## 6 Simulation Results
\begin{table}
\begin{tabular}{l c c c c} \hline
**Queue Length of Vehicles** & **Intersection** & **Without Controller** & **With Controller** & **Improvement (\%)** \\ \hline  & (a) Q1 & 3 & 1 & 66.67 \\
1 & (b) Q2 & 7 & 1 & 85.71 \\  & (c) Q3 & 40 & 7 & 82.50 \\  & (d) Q4 & 47 & 4 & 91.49 \\ \hline
**Total** & & **97** & **13** & **86.60** \\ \hline  & (a) Q1 & 55 & 7 & 87.27 \\
2 & (b) Q2 & 7 & 3 & 57.14 \\  & (b) Q2 & 7 & 3 & 57.14 \\
2 & (c) Q3 & 50 & 38 & 24.00 \\  & (d) Q4 & 47 & 4 & 91.49 \\ \hline
**Total** & & **159** & **52** & **67.30** \\ \hline  & (a) Q1 & 55 & 12 & 78.18 \\
3 & (b) Q2 & 7 & 3 & 57.14 \\  & (c) Q3 & 53 & 17 & 67.92 \\  & (d) Q4 & 47 & 1 & 97.87 \\ \hline
**Total** & & **162** & **33** & **79.63** \\ \hline  & (a) Q1 & 49 & 1 & 97.96 \\
4 & (b) Q2 & 7 & 6 & 14.29 \\  & (c) Q3 & 2 & 1 & 50.00 \\  & (d) Q4 & 47 & 1 & 97.87 \\ \hline
**Total** & & **105** & **9** & **91.43** \\ \hline  & (a) Q1 & 150 & 31 & 79.33 \\
5 & (b) Q2 & 32 & 3 & 90.63 \\  & (c) Q3 & 150 & 10 & 93.33 \\  & (d) Q4 & 28 & 3 & 89.29 \\ \hline
**Total** & & **360** & **47** & **86.94** \\ \hline  & (a) Q1 & 175 & 12 & 93.14 \\
6 & (b) Q2 & 32 & 3 & 90.63 \\  & (c) Q3 & 2 & 3 & \(-50.00\) \\  & (d) Q4 & 28 & 3 & 89.29 \\ \hline
**Total** & & **237** & **21** & **91.14** \\ \hline  & (a) Q1 & 3 & 0 & 100.00 \\
7 & (b) Q2 & 20 & 3 & 85.00 \\  & (b) Q2 & 20 & 3 & 85.00 \\  & (b) Q4 & 3 & 0 & 100.00 \\ \hline
**Total** & & **348** & **22** & **93.68** \\ \hline \end{tabular}
\end{table} 
Table 3: The comparison of results in length of queue of vehicles using model predictive control. The Comparison of the Proposed Method with Other Existing Studies  
This section has compared different models and intersections with the proposed model, such as fuzzy logic, model predictive control, and machine learning methods shown in the table. Additionally, each model has been applied on different intersections, including single intersections, four intersections, six intersections, and nine intersections. This paper [35] has been used as a fuzzy logic control for traffic flows under both normal and exceptional traffic conditions. Still, the dynamic model is not stable on a single intersection. Here, [53] has been considered at only one intersection for reducing queue length of the vehicle. Algorithms derived from RL techniques operate based on biological principles. Developed creatures can change their behavior based on their environment and optimize their efforts to improve, getting better compensations. In RL algorithms, this ability is made achievable by making agents. This paper [54] considered the speed of vehicles and the iteration number by using Multi-Agent Deep Reinforcement Learning to reduce traffic. The traffic signal control system used in intelligent transportation analyzes and controls traffic flow in real-time. This article [55] presented a Deep Q-Network model, which is determined by the optimal demand of a green signal. Another study on the multi intersection has [56] shown a cooperative deep Q-network for signal control modeled as a multiagent reinforcement learning system. At the proposed model, we expanded one intersection to several intersections. However, in the model predictive control, in addition to having all the advantages of all intelligent methods, the superiority of the model-based predictive control over the rest of the fuzzy control is inherent predictive property. It does not depend on anything. Model predictive control also has the intrinsic ability to compensate for dead time, while in fuzzy, it depends on the expert. Additionally, our proposed method results show the proposed model's good performance. In the other existing studies, these types of learning systems are not present. Available traffic control methods do not consider the latest multiagent deep reinforcement learning progress. In addition, current traffic congestion management explanations based on deep reinforcement learning (DRL) do not consider vehicles cooperating with traffic lights but only controlling traffic lights signals.