## 5 Simulation Results and Discussion
### Number of Active Nodes  
Figure 3 shows the number of active nodes related to rounds. The simulated terrain is 500 m \(\times\) 500 m wide. The simulation is running until the last node switch off in the CH-active algorithm. The simulation ends when none of the nodes is active anymore (more than 900 rounds in case of the CH-active algorithm). The proposed algorithms showed significant improvement. It can be seen that when the instability period begins, the CH-active algorithm brings an advantage over LEACH in this application. Along with decreasing the number of active nodes, the distance between nodes is increasing, and then moving to the center of active nodes begins to gain a notable advantage. The LEACH algorithm has no more active nodes in the region of 480 rounds. The proposed algorithms have about 40 active nodes at this time. While most batteries are in good condition, both of the proposed algorithms have very similar performances. However, CH-active begins to be more advanced than CH-partially-active, after 40% of the nodes die. It is shown that the rest of the nodes in the following rounds stay active for 10% more rounds, so that the network is alive for a longer period with CH-active than with CH-partially-active. However, the difference in the number of active nodes is not large at any time. This difference does not exceed 10 (in the region of round 500) and in most cases, it is less than 5.  
Figure 4 shows the number of active nodes per round on a 1000 m \(\times\) 1000 m field, with 100 uniformly distributed nodes. The energy assigned to each node at the simulation start is 2 J. Because of their nature, it is expected that CH-active and CH-partially-active algorithms will accomplish better results from the very reconfiguration, when the terrain itself is wider. The optimum exploitation of the proposed algorithms is on a wider terrain, and in a harsh environment with periodical and not intensive reporting. In optimum application, the CH has enough time to move to the gravity center and collect all the data from the appertaining clusters there. After that, CH returns to its initial position and reports to the BS from the initial position. In the meantime, data aggregation is done.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Case 1** & **Case 2** \\ \hline Sensing field (terrain dimensions) & 500 m \(\times\) 500 m & 1000 m \(\times\) 1000 m \\ BS position (x\_sink, y\_sink) & (0, \(-\)100) & (0, \(-\)100) \\ Number of sensor nodes in the field (\(n\)) & 100 & 100 \\ Data packet length (message length) & 2000 bytes & 2000 bytes \\ Signal packet & 100 bytes & 100 bytes \\ Eelec & 50 nanoJoules/bit & 50 nanoJoules/bit \\ E0 (initial\_node\_energy) & 2 J & 2 J \\ The percentage of the path to the center & 25\% & 25\% \\ of the masses that is covered & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters.  
As it was expected, the normalized gain in a number of rounds is bigger on wider terrain (compare Figures 3 and 4). The LEACH algorithm has no more active nodes around 140 rounds. The proposed algorithms have about 35 active nodes at this time. On a 1000 m \(\times\) 1000 m terrain, the difference in duration between the CH-active algorithm and LEACH is 250 rounds. As shown in Figure 4, when the number of live nodes is decreased, and/or if the distance between the nodes is bigger, the CH-active algorithm begins to gain an advantage over the CH-partially-active after 65% of the nodes die. The difference between the proposed algorithms does not exceed 8 (in the region of round 180) and in most cases, it is less than 5.