## 5 Discussion  
In this paper, we proposed a deep reinforcement learning method having vehicle platooning at an isolated signalized intersection with partial detection. Other papers often assume that all vehicles are detected to collect data. This is not true because only vehicles equipped with a wireless communication system can be connected. In addition, our study considered the formation of platoons between CVs of different sizes. After the training, the cumulative waiting time of all vehicles decreased by around 70% compared to that before the training. Through the learning process, the agent learned gradually, and the total waiting time of all vehicles decreased. It is 50% and 65% better than that of the MP and ATST-based scenarios for platoons with three vehicles. The results of this paper demonstrated the advantage of applying DRL in traffic management, similar to other papers [20, 36, 47]. However, our model combines DRL with platoon formation, so the results are much improved compared to that of other papers. Compared with the cumulative reward curve in [36], our model has higher stability with small fluctuations. Because the platoon formation changed the behavior and characteristics of car-following models and affected overall traffic performance. It makes traffic flow stable with a lower waiting time. This is also shown at the beginning of the learning process, the waiting time in our model also has a smaller value. Simulation results have shown that the DRL-based intersection management method is the most effective. Compared with the ATSC- and MP-based scenarios, the average waiting  
Figure 14: Cumulative negative reward and delay time with different CV penetration rates. time of vehicles in the DRL-based scenario was improved by 20% and 28%, respectively (in the case of a platoon having three vehicles). Therefore, other metrics, such as delay time, travel time, and CO2 emissions, were also reduced compared to other policies. The DRL-based intersection management policy has also proven its effectiveness. Our model also shows that as the CV penetration rate increases, traffic efficiency also improves. At a rate of 20%, although the cumulative negative reward curve seems to converge, the reward fluctuates between \(-\)30,000 s and \(-\)50,000 s, which is very unstable. The model is only truly improved when the CV penetration rate is greater than 20%. As the CV penetration rate is higher, the model performance is further improved, further reducing the waiting times of all vehicles. This was also demonstrated in several papers on the influence of CV penetration rates on traffic efficiency [39; 46]. Platoon size is an important factor in the traffic model. The simulation model also tested the influence of the number of vehicles in the platoon. As the number of vehicles in the platoon increases, the model's stability also reduces. The delay time increases by 7% and 10% when the number of vehicles in the platoon increases from 1 to 2 and 3 vehicles. Therefore, an appropriate platoon size may be more suitable in urban areas because it could dampen perturbance better. We assumed the models perform under ideal conditions and perfect communication between CVs. So, there was no damage, data package loss, or time delay during the transmission. In addition, we did not consider the influence of other modes such as buses, bicycles, or pedestrians. There were only two types of vehicles in our model (CVs and RVs). Therefore, to implement the model in practice, it is necessary to add more factors to the model. Although this approach has been successful for an isolated signalized intersection, many problems need to be addressed when applying the model to multi-intersection networks. Many agents (intersections) learn simultaneously to solve a task by interacting with the same environment in a road network. The algorithm, in this case, is more complex than the one we used in this study. An action performed by a particular agent can achieve different rewards depending on the actions performed by other agents.