# A Game Theoretic Approach for Balancing Energy Consumption in Clustered Wireless Sensor Networks
## 6 Performance Evaluations
Figure 8 gives the comparison of number of nodes alive versus the number of rounds among LEACH, CROSS, LGCA and GTAB. The round interval from the first node dies to the last node dies in our proposed protocol GTAB is the shortest among these protocols, and that in LGCA is the longest. This implies that the energy balancing performance of GTAB is the best, and that of LGCA is the worst. This is because a penalty mechanism is introduced in GTAB to punish the selfish sensor nodes which abandon the duty of serving as CHs for energy saving, so that sensor nodes which have more energy have bigger probabilities to be CHs that can well balance the energy among nodes. However in LGCA, once a sensor node has served as a CH, it will not be selected as the CH again until all its neighbor nodes have served as the CHs. Thus sensor nodes with more neighbor nodes have less chance to be CHs which results in a poor energy balancing performance among nodes. Figure 8 also shows that LEACH and CROSS almost have equivalent round intervals from the first node dies to the last node dies, which means these two protocols have equivalent energy balancing performance among sensor nodes. This phenomenon can be explained as follows: as the average number of CHs per round in CROSS and LGCA is approximately equal to 4 when the network size is 100 \(\times\) 100 m\({}^{2}\). For a sensor node in CROSS, once it has been selected as the CH, it will not be the CH again until all other nodes have served as the CHs in the network. Then once a node has been the CH in one round, it will have  
Figure 7: Average number of CHs per round versus different network sizes. no chance again to be the CH in the following 24 rounds. In other words, a sensor node will be selected as the CH once every 25 rounds in CROSS, and this mechanism of sensor nodes taking turns to be CHs is very similar to that used in LEACH. In order to analyze the trend of network lifetime when communication radius of sensor nodes increases, Figure 9 gives the comparison of network lifetime versus different communication radius of sensor nodes among LEACH, CROSS, LGCA and GTAB. From Figure 9, we can find that there is no effect of the communication radius on network lifetime in LEACH and CROSS. This is because these two protocols have no limitations to sensor nodes with regard to the communication radius. Both GTAB and LGCA display their shortest network lifetimes when the communication radius equals the minimum value of 10 m, this is because too many CHs are selected in both GTAB and LGCA when the communication radius is very small. With the increase of communication radius, the network lifetime in GTAB first increases and then decreases gradually, and that in LGCA keeps increasing slowly. We can explain this phenomenon as follows: too many CHs will be selected if the communication radius is very small in GTAB and LGCA. Less CHs will be selected when the communication radius increases which results in a heavier data burden per CH. Thus the network lifetime will be affected negatively if the communication radius keeps increasing or decreasing. However, we only find the downtrend of network lifetime in GTAB but not in LGCA when communication radius increases, this case ascribes to that GTAB achieves the optimal number of CHs earlier than LGCA with the increase of communication radius. Figure 8: Number of nodes alive versus the number of rounds. Figure 9: Network lifetime versus different communication radiuses of sensor nodes. At last, to find the effect of node density on network lifetime, we conduct a simulation under the case that network size is set to be 100 \(\times\) 100 m\({}^{2}\), communication radius is 35 m and node density increases from 0.2 to 1 node/100 m\({}^{2}\). Figure 10 gives the comparison of network lifetime versus different node densities among LEACH, CROSS, LGCA and GTAB. It shows that our proposed protocol GTAB outperforms other three protocols for all cases of the node density.