## 5 Results
### Communication Range Dynamics
\[J_{d}=\sum_{i=0}^{N}\sum_{k=0}^{M}\chi_{i}(k) \tag{20}\]  
The results of applying Equation (20) to the obtained data from the experiments is shown in Table 3.  
There are several conclusions we can derive from both the figures and the values listed in Table 3. The first and easiest thing we can conclude is that Experiment e05 has the best performance regarding the number of actions on the transmission power, as it uses just only 58 changes during the experiment and reaches a good enough connectivity after just six iterations of the control loop, achieving a 92.48% PDR in the seventh iteration. Indeed, as we will see later, the expected delivery rate of this experiment reaches a 99% after the 10 th iteration. Another thing we can observe is that although the dynamics estimation provides interesting information, it has to be considered along with other performance measurements. For instance, Experiment e07 has one of the worst dynamics figures, with 205 changes of the transmission power during the experiment, but it has valid connectivity results, reaching an expected delivery rate of 90% in its 16 th iteration, with connectivity values over the 80% PDR from the 10 th iteration, as seen in Figure 11(e). The same happens the other way. Experiment e10 has the third best figure for the transmission power dynamics, but due to a bad choice of the configuration parameters, it provides a really bad connectivity, never reaching even an expected delivery of 50% of the messages transmitted, as seen in Figure 11(h). Thus, we cannot use just the dynamics estimation to evaluate the performance of the system. However, it still provides good complementary information to other performance measurements, like the energy consumption and the connectivity performance explored in [10]. It also produces other valuable information, like the evidence that the node degree is different for each node even when the network has reached a steady state. This can be observed when comparing Figures 9(c) and 10(c). This allows us to reformulate the question proposed in [34] about the adjustment of the desired node degree for each node according to its location in the network. Moreover, the node degree also changes when there is no change in the transmission power. For instance, in the aforementioned figures, we can observe that there is no change in the transmission power from Round 11 to Round 16 for Experiment e05. However, when observing the same interval for the node degree dynamics, we can see that the node degree changes among rounds. Additionally, this occurs without losing connectivity, as shown in Figure 11(c). Of course, this resilience to the changes in the node degree is due to the use of the tolerance parameter \(\xi_{ND}\), but it also illustrates that events external to the nodes affect the node degree. Therefore, the question that remains is if there is another way to solve the unexpected changes in the node degree beyond the use of a tolerance factor. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Experiment** & \(\mathbf{J_{d}}\) & **Rounds to 90\%PDR** & **Rounds to 99\% PDR** & **PDR at Round 30 (\%)** \\ \hline e03 & 150 & \textgreater{}30 & \textgreater{}30 & 59.94 \\ e04 & 211 & \textgreater{}30 & \textgreater{}30 & 76.40 \\ e05 & 58 & 7 & 12 & 99.99 \\ e06 & 83 & 25 & \textgreater{}30 & 93.15 \\ e07 & 205 & 16 & \textgreater{}30 & 98.20 \\ e08 & 182 & 24 & \textgreater{}30 & 94.64 \\ e09 & 127 & 22 & \textgreater{}30 & 96.14 \\ e10 & 84 & \textgreater{}30 & \textgreater{}30 & 42.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Figure of merit for the communication range dynamics and PDR estimations.