# Reservation-Based 3D Intersection Traffic Control System for Autonomous Unmanned Aerial Vehicles
## 8 Simulation Results
### Comparison of Our Proposed System with the 2D Optimal Static Traffic Light Intersection System  
We also compared the performance of our system with an optimal static traffic light system in 2D roads. In the statically optimal traffic light system, the time durations of the green, yellow, and red lights of a traffic signal are fixed and optimized based on the average arrival rates of the vehicles. Their performances are compared using the queueing delay and the average number of UAVs in the intersection. Queueing delay is measured as the additional time spent in the system due to queue of UAVs. In addition, we evaluated their performances on two scenarios. In Scenario 1, all UAVs move straight in the intersection, while in Scenario 2 a UAV can turn left, move straight, or turn right in the intersection with equal probabilities. To show a fair comparison with the 2D optimal static traffic light system, we applied our scheduling scheme to a 2D intersection model. In the 2D intersection model, there are three lanes per way. Figure 23a shows the intersection model for Scenario 1 and Figure 23b shows the intersection model for Scenario 2. In Scenario 1, since all UAVs move straight,  
Figure 22: Number of UAVs that crossed the intersection per lane within 1 min using mode 2 and \(G=80\). a UAV can travel on any lane. The blue arrows represent the paths of the UAVs from the north and south ways, while the black arrows represent the paths from the east and west ways. In Scenario 2, left turning UAVs can only travel along the left-most lane, straight moving UAVs can travel on the middle lane or right-most lane, and right turning UAVs can travel on the right-most lane. This is applied to all ways. In the statically optimal traffic light system, a phase indicates the traffic signals that have the same cycle start time and cycle length. In Scenario 1, since all UAVs move straight, there is one traffic signal for each way and there are two phases as shown in Figure 24a. In phase 1 of Figure 24a, the UAVs from the west and east ways are allowed to enter the intersection while in phase 2 of Figure 24a, the UAVs from the north and south ways are allowed to enter the intersection. In Scenario 2, there are two traffic signals for each way because there are left turning UAVs. For each way, one traffic signal is used for the left-most lane while another traffic signal is used for both the middle and right-most lane. Figure 24b shows the four phases of Scenario 2. Figure 24: _Cont._  
Figure 23: 2D intersection model of **(a)** Scenario 1: when all UAVs move straight and **(b)** Scenario 2: when UAVs can turn left, move straight, or turn right. The blue arrows represent the paths of the UAVs from the north and south ways, while the black arrows represent the paths from the east and west ways. The traffic light system simulations are implemented using Table 4 and our proposed system is implemented using the simulation parameters in Tables 4 and 5. In our system, the intersection is divided into 2D sections which we will denote as cells instead of cubes. Also, the UAVs can only travel at a constant speed in the intersection to be fair with the traffic light system. Scenario 1: All UAVs move straight in the intersection  
The queueing delays on this scenario are shown in Figure 25. In the traffic light system, there is a delay even when traffic is low because UAVs cannot enter the intersection, even when there are no UAVs traveling in the intersection from the other ways, when the traffic light on their lanes are yellow or red. For example, when the arrival rate is low, that is six UAVs per minute, every traffic light has a green time duration of 4 s and a yellow time duration of 5 s. Thus, when a UAV is the first in the queue to enter the intersection, then it can wait up to 9 s before it enters the intersection. While when a UAV is in queue and there