This paper introduces an innovative solution to enhance transportation in smart traffic systems by combining federated learning with edge computing. However, traditional synchronous federated learning lacks efficiency for real-time requirements, while asynchronous federated learning consumes more energy and exhibits unstable training. To address these challenges, the paper proposes an Adaptive Waiting Time Asynchronous Federated Learning (AWTAFL) algorithm based on the Dueling Double Deep Q-Network (D3QN). This algorithm dynamically adjusts the waiting time using D3QN, considering task progress and energy consumption, to accelerate convergence and save energy. Furthermore, the paper improves global model aggregation in federated learning by incorporating data volume weights, freshness level of client parameters, and client contribution level. This comprehensive parameter weighing ensures stability during asynchronous federated learning and aids in achieving convergence. Experimental simulations confirm that the proposed algorithm significantly reduces convergence time, maintains model quality, and effectively reduces energy consumption during asynchronous federated learning. Moreover, the improved global aggregation update method enhances training stability and reduces oscillations in the global model convergence.