# A Game Theoretic Approach for Balancing Energy Consumption in Clustered Wireless Sensor Networks
## 6 Performance Evaluations
This condition indicates that the LGCA protocol is more suitable for use in larger scale networks than CROSS since its implementation is completely distributed. Figure 4: Network lifetime versus different network sizes. \begin{table}
\begin{tabular}{c c} \hline \hline
**Routing Scheme** & **Network Lifetime** \\ \hline LEACH & 856 \\ Only-clustering & 986 \\ GTAB & 1081 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Lifetimes of the network when using LEACH, Only-clustering and GTAB. The round until the last node dies is also an important criterion for performance evaluation in clustering. Figure 5 gives the comparison of the rounds until the last node dies versus different network sizes among LEACH, CROSS, LGCA and GTAB. Figure 5 shows that when the network size increases, LEACH, CROSS and LGCA have downward trends regarding the round until the last node dies, but our proposed protocol GTAB has a relative stable level about the round until the last node dies. This case indicates that with the increase of the network size, the duration of the network decreases when adopting the protocol LEACH, CROSS or LGCA, but the effect of network size on the network duration is relatively smaller when adopting the GTAB scheme. As mentioned before, the network lifetime when using GTAB decreases with the increase of network size, which results in the increase of round interval from the first node dies to the last node dies. This means that GTAB runs more energy-efficiently when network size increases so that it is very suitable for large scale networks. Figure 6 gives the comparison of average number of packets per node versus different network sizes among LEACH, CROSS, LGCA and GTAB. Figure 6 shows that GTAB has the greatest average number of packets per node among these protocols for all cases of network size, which means the energy efficiency of GTAB is the highest. In addition, the difference of average number of packets per node between GTAB and other three protocols increases with the increase of network size. This phenomenon implies that compared with other three protocols, GTAB has a relatively increasing energy efficiency when the network size increases. Figure 5: Rounds until the last node dies versus different network sizes. Figure 6: Average number of packets per node versus different network sizes. Figure 7 gives the comparison of average number of CHs per round versus different network sizes among LEACH, CROSS, LGCA and GTAB. From Figure 7, we can see that LEACH has the most number of CHs per round for all cases of network size. It also has the highest increase rate of the number of CHs per round when the network size increases. This is due to the constant expected percentage of CHs in LEACH. The number of CHs in CROSS is relatively stable. This is because for any sensor node in CROSS, once it has been selected as a CH, then it has no chance to be the CH again until all other sensor nodes have served as CHs in the network. Figure 7 also shows that with the increase of network size, the average number of CHs per round increases in both LGCA and GTAB. Furthermore, LGCA has more average number of CHs per round than GTAB for all cases of network size. This can be explained as follows: due to the completely distributed implementation of both LGCA and GTAB, CHs will be selected within every localized area. Thus, the larger the network size becomes, the more the number of CHs that will be selected. Moreover, the probability of being the CH in LGCA strongly depends on the predefined parameter \(w\), and it increases with the decrease of \(w\). Then in the following simulations, the network size is set to be 100 \(\times\) 100 m\({}^{2}\) and the node density is 1 node/100 m\({}^{2}\). We first show the detail of number of nodes that still alive in each round when communication radius is 35 m. Then we gives comparison of network lifetime versus different communication radius among these protocols, for the purpose of analyzing the effect of the communication radius on network lifetime.