## 4 Experiments
### Comparison with Baseline Methods  
To demonstrate the superiority of the proposed Hybrid MARL framework, we compare its performance with several baseline methods, including traditional rule-based approaches and state-of-the-art deep reinforcement learning (DRL) models. The baseline methods include the following:  
1. Fixed-Time Control (FT): A conventional method that assigns pre-defined green time intervals to each phase, irrespective of real-time traffic conditions.
2. Actuated Control (AC): A semi-adaptive method that adjusts signal timings based on real-time vehicle detection sensors.
3. Max-Pressure Control (MP): A widely used optimization-based approach that balances incoming and outgoing vehicle flows at intersections.
4. Deep Q-Network (DQN): A reinforcement learning approach that uses a single-agent Q-learning framework for traffic signal control.
5. Proximal Policy Optimization (PPO): A policy-gradient reinforcement learning model designed for continuous control tasks. Multi-Agent Deep Deterministic Policy Gradient (MADDPG): A standard multi-agent RL approach that enables decentralized traffic control with policy sharing.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Traffic Intensity (vehicles/h)** & **Fixed-Time Control (FT)** & **Actuated Control (AC)** & **Max-Pressure Control (MP)** & **Deep Q-Network** & **Proximal Policy Optimization (DQN)** & **MADDPG** & **Hybrid MARL** \\ \hline Low (800) & 45.6 & 38.2 & 32.4 & 28.9 & 26.7 & 24.5 & 18.3 \\ Medium (1200) & 62.5 & 55.8 & 48.2 & 41.3 & 38.9 & 35.7 & 27.4 \\ High (1600) & 85.3 & 78.9 & 67.1 & 59.8 & 54.6 & 49.3 & 38.1 \\ Very High (2000) & 110.7 & 103.2 & 89.4 & 82.5 & 76.2 & 70.4 & 52.7 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of average vehicle waiting times across different traffic control strategies.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Throughput (vehicles/h)** \\ \hline Fixed-Time Control (FT) & 1250 \\ Actuated Control (AC) & 1360 \\ Max-Pressure Control (MP) & 1485 \\ Deep Q-Network (DQN) & 1620 \\ Proximal Policy Optimization (PPO) & 1680 \\ MADDPG & 1745 \\ Hybrid MARL & 1890 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of throughput (vehicles/hour) among different models.  
Table 1 presents the comparison of average vehicle waiting times for different methods. It is evident that our proposed Hybrid MARL framework significantly outperforms traditional rule-based methods and single-agent RL models. The reduction in waiting time demonstrates the effectiveness of multi-agent coordination and hierarchical optimization in alleviating congestion.  
The 25% improvement refers to the reduction in average vehicle waiting time using our proposed method, compared to fixed-time control (FT) and actuated control (AC) baseline methods. This improvement was observed under three traffic density settings: low (800 vehicles/h/lane), medium (1200 vehicles/h/lane), and high (1600 vehicles/h/lane). The reduction was calculated as the difference in waiting times between our proposed Hybrid MARL framework and the baseline methods under the same traffic conditions.  
Additionally, we measure throughput, which quantifies the number of vehicles successfully passing through intersections within a given time frame. Table 2 shows that Hybrid MARL achieves the highest throughput compared to all baseline methods, demonstrating its effectiveness in improving network-wide efficiency, indicating that the proposed model facilitates smoother and more efficient traffic flow.