In recent years, traffic prediction has achieved remarkable success and has become an integral component of intelligent transportation systems. However, traffic data is typically distributed among multiple data owners, and privacy constraints prevent the direct utilization of these isolated datasets for traffic prediction. Most existing federated traffic prediction methods focus on designing communication mechanisms that allow models to leverage information from other clients in order to improve prediction accuracy. Unfortunately, such approaches often incur substantial communication overhead, and the resulting transmission delays significantly slow down the training process. As the volume of traffic data continues to grow, this issue becomes increasingly critical, making the resource consumption of current methods unsustainable. To address this challenge, we propose a novel variable relationship modeling paradigm for federated traffic prediction, termed the Channel-Independent Paradigm(CIP). Unlike traditional approaches, CIP eliminates the need for inter-client communication by enabling each node to perform efficient and accurate predictions using only local information. Based on the CIP, we further develop Fed-CI, an efficient federated learning framework, allowing each client to process its own data independently while effectively mitigating the information loss caused by the lack of direct data sharing among clients. Fed-CI significantly reduces communication overhead, accelerates the training process, and achieves state-of-the-art performance while complying with privacy regulations. Extensive experiments on multiple real-world datasets demonstrate that Fed-CI consistently outperforms existing methods across all datasets and federated settings. It achieves improvements of 8%, 14%, and 16% in RMSE, MAE, and MAPE, respectively, while also substantially reducing communication costs.