# Reservation-Based 3D Intersection Traffic Control System for Autonomous Unmanned Aerial Vehicles
## 8 Simulation Results  
### Performance of the System in Mode 1 and Mode 2  
To compare the performance of the system in mode 1 and mode 2, simulations were run using both modes and the parameters in Tables 2 and 3. The parameters of the intersection model are listed in Table 2, while the scheduling parameters, including the parameters of the Genetic Algorithm are listed in Table 3.  
As listed in Table 2, there are five lanes per way in a four-way intersection. In each mode, simulations were run on different arrival rates per direction and the arrival rates are \begin{table}
\begin{tabular}{l} \hline \hline
**Intersection Parameters** \\ \hline \(s_{min}=17\) m/s \\ \(s_{max}=19\) m/s \\ \(r_{min}=-3.5\) m/s\({}^{2}\) \\ \(r_{max}=4\) m/s\({}^{2}\) \\ UAV diameter is randomly assigned between 1 to 4 m \\ \(l_{rz}=190\) m \\ \(l_{qz}=52\) m \\ \(l_{az}=46\) m \\ 5 lanes per way \\ Lane width = 5 m \\ Intersection layer height = 5 m \\ Intersection size = 50 m \(\times\) 50 m \\ Cube size = 1 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Intersection parameters. Figure 12: Top view of the intersection showing the minimum distance between UAVs on different cube sizes. (**a**) Size of a cube is 2.5 m. (**b**) Size of a cube is 1 m. \begin{table}
\begin{tabular}{l} \hline \hline
**Redeuling Parameters** \\ \hline \(\Delta t=0.05\) s \\ \(k\Delta t=5\) s \\ GA’s population size per generation = 100 \\ GA’s number of generations = 50 \\ GA’s mutation rate = 10\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Scheduling parameters. identical for all ways. The UAVs are generated with exponentially distributed inter-arrival time. The values of \(s\)Figure 13 shows that the average time spent in the system of the UAVs in both modes is 20 s when the arrival rate is at most 60 UAVs per minute. This means there is no delay in the intersection when arrival late is at most 60 UAVs per minute. When the arrival rate is higher than 60 UAVs per minute, the average time spent in the system of the UAVs in mode 2 is always shorter than mode 1. For the remaining part of this subsection, we illustrate why mode 2 performs better than mode 1. Consider scheduling 20 UAVs at the scheduling instant \(t_{i}\) where one UAV is located at each lane and there are no other reservations in the intersection. The resulting trajectories of the UAVs using mode 1 are shown in Figure 13(a), while the resulting trajectories using mode 2 are shown in Figure 13(b). The spheres in the figure represent the center position of the UAVs. One UAV is represented by one color and UAVs coming from the same way have the same color. Note that the time is not reflected in the figure hence there are no collisions, even though there are more than one UAV at the same space in the figure. Since there are no other reservations in the intersection at \(t_{i}\), all the UAVs will not experience delay in mode 1 and mode 2. Also, the same UAVs will change layer once both in mode 1 and mode 2. Hence, the total time in the system of the UAVs is the same in both modes. The trajectories of the UAVs that will change layer are different between mode 1 and mode 2. Figure 14(a) shows the trajectories of the UAVs that will change layer in Figures 13(a) and 14(b) shows the trajectories of the UAVs that will change layer in Figure 13(b). As expected in mode 2, shown in Figure 14(b), the UAVs only changed layers at the start and end of the intersection. At the next scheduling instant \(t_{i+1}\), suppose there are new 20 UAVs to be scheduled and there is one UAV coming from every entrance lane. The UAVs scheduled at \(t_{i}\) are still in the intersection at the time the UAVs to be scheduled at \(t_{i+1}\) will enter the intersection. Thus, the trajectories of the UAVs scheduled at \(t_{i}\) will affect the availability of the cubes for the UAVs to be scheduled at \(t_{i+1}\). The trajectories of all the UAVs scheduled at \(t_{i+1}\) are shown in Figure 15(a),b for mode 1 and mode 2, respectively.