# On Analyzing Routing Selection for Aerial Autonomous Vehicles Connected to Mobile Network
## 5 Test Results
### Test Results  
When analyzing the prediction models used in ML\({}_{1}\), ML\({}_{2}\), and ML\({}_{3}\), we may observe that the epidemic model overestimates the throughput whereas the Autoregressive Integrated Moving Average model underestimates the throughput. It is a suitable situation for introducing a weighted average mechanism, which corrects over- and underestimation. The first results (see Figure 6) show that the ML overfits results for up to 30 training samples. If the samples go beyond 30, then the ML accuracy is similar in training and in validating phases. One sample is considered positive in the case that the estimated (by the algorithm) throughput and the measured throughput differ by less than 5%, i.e., Est_thr e [0.95 xMeas_thr, 1.05 xMeas_thr]. Moreover, it is important to remark that Figure 6 is based on one test containing 150 training samples and 50 validation samples (in this case we use holdout cross-validation instead of \(k\)-fold cross-validation)  
The second important conclusion of Figure 6 is that the results achieve around 86-87% accuracy. The reason that the algorithms does not reach higher accuracy is due to the variability of throughput in the commercial network, as shown previously in Figure 4.  
Table 1 shows the differences of accuracy (of validation samples) between ML\({}_{1}\), ML\({}_{2}\) and ML\({}_{3}\). These results are based on 3-fold cross-validation methodology and the confidence intervals presented in the results are based only on three measurements. Figure 6: Accuracy of ML\({}_{1}\) for increasing number of training samples and validation samples. The input data of ML\({}_{1}\) and ML\({}_{2}\) are different, so one could expect that the results differ between the two algorithms, however the table shows that the results are very similar. We may conclude that the gain of having a higher number of parameters in the prediction models is negligible in comparison to the gain of having two prediction models properly \"weighted\". On the other hand, ML\({}_{3}\) achieves also similar accuracy than ML\({}_{1}\) and ML\({}_{2}\). ML\({}_{3}\) estimates the throughput in end-to-end path containing radio links (UAV-antenna and antenna-control station) and fixed links (antenna-core-antenna, i.e., fronthaul and backhaul). The fact that the results are similar in end-to-end path means that the variability of the network (which decreases the accuracy) is present, most of all, in the radio links. The last tests aim to define which utility function of the hypothesis space defined above is the optimal for estimating the end-to-end throughput. The first step is to train ML\({}_{1}\), ML\({}_{2}\) with all the 150 measurement samples obtained in link 1 and link 2. In this test we assume that ML\({}_{1}\), ML\({}_{2}\), and ML\({}_{3}\) do not need to be validated, so all the data can be used for training the machines. Afterwards, ML\({}_{3}\) is trained with the 150 samples of end-to-end connection. With the 300 measurements (100 samples/operator) taken at the same time in link 1, link 2 and end-to-end connection, we estimate the throughput in link 1 (by using the trained ML\({}_{1}\)), in link 2 (by using the trained ML\({}_{2}\)) and in end-to-end connection (by using the trained ML\({}_{3}\)). Table 2 presents the estimated values of throughput for one example sample. Let us remark that the throughput is measured in uplink direction. For this concrete example sample, end-to-end routing would be selected by using Operator 2 (11.1 Mbps is the biggest throughput in end-to-end connection). On the other hand, \(G_{1}\) is equal to 11.3 Mbps, see formula (4), and the Operator selected by \(G_{1}\) is Operator 2; whereas \(G_{2}\) is equal to 14.1 Mbps, see formula (5), and the Operator selected by \(G_{2}\) is also Operator 2. In this example the values of throughput for Operator 2 are really much better than for other Operators, so it is logic that all the functions aiming to maximize the throughput will select Operator 2.