# Data Aggregation Based on Overlapping Rate of Sensing Area in Wireless Sensor Networks
## 5 Performance Evaluation
### Experiment Results  
We evaluate the performances of four schemes, i.e., HEER, EEUC, AggOR-CP and AggOR, and the results are illustrated in Figure 7. Note that the experiments are conducted in Scenario SP. With the number of sensors increasing, the density of nodes does not change. In other words, the results are obtained under different network scales with the same density. Specifically, the networks with 40, 80, 120, 160 and 200 nodes cover approximately 20%, 40%, 60%, 80% and 100% of the whole \(100\times 100\,\mathrm{m}^{2}\) scenario, respectively. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Scenario (\(\mathrm{m}^{2}\)) & 100 \(\times\) 100 \\ Number of sink node & 1 \\ Number of sensor nodes, \(N\) & 40, 80, 120, 160 and 200 \\ Sensing radius (m) & 25 \\ Communication radius (m) & 52 \\ Data collection cycle (s) & 60 \\ \(OR_{T}\) & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. As Figure 7a shows, when there are 40 nodes in the network, EEUC has the longest lifetime of the network, and AggOR tightly follows. However, with the number of nodes increasing, the lifetime of AggOR which is longer than AggOR-CP, gradually exceeds EEUC from the scale of 120 nodes, and the lifetime of HEER is the shortest. Even though in EEUC scheme, the clusters output a single length-fixed packet after aggregation, which is smaller than the output of gathering nodes in AggOR, the main reasons of the result lie in two aspects. (1) The redundant data is forwarded for several hops in EEUC while redundancy is only relayed once in AggOR; (2) Compared with EEUC in which the cluster heads may be at lower levels, in AggOR, the gathering nodes are mainly the upper-level nodes, and thus sensor data are always forwarded up avoiding the back and forth relay. Note that there are different ways to define the dead time of the network. If the sensing range of the first dead node is covered by others, the network might continue to work. Therefore, beside the death of the first node, we analyze the network lifetime, which takes the time when some area cannot be sensed any longer or some data cannot be delivered to the sink as the dead time. The results are shown in Figure 8. The network lifetimes of all the four schemes in Figure 8 are a little longer than or the same as those in Figure 7a, because the sensing areas of some first dead nodes are covered by others and some first dead nodes are the gathering nodes or the forwarders for others. However, the trends of the results in these two figures are similar, both showing that our scheme AggOR achieves a similar network lifetime to EEUC and a little longer lifetime than HEER. Figure 7b demonstrates that the transmission overhead in AggOR is a little smaller than those in AggOR-CP and EEUC schemes when the number of nodes is 80. As the number of nodes increases, the transmission overheads of HEER, EEUC and AggOR-CP are increasing faster than AggOR. AggOR has a smaller transmission overhead than AggOR-CP, EEUC and HEER by about 4%, 10% and 17% respectively in the scenario with 200 nodes. HEER always has the highest overheads among the compared schemes. Figure 7: Experiment results. (**a**) network lifetime; (**b**) transmission overhead; (**c**) maximum hops to the sink; (**d**) information accuracy. Because the maximum hops in multiple tests for HEER is not stable, we use median values rather than average values in Figure 7c. From the figure, AggOR-CP has the smallest and stable number of hops, while AggOR in some rare cases has more hops than others. This is because in our scenarios with \(OR_{T}=0.5\), all the gathering nodes in AggOR-CP are the upper-level nodes, while there are some neighbor nodes as gathering nodes in AggOR, slightly increasing the number of hops in data transmission. As the number of nodes increases, the maximum hops of EEUC and HEER schemes are more unstable and larger than AggOR, especially HEER. When there are 200 nodes, the maximum hops in AggOR is smaller than EEUC and HEER by 12% and 25% respectively.