# A Type of Low-Latency Data Gathering Method with Multi-Sink for Sensor Networks
## 5 Simulation Results
### Network Coverage and Redundancy  
To evaluate the performance of LDGM on reducing redundancy on coverage, experiments are carried out in the following cases. Network size is 100 m \(\times\) 100 m and the results of these experiments are shown in Figure 14.  
Case 1:Nodes are deployed randomly in the network without doing any optimization. Case 2:Nodes in the network carry out sleep scheduling strategy after being deployed. Case 3:Nodes in the network execute both of the sleep scheduling and the sensing radius adjustment algorithms. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline Network Size & \(M\times L\) & 100 \(\times\) 100–200 \(\times\) 200 & m\({}^{\text{2}}\) \\ Radius of DGU & \(R\) & 5–20 & m \\ Number of Nodes & \(N\) & 100–800 & \\ Number of Mobile Sinks & \(N\)s & 1–4 & \\ Weight Coefficient & \(a\) & 0.2 & \\ Weight Coefficient & \(\beta\) & 0.8 & \\ Adjustable Parameter & \(\lambda_{1}\) & \(2\times 10^{-6}\) & J/(m\({}^{\text{2}}\cdot\)s) \\ Sensing Rate & \(u_{k}\) & 0.05–0.5 & bit/(m\({}^{\text{2}}\cdot\)s) \\ Data Collection Rate of the Mobile Sink & \(v^{\prime}\) & 100 & Kbps \\ Moving Speed of the Mobile Sink & \(v\) & 5–20 & m/s \\ Initial Energy of Nodes & \(E_{0}\) & 2.0 & J \\ Threshold of the Residual Energy & \(E_{th}\) & 0.7 & J \\ Buffer Size of One Node & \(Cache\) & 4 & KB \\ Energy Consumption of Sending and Receiving Circuit & \(E_{cice}\) & 50 & n! \(\cdot\) b\({}^{-1}\) \\ Energy Consumption of Amplifier in Free-Space Model & \(\mu_{b}\) & 10 & p! \(\cdot\) (b/m\({}^{\text{2}}\))\({}^{-1}\) \\ Energy Consumption of Amplifier in Multi-Path Fading Model & \(\mu_{emp}\) & 0.0013 & p! \(\cdot\) (b/m\({}^{\text{4}}\))\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter values in simulation. Network coverage rate under different number of nodes is shown in Table 2. As mentioned in Section 4, LDGM does not change the network coverage rate. So when the number of nodes is fixed, the coverage rates in the above three cases are the same. Without loss of generality, the \"virtual grids\" described in Section 4.2 is used to calculate the network redundancy on coverage (defined as \(\eta\)). \(Q_{i}=1\) when \(g_{i}>1\), otherwise \(Q_{i}=0\). \[\eta=\left(m\times l\times\sum_{i=1}^{(\text{M}/m)\times(N/n)}Q_{i}\right)/(M \times L) \tag{30}\]  
In Figure 14, it is known that with the rise of the number of nodes, redundancy on coverage also increases. Moreover, the increasing rate is faster when the number of nodes increases from 100 to 400. At the same time, the coverage rate has also enhanced from 79.8% to 99.9%. This is the main reason why the redundancy increases sharply. However, after doing sleep scheduling as well as sensing radius adjustment, the redundancy on coverage decreases a lot (in some cases, more than 10%). Figure 15 shows the number of active nodes before and after sleep scheduling. According to the description in Section 4, it is known that the node whose sensing area is completely covered by other nodes will be in sleep mode without reducing the network coverage rate. Therefore, as shown in Figure 15, the number of active nodes is significantly decreased after sleep scheduling. Moreover, this number is nearly stable (no more than 260 in this experiment) when the number of nodes increases. It is necessary to mention that by carrying out a series of experiments, we found that the number of active nodes was not significantly reduced. This is because only the nodes near the boundary of the DGA would go into the sleeping mode during the sensing radius adjustment process. Thus in Figure 15, the two broken-lines with circular mark and diamond mark almost coincide.