## 5 Performance Evaluation
### Simulation results  
Figure 7 shows the relationship between the number of cluster heads, the number of independent connected components, and network size. As the network size increases, it can be seen that the number of independent components is increasing too. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Value** \\ \hline Network Filed & _(0,0)-(100,100)_ \\ Node numbers & _100–500_ \\ Cluster radius \(r\) & _30 m_ \\ Sensing radius \(r_{s}\) & _10 m_ \\ Sink position & _(50,200)_ \\ Initial energy & _2 J_ \\ Data packet size & _525 Bytes_ \\ Broadcast packet size & _25 Bytes_ \\ \(E_{threshold}\) & _0.01 J_ \\ \(E_{elec}\) & _50 nJ/bit_ \\ \(e_{fs}\) & _10 nJ/bit/m\({}^{2}\)_ \\ \(e_{amp}\) & _0.0013 pJ/bit/m\({}^{4}\)_ \\ \(E_{DA}\) & _5 nJ/bit/signal_ \\ Threshold distance \(d_{0}\) & _75 m_ \\ Data Cycles per round(\(L\)) & \(5\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation Parameters. Figure 7: The number of heads and the number of connected components. When the network size is (100 x 100), the number of connected components equals 1 in most cases, which means the graph composed of cluster heads is connected. When the network size is (400 x 400), after the clustering phase, almost sixty cluster heads will be generated. However, such a large number of nodes cannot guarantee the connectivity of all cluster heads. As shown in Figure 7, the number of independent components almost reaches 20. Obviously, our algorithm can work well when the node density is high enough, that is, more than 0.01/m\({}^{2}\). Figure 8 proves that EAP can effectively provide the required QoS. On the one hand, providing QoS lower than the required one may save energy at a risk of failing to meet the application's requirement. On the other hand, providing a higher QoS than required by a specific application will decrease the efficiency of energy utilization. However, EAP cannot provide a perfect matching between expected QoS and obtained QoS. It maybe does not work well in some applications, which strictly require that the deviation between expected QoS and obtained QoS is small enough. As shown in Figure 8, if there are 100 nodes deployed in monitoring area, the obtained QoS cannot meet the application requirement when the expected QoS exceeds 95%, because even if all nodes are turned on, they cannot cover a 95% fraction of the whole monitoring area. Because HEED and LEACH cannot provide the topology control function, each node needs to collect the temperature information and transmit it to its cluster head, even if it is a redundant node. So, the two algorithms fail to prolong network lifetime when node density is high. Conversely, for the EAP protocol, through the intra-cluster coverage method, the number of actual active nodes is only determined by the expected QoS. As shown in Figures 9 and 10, it is easy to find that the sensor network lifetime will be almost be linear in the number of nodes which are deployed in monitoring area. Figure 8: Expected QoS vs. obtained QoS. Assume that there are 100 nodes distributed in a monitored region which area is 100\(\times\)100 m2, where the sink node's position ranges from (50, 175) to (50, 400) and the cluster range (for intra cluster communications) in EAP and HEED is set to 30m. The monitored region requires being a hundred per cent covered, i.e. all the nodes are working nodes. The stimulation results are shown in Figure 11. With the increase of the distance between the sink node and the network, the energy consumption of the nodes that can directly communicate with the sink node will increase remarkably. In this case, the larger the number of the nodes that can directly communicate with the sink node is, the more rapidly the performance of protocols degenerates. Therefore, EAP and HEED, in which protocols there is only a single node to communicate with the sink node, perform remarkably better than  
Figure 10: The number of nodes vs. network lifetime (expected QoS = 0.99). Figure 9: The number of nodes vs. network lifetime (expected QoS = 0.95).