our method utilizes federated learning technology to integrate local models scattered in different areas into a global model, thereby achieving knowledge sharing and optimization. Subsequently, traffic data is segmented by time periods to capture the unique traffic characteristics of each period. Through this method, we have not only improved the adaptability of the model to traffic features of different regions and time periods but also enhanced its generalization capability. Experimental results show that compared with traditional traffic prediction methods, the proposed method has achieved a certain improvement in prediction accuracy. In addition, the application of federated learning also ensures the privacy and security of data, providing effective technical support for the construction of smart cities.