# A Service-Constrained Positioning Strategy for an Autonomous Fleet of Airborne Base Stations
## 6 Evaluation and Results
### Scheduling Evaluation  
The first experiment consists in the evaluation of the two schedulers presented in Section 3 using the models presented in Section 2. The simulations evaluate the aggregated rate obtained by each scheduler in a single cell served by a UAV placed in the center. Thus, in the case of the round robin, this rate is calculated by multiplying the number of users \(N_{i}\) in the region by the average rate per user detailed in Equation (18). In the case of the equal rate, \(N_{i}\) is multiplied by the user rate detailed in Equation (22).  
Although in this experiment only one UAV is considered, the shape of the coverage area has already been selected taking into account the initial distribution of the fleet of UAVs in the proposed strategy, which is implemented in the following experiments. Thus, as this distribution is uniform, the shape of this single region has been selected square. Regarding the distribution of users, a constant users spatial density (\(\lambda(x,y)=\lambda_{0}\)) has been considered. It is important to take into account that the value of \(\lambda_{0}\) does not modify the plots, as in both schedulers the product \(\left.\overline{R}\right|_{A_{i}}\cdot N_{i}\), which is the aggregated rate, leads to the cancellation of \(\lambda_{0}\).  
Figure 2 shows the resulting aggregated rates. As can be checked, the altitude of the UAV impacts differently on the aggregated rate. Specifically, in small regions, the higher the altitude of the UAV is, the lower the aggregated rate is, whereas in big regions the behavior is inverted.  
This behavior is related to three different factors, whose dependence with the altitude is also analyzed in [7]: the UAV-user distance, the orientation between the user and the main lobe of the UAV antenna and, finally, the obstruction of the direct channel produced by the presence of buildings. In the case of small regions, all the users are under the main lobe of the UAV antenna and have LOS with the UAV. Thus, the only important factor is the UAV-user distance, which is directly related to the altitude of the UAV. However, in the case of big regions, the users at the cell edge are not under the main lobe of the radiation pattern of the antenna and, consequently, their percentage of NLOS is higher as the elevation angle in the edge is lower. Thus, in big regions, these two factors are more important than the distance and, as a consequence, the dependence of the aggregated rate and the altitude is inverted.  
Regarding the effect of this behavior in the positioning strategy, if the regions at the initial step have a side of, for instance, 3000 m, then the altitude of the UAV serving the region with the lowest user rate will increase. However, as the movement of its neighbors tends to reduce the size of the region of  
Figure 2: Aggregated rate of the round robin (RR) and the equal rate (ER) schedulers as a function of the cell side.  
this UAV, after some iterations, the region will be small enough and, as a consequence, the altitude of this UAV will start to decrease.  
Finally, regarding the comparison between both schedulers, this experiment shows that round robin achieves higher aggregated rates than the equal rate scheduler regardless the size of the region and the UAV altitude. However, this difference is not very high, especially in small regions, and, as mentioned in Section 2, it exhibits a worse user fairness.