# A Delay-Aware and Reliable Data Aggregation for Cyber-Physical Sensing
## 5 Performance Evaluation
### Evaluation on the Proposed Scheme with Different Parameters  
The proposed scheme is evaluated firstly. Here, the performance evaluation mainly focuses on two metrics, namely the reliability and network delay. We investigate the performance of TSR-DARDA through simulations. When \(\delta\) = 0.6, according to the implementation of the optimized TSR-DARDA shown in Figure 7, the network is divided into surface circular tiers from outer tier to inner tier. The network circular partitions for a network with 100 nodes and 500 nodes are as shown in Tables 1 and 2, respectively, wherein \(d_{1}\) represents the hotspots. Tables 3 and 4 respectively show the number  
Figures 9 and 10 respectively demonstrate the comparison of the number of packet lost and data aggregation delay under different \(p\) and \(\mu\) for a network with 100 nodes. As shown in Figures 9 and 10, the changing overall trend of the number of packets lost and delay decreases as \(p\) becomes bigger, which is reasonable. Moreover, the number of packets lost is reduced with the increasing number of retransmission times \(\mu\), which leads to more data aggregation latency. When \(\mu=0\), it means no retransmission of data packets in the data aggregation procedure, so there is the same network delay under different \(p\). Figures 11 and 12 respectively illustrate the comparison of the number of packets lost and delay with different parameters of \(p\) and \(\mu\) for the network with 500 nodes. As can be seen from the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number of Packets** & & & & \\
**Lost/Delayed** & & & & \\ \hline \(\mu\) & \(p=0.4\) & \(p=0.5\) & \(p=0.6\) & \(p=0.7\) & \(p=0.8\) \\ \(\mu\) =0 & 194.5000/24.0000 & 166.7000/24.0000 & 133.8000/24.0000 & 98.5000/24.0000 & 63.5000/24.0000 \\ \(\mu\) =1 & 109.8000/36.3000 & 74.9000/33.6000 & 49.1000/30.9000 & 29.2000/30.3000 & 10.9000/27.9000 \\ \(\mu\) =2 & 62.0000/43.2000 & 38.9000/41.4000 & 18.7000/36.9000 & 6.9000/32.4000 & 34.0000/28.2000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The number of packets lost and network delay under different \(p\) and \(\mu\) for a network with 500 nodes. Figure 10: Comparisons of network delay under different \(p\) and \(\mu\) for a network with 100 nodes. Figure 9: Comparisons of the number of packets lost under different \(p\) and \(\mu\) for a network with 100 nodes. two network partition cases mentioned above, the circular tiers partition are shown in Tables 5 and 6 for networks with nodes 100 and 500, respectively. Comparing TSR-DARDA with IWTSR and GVWTSR under the abovementioned circular tiers partition for network with 100 nodes, we randomly selected two cases of \(p=0.6\) and \(p=0.8\) under different \(\mu\) to compare the number of packets lost and network delay. The comparison results are respectively shown in Tables 7 and 8. For the sake of intuition, Figure 13a,b respectively show the corresponding comparisons on the metrics of the number of packet lost and network delay by exploiting the different schemes of TSR-DARDA, IWTSR and GVWTSR when \(p=0.6\). As shown in Figure 13a, the proposed TSR-DARDA is superior in delay though the network reliability changes not obviously as shown in Figure 13b. When \(\mu=0\), the network delay is respectively improved by 22.22% and 30.00% compared with IWTSR and GVWTSR. It can be seen from the Figure 14 that it holds the same conclusion with Figure 13. This demonstrates that the proposed TSR-DARDA could effectively minimize data collection latency with the assurance of network reliability. number of packets lost and network delay by exploiting the different schemes of TSR-DARDA, IWTSR and GVWTSR. As shown in Figure 15a,b, the proposed TSR-DARDA is superior both in reliability and delay than the other two schemes when \(p=0.6\) for a half spherical network with 500 nodes, which further demonstrates that the proposed TSR-DARDA could effectively reduce data collection delay with satisfactory network reliability.