## 5 Experiments
### Algorithms Comparison  
The next set of experiments was aimed at comparing the performance of both algorithms for networks of varying sizes. For every network, the entire scenario was computed, i.e., the problems were solved for all frames providing that all nodes except the base station were able to send their data. As the number of nodes sending data within a frame was set to 4, the number of frames was \([(N-1)/4]^{+}\), and in the case when \(N-1\) was not fully divisible by 4, the last frame consisted of less sending nodes. It is important to note that the number of variables and constraints grows significantly with network size--see Table 5. In total energy formulation, all variables are binary or integer. The maximum node energy version uses a single additional continuous variable. Even using highly efficient solvers like CPLEX problems, over a thousand variables may be considered hard, especially when a specific structure of bounds is present. Results of this may be easily observed in Tables 6 and 7. The tables present average and extreme values of time and performance index for all frames forming subsequent scenarios. One of the most visible features is that computation times for algorithm using total energy consumption index (Table 6) tends to be, at least for larger networks, relatively high, making its application for networks with more than 16 nodes questionable. For algorithms using maximal energy consumption index the computation times seems to be growing \begin{table}
\begin{tabular}{p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt}} \hline \hline \multicolumn{2}{c}{**Number of Nodes**} & \multicolumn{3}{c}{**Computation Time [s]**} & \multicolumn{3}{c}{**Performance Index**} \\ \hline
**Total** & \
\begin{tabular}{c} **Having** \\ **Data** \\ \end{tabular} & **Average** & **Min.** & **Max.** & **Average** & **Min.** & **Max.** &
\begin{tabular}{c} **Frames** \\ **Number** \\ \end{tabular} \\ \hline
9 & 3 & 0.09 & 0.047 & 0.137 & 93.7 & 85 & 98 & 3 \\ \hline
16 & 4 & 7.8 & 2 & 18 & 112 & 112 & 4 \\ \hline
25 & 5 & 18.4 & 1.38 & 35.7 & 112 & 112 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results for algorithm using maximal energy consumption index. \begin{table}
\begin{tabular}{p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt}} \hline \hline \multicolumn{2}{c}{**Number of Nodes**} & \multicolumn{3}{c}{**Computation Time [s]**} & \multicolumn{3}{c}{**Performance Index**} \\ \hline
**Total** & \
\begin{tabular}{c} **Having** \\ **Data** \\ \end{tabular} & **Average** & **Min.** & **Max.** & **Average** & **Min.** & **Max.** &
\begin{tabular}{c} **Frames** \\ **Number** \\ \end{tabular} \\ \hline
9 & 3 & 0.07 & 0.024 & 0.16 & 996.3 & 874.3 & 1118.2 & 3 \\ \hline
16 & 4 & 6 & 0.1 & 13.3 & 1334.5 & 1079.5 & 1583.5 & 4 \\ \hline
25 & 5 & 3813 & 2.9 & 10,800 * & 1688.1 & 1541.7 & 2238.7 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results for algorithm using total energy consumption index, (*) optimization of one of the frames for 25 nodes scenario was terminated after 180 min as computer memory was nearly exhausted, the maximum time and performance index values are related to this frame. \begin{table}
\begin{tabular}{p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt}} \hline \hline \multicolumn{2}{c}{**Number of Nodes**} & \multicolumn{3}{c}{**Number of Variables**} & \multicolumn{3}{c}{**Number of Constraints**} \\ \hline
9 & 432 & 452 \\ \hline
16 & 768 & 802 \\ \hline
25 & 1200 & 1252 \\ \hline
36 & 1728 & 1802 \\ \hline
49 & 2352 & 2452 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Problem sizes for algorithm using total energy consumption index, for algorithm using maximal energy consumption index number of variables and the number of constraints must be incremented by 1. Note that problem size does not depend on the number of nodes having data to send. much slower. They may be considered acceptable when the slot allocation is repeated rarely, e.g., on a time scale of several hours or days.