## 4 Results
### Communication Reliability  
In Figure 10 we can see the evolution of the error rate per experiment, and the fitted curve to each one. \begin{table}
\begin{tabular}{c c c c c} \hline
**Experiment** & \(\mathbf{\beta_{e}}\) & \(\mathbf{J_{e}}\) & \(\frac{\beta_{e}}{\max_{\beta_{e}}}(\%)\) & \(\frac{\mathbf{J_{e}}}{\max_{\mathbf{J_{e}}}}(\%)\) \\ \hline e01 & 0.3358 & 4283.19 & 100.00 & 100.00 \\ e02 & 0.2353 & 3408.00 & 70.07 & 79.57 \\ e03 & 0.2691 & 3921.53 & 80.14 & 91.56 \\ e04 & 0.2928 & 3947.76 & 87.19 & 92.17 \\ e05 & 0.2976 & 3639.89 & 88.62 & 84.98 \\ e06 & 0.2815 & 3817.46 & 83.83 & 89.13 \\ e07 & 0.2848 & 3846.54 & 84.81 & 89.81 \\ e08 & 0.2511 & 3865.22 & 74.48 & 90.24 \\ e09 & 0.2647 & 3798.83 & 78.83 & 88.69 \\ e10 & 0.2665 & 3952.63 & 79.36 & 92.28 \\ \hline \end{tabular}
\end{table} 
Table 3: Battery consumption slope and discrete integration per experiment. Figure 10: Evolution of the total transmission error rate per experiment. The curve for the experiments where the self-adaptive system is running seems to follow a negative exponential equation like the one described in Equation (3). \[\epsilon_{c}=\alpha_{c}e^{-\beta_{c}} \tag{3}\]  
We estimate the performance regarding the error rate using the numerical integration as defined in Equation (4). \[J_{c}=\sum\epsilon_{c} \tag{4}\]  
And Figure 11 shows the comparison for the \(J_{c}\) value obtained for the total transmission error rate per experiment. The values for \(J_{c}\), \(\alpha_{c}\) and \(\beta_{c}\) per experiment are also shown in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Experiment**} & \multicolumn{3}{c}{**Per Experiment**} & \multicolumn{3}{c}{**Per Round Per Experiment**} \\ \cline{2-7}  & \(\alpha_{\text{c}}\) & \(\beta_{\text{c}}\) & \(J_{\text{c}}\) & \(\alpha_{\text{c}}\) & \(\beta_{\text{c}}\) &  
As expected, at the beginning of each experiment there is an adjustment time that shows a dependence on the parameters used in the control system. At this point we can notice in the last experiment there is a huge error rate. There are two aspects that had its effect on this:  
1. The parameters chosen for this experiment allowed the nodes to stop adjusting their transmission power when the reached \(2\pm 1\) neighbors. This, in fact, caused that some of the nodes created isolated islands unable to communicate with the rest of the network. 2. Two nodes readjusted their \(ND_{R}\) value at some point in the middle of the experiment, as their batteries reached values below the selected \(E_{CR}\). This worsened the situation, as these two nodes were allowed to remain at a given transmission power if they reached at least one or two neighbors. Another remarkable result is that at a fixed transmission power set to a medium one, the error rate seemed to be high and constant, so almost every experiment with the self-adaptive system reached better error rates. However, the total error rate only shows us the evolution of the network connectivity. The error is high at the beginning, given that all the nodes started from the lowest transmission power available in the adaptive experiments. This implies that although the connectivity can be good enough at a given instant, the accumulative will show just a little improvement. To realize how good the connectivity is, we explore the error rate for each iteration, that is, the current error rate per round, as shown in Figure 12.  
Again we see that the distribution of the error rate follows a negative exponential for those experiments using the adaptive control system. Then the Equations (3) and (4) are still valid for the new results. Figure 12: Round transmission error rate per experiment.