This paper presents an innovative approach to traffic signal control (TSC) using Deep Reinforcement Learning, focusing on Green Wave Coordination for efficient urban mobility. Traditional methods of TSC aim to optimize traffic flows and ensure user safety but with varying levels of success. Reinforcement Learning for TSC (RL-TSC) has seen notable advancements, particularly with the shift from classical algorithms to deep reinforcement learning algorithms. This study introduces a new mode of coordination for RL-TSC, known as Green Wave Coordination, which maximizes vehicular throughput over arterial routes. We compare this novel Green Wave Dueling Deep Q-Network (GW-2DQN) method with a state-of-the-art independent RL-TSC method, Independent Dueling Deep Q-Network (I-2DQN), in simulated traffic conditions. Our results demonstrate that GW-2DQN outperforms I-2DQN in average and variance of cumulated waiting time under normal traffic conditions, highlighting the benefits of green wave coordination. However, this superiority reverses under saturated traffic conditions, where GW-2DQN's performance significantly drops. This finding suggests that while green wave coordination can offer performance gains in certain conditions, its effectiveness is limited in the presence of traffic congestion. Future work may explore hybrid RL-TSC methods that switch between I-2DQN and GW-2DQN based on congestion levels, potentially offering the best of both methods. This research contributes to the field of intelligent transportation systems, demonstrating the potential of deep reinforcement learning in optimizing traffic signal control for urban mobility.