# Energy Prediction of Access Points in Wi-Fi Networks According to Users' Behaviour
## 7 Experimental Validation  
Figure 1 includes a work phase for the experimental validation of the proposed prediction method. The validation comes from collecting new energy and roaming data in the same wireless network where \(AP_{8}\) was really removed. Obviously, the corresponding new period is different to the one considered for the prediction works, because it is later and can have a different number of days. However, this circumstance does not impede the validation works for two reasons. On the one hand, the users' behaviour is supposed to be similar in two different periods when both consider enough working days in the same academic environment; on the other hand, the users' behaviour is responsible for the roaming distribution among the different access points of the network, with the corresponding effect in their energy consumption. The experimental validation starts by removing \(AP_{8}\) from the wireless network, not in a simulation mode as in the prediction, but in reality. The resulting network is called the \"new network\" from this point onwards. Next, we collect roaming and energy data in the access points during a determined period. Once we stop collecting data, we can calculate the relationship between roamings and energy for the new network. Finally, we compare the energy distribution among the access points of the new and simulated networks for a qualitative validation of the prediction method proposed. Figure 7 shows the period considered for collecting data in the new network. It consists of 63 days, 40 of which were working days with usual academic activity, useful for comparison purposes (the building was closed for 22 days and the network failed one day). As in the prediction works, we filter the collected data for the daily time slot reduced (12 h, from 9:00 to 21:00), because the usual network demand takes place in that slot. The new period considers the activity of 3083 users. Figure 6: Energy prediction (\(TPE\)) in the simulated network, obtained from the roamings predicted (\(TPR\)) considering the same point coefficients \(C\) that define the relationship between roamings and energy for the full network. We build three datasets from the collected data:  
* \(NR\) (\"New Roamings\"). It is a \(S\times I\) matrix, where \(S\) is the number of users (\(S=3083\)) and \(I\) is the number of APs (\(I=10\)). The cell \(nr_{s,i}\) is the number of total roamings due to user \(s\) in the AP \(i\) during the entire period. As \(AP_{8}\) was removed, the entire column \(i=8\) is set to zero in the matrix. * \(TNR\) (\"Total New Roamings\"). It is an array of size \(I\) where \(TNR_{i}\) is the number of roamings stablished in the AP \(i\) by all the users during the period. This value is calculated by adding the entire column \(i\) in \(NR\). * \(TNE\) (\"Total New Energy\"). It is an array of size \(I\) where \(TNE_{i}\) is the total energy in the AP \(i\) in the period. As in the prediction, the energy values in this array are filtered to consider only the period (40 days) where the network was available for the users. Therefore, we assure these energy values show the users' behaviour. We can calculate the relationship between users' activity (\(TNR\)) and energy consumption in the access points (\(TNE\)) by means of point coefficients \(CN_{i}\) (16), following a similar formula as for the prediction process. The link between both datasets is reasonable because the roamings were generated during the days when the network was available for the users, which are the same days taken into account to calculate the array \(TNE\). \[TNE_{i}=CN_{i}\,TNR_{i}=CN_{i}\,\sum_{s=1}^{S}cnr_{s,i} \tag{16}\]  
The experimental validation of the prediction proposal comes from the comparison between the \(TPE\) and the \(TNE\) datasets. The first dataset contains the energy predicted in the APs of the simulated network during the first period; these energies were obtained applying the prediction model to the entire network using \(TCR\) (roamings) and \(TCE\) (energies).