## 4 System Evaluation and Analysis
### Effect of Network Lifetime on Different Device Densities  
In this simulation, we compared the effective energy conservation from the proposed WQS method with EQS and DISCO for different device densities. The effect of device densities on energy consumption, represented by the average duty cycle time of all devices in the network, is shown in Figure 8. A duty cycle is the percentage of one period in which a signal is active, and a period is the time of system takes for a signal to complete an on-and-off cycle. In Figure 8, the \(x\)-axis is the sensor index number, and the \(y\)-axis represents the average time of duty cycles for the sensors. The execution time is from the network starting to all nodes stopping. A shorter duty cycle denotes superior sensor performance. Thus, the performance of WQS is considerably superior to DISCO and EQS. A remarkable difference exists between WQS and EQS, which is based on the selection of the intermediate nodes. Figure 8 shows the difference; when the device density increases, the time of the average duty cycle increases in EQS, because the nodes in EQS cannot balance the communication burdens to the others. Many pairwise connections are concentrated on the same nodes, that will require more wakeup instances to handle the communication. The same situation exists for DISCO. By contrast, the proposed WQS method is based on the balanced selection of intermediate nodes, which can facilitate connecting two rows. When the proposed system attempts to select a pairwise node, the balance condition between the remaining power and referencing time is considered. Hence, more connection burdens can share to those nodes in the network, when the network structure has been changed. In general, the average duty cycle time is decreased from 8.88% and 58.28% than EQS and DISCO respectively.  
Figure 7: Final result of our example.  
Accordingly, Figure 9 shows the average times of the loop index for each node in the different network density. In software engineering, a loop index is the variable that counts the iteration of a loop. In this simulation, the numbers of loop index are computed for the comparison of our proposed method and the other two methods, the index numbers are accumulated until energy exhausts the nodes. The bigger index numbers means better performances of scheduling flexibility and resource allocation. In Figure 9, the average times of the loop index for the comparison of DISCO, EQS, and WQS are based on the different network size, from 2 to 50 nodes. Figure 9 shows that the index times of the proposed method is considerably superior to that of the other two methods. That is, for the same job, the loop in our proposed method can execute faster and exchange more information than the other two methods. This advantage happens by the balance condition for each node. Besides, Figure 9 illustrates the WQS method has the advantages on the heavy loading network, the more nodes can share the connection burden and keep the stable increasing times obviously. The robust power can be proven herein. According to our accumulation, in the same execution time, the average loop index times in our proposed method have 69.94% and 78.39% more than the EQS and DISCO methods.  
Figure 8: The average duty cycle time on different device densities.  
Figure 9: The network lifetime on different device densities.