# A Type of Low-Latency Data Gathering Method with Multi-Sink for Sensor Networks
## 5 Simulation Results
### Time Delay in Data Gathering  
As mentioned above, in LDGM each Sink is required to move to each traverse point once and only once during one round of data gathering period. Thus for any \(TP_{j}\), the maximum time interval (defined as \(TP_{j}(\Delta t_{max})\)) between two consecutive visits is,  
\[TP_{j}\left(\Delta t_{\max}\right)=MAX\left(t_{i+1}^{j}-t_{i}^{j}\left|i=1,2,...,k-1\right.\right) \tag{31}\]  
\(t_{i}^{j}\) refers to the time when _Sink(i)_ moves to \(TP_{j}\) while \(k\) is the number of Sinks. Therefore, the maximum time delay on data gathering could be defined as,  
\[\Delta T_{\max}=MAX\left(TP_{j}\left(\Delta t_{\max}\right)\left|j=1,2,...,Num \left(R\right)\right.\right) \tag{32}\]  
Similarly, average time delay on data collection is defined as,  
\[\Delta T_{avg}=\sum_{j=1}^{Num\left(R\right)}TP_{j}\left(\Delta t_{\max} \right)/Num\left(R\right) \tag{33}\]  
Experiment results of \(\Delta T_{max}\) and \(\Delta T_{avg}\) with different \(R\) and \(N_{s}\) in a 100 m \(\times\) 100 m network are shown in Figures 20 and 21. When \(N_{s}\) is fixed, the value of \(\Delta T_{max}\) decreases with the increase of \(R\). This is because when \(R\) is larger, there will be fewer DGAs in the network and the number of TP will decrease. Thus, the total time spent by delaying at these traverse points also decreases time spent during data gathering.  
On the other hand, when the value of \(R\) is fixed, time delay in a multi-Sink based network is much smaller than the network that has only one Sink. However, decrease in time delay is not obvious when the number of Sinks increases from three to four. Because when there are more Sinks moving in the network, the possibility that different Sinks visit the same TP at the same time or during a short time interval increases. That is, the value of \(TP_{j}(\Delta t_{max})\) increases according to Formula (31). As a result, \(\Delta T_{max}\) is stable.  
When the value of \(R\) is larger, there will be less traverse points in the network. Thus, the effect on reducing time delay is not very obvious no matter how many Sinks are moving in the network. As shown in Figure 20, when \(R\) is 20 m, the maximum time delays on data gathering with different Sinks are nearly the same. Therefore, the time efficiency of LDGM will be better when the network size is large and \(R\) is small.  
Figure 20: Maximum time delay on data gathering (100 m \(\times\) 100 m, 200 nodes).  
Similarly, the average time delay in a multi-Sink based network is obviously shorter than that in the single Sink based one, as shown in Figure 23. The value of it decreases slowly with the increase of \(R\).  
Experiment results about the maximum and average time delay with different moving speeds of Sinks are shown in Figures 24 and 25 respectively. When the value of \(v\) increases, the delay decreases in LDGM. However, this decreasing rate becomes slower and slower when the speed of Sink further increases. This is because the length of time the mobile Sink is staying at each TP is a constant value in LDGM. In this case, the increase of speed could only shorten the time spent on moving. In addition, no matter how fast the moving speed is, time efficiency of the multi-Sink based network is always higher than that of single Sink based network.  
Figure 23: Average time delay on data gathering (200 m \(\times\) 200 m, 500 nodes).  
Figure 24: Maximum time delay with different moving speeds of Sinks.