# Time Series Analysis to Predict End-to-End Quality of Wireless Community Networks +
## 4 Time-Series Analysis to Predict EtEQ
### Computational Cost of the Predictions  
We analyzed the computational cost of the training algorithm and the prediction process in a real environment. The aim of this analysis was to verify that this cost is low and does not represent a significant increase in terms of computational resources nor energy. For this purpose, we executed the prediction software in a typical mini-PC, which acts as router, using the WEKA [52] environment with the FunkFeuer network open datasets [6]. The mini-PC is a Jetway JBC372F36W-2600-B [53]. The processor is an Intel ATOM N2600 at 1.6 GHz with two cores and multithread support. It has 4 GB of RAM and a SSD connected to a SATA2 port. The system was configured with a Linux kernel 4.4.0-140 in 64 bit mode inside an Ubuntu 16.04 LTS distribution. To execute the WEKA environment, the Java openjdk version 1.8.0-191 was installed. We considered three parameters: CPU utilization, energy consumption and temperature. For the first one, we split the measurements into two parts: in one side the cost of the prediction and on the other side the cost of the training. We evaluated the execution assuming the worst case, which  
Figure 16: RBR Mean Absolute Error of EtEQ predictions, depicted as a box plot. Figure 15: RBR average Mean Absolute Error (MAE) of the EtEQ predictions. means executing the prediction every 5 s and the training every 5 min (in a real scenario, the training frequency should be once every few hours). WEKA environment takes a huge amount of time to wake-up compared to the cost of making a single prediction; that is around 3 s versus a few milliseconds. To isolate the cost of one prediction, we executed multiple times (100-1000) several routing tables from FunkFeuer network open datasets [6] with the statistical model preloaded. Figure 17 shows the difference in time of one prediction obtained from the subtract of just 13 predictions--the minimum possible value--over 14 predictions (one step), and the difference in time from the subtract of just 13 predictions over 23 predictions divided by 10 (ten steps). Then, we estimated the execution time of one prediction once the WEKA environment was started and the model was loaded. We observed a computational cost in the range from 20 ms to 80 ms with a 35 ms on average. This result led us to conclude that computational cost of predictions is negligible. In the same way, we also executed the training part using WEKA. One execution of the training part allocates both CPUs at 100% for a period of time from 5 to 22 s. Figure 18 shows the execution time of several samples from FunkFeuer network open datasets. We observed that it takes about 15 s on average, which is a substantial amount of time. However, we have to consider that this training is performed every few hours in a real environment, thus the impact in CPU utilization is very low. Moreover, we decided to test an extreme situation, presented in Figure 19, where we executed the training algorithm every 5 min over 24 h to observe that just a 3.78% of CPU is needed to execute the training part of the model. The second parameter that we evaluated was the energy consumption of the training algorithm. To do this, we attached a voltmeter and an ammeter to the 12 V jack of the mini-PC. This allowed us to measure real volt and amp consumption when the system is in idle state, and when the system  
Figure 17: Execution time for one prediction with a preload model. One step means just the time of the next prediction. Ten steps means the average of ten subsequent predictions. Figure 18: Execution time for Training WEKA model: mean is 14.68 s, maximum is 21.79 s and minimum is 5.31 s.  
is executing the training model at full CPU utilization. Figure 20 shows the energy consumption in watts for a period of 20 min. The system executed training models continuously and sequentially. We observed that the increase is 1.86 W on average, but in a real environment, this only happens for a period of 15 s every few hours.