# A Matrix-Based Proactive Data Relay Algorithm for Large Distributed Sensor Networks
## 5 Model Maintenance Algorithm
### Updating the Data Distribution Matrix D
### Impact of Environmental Settings

#### 6.3.1 Network Size

In this experiment, we studied how CDU scales to large networks for data relay. The number of sensors in the system are 100, 500 and 1000 while the side length of the squares are 250, 600, 850 to guarantee the same node density. The number of events is kept at 100. Figure 5 shows that regardless of the network size, CDU can well balance the broadcasting and saving energy, and its efficiency is always about 2 times as efficiency of the other algorithms. Figure 4: Experimental results for 500 sensors using different algorithms to fuse revelent data. (**a**) introduces the comparisons of the number of fused information. (**b**) introduces the comparisons of the energy cost on communication. (**c**) introduces the comparisons of the fusion efficiency. #### 6.3.2 The Ratio of Moved Sensors

In this experiment, we evaluated the performance of these four algorithm to investigate if CDU can adapt to the dynamic network. We varied the move ratio of sensors at each time step from 0 to 0.22. In SBA, sensors update two hop neighbor knowledge by periodic hello messages. For GRAB, sink nodes periodically broadcast advertisement messages, which help sensors update their cost field. However, in CDU, there is no periodic hello messages. A sensor will not broadcast hello message until it moves. Figure 6 shows that the performance of these four algorithms is unaffected by the variation of move ratio and CDU is always way ahead in efficiency. #### 6.3.3 Threshold

We first varied the minifusedNum from 3 to 8, while using a fixed 0.75 minifusedConfidence. Then, we varied the minifusedConfidence from 0.4 to 0.85 while using a fixed 6 minifusedNum threshold. Figure 7 shows that when the threshold of minifusedNum or minifusedConfidence is higher, less information can be fused in the same 100 time steps. However, more energy consumption and lower efficiency on data relay for a sensor is needed to aggregate more data to reach the number and confidence threshold. Figure 7c,f show CDU has the highest efficiency of all these algorithms. Figure 5: Experimental results with different network size using different algorithms. (**a**) introduces the comparisons of the number of fused information; (**b**) introduces the comparisons of the energy cost on communication; (**c**) introduces the comparisons of the fusion efficiency. Figure 6: Experimental results with different move ratio using different algorithms. (**a**) introduces the comparisons of the number of fused information; (**b**) introduces the comparisons of the energy cost on communication; (**c**) introduces the comparisons of the fusion efficiency. ### Energy Distribution

In this subsection, we compare the energy distribution between CDU and SBA, and the routing protocol GRAB. Figure 8 shows the final energy distribution after relaying data for 100 and 200 events while the network size is 500. As shown in these figures, the three algorithms all consume more energy in Figure 8b, where more events happened than in Figure 8a. In SBA and CDU, energy consumption is better distributed than in GRAB. For GRAB, data should be relayed to sink node to fuse and sink nodes, and nodes near sink nodes distinctly consume more energy. However, in SBA, sensors try to cover every node with data until fused, and the energy is much more than CDU. Figure 7: Experimental results for different threshold using different algorithms. (**a**) introduces the comparisons of the number of fused information with minifusedNum from 3 to 8; (**b**) introduces the comparisons of the energy cost on communication with minifusedNum from 3 to 8; (**c**) introduces the comparisons of the fusion efficiency with minifusedNum from 3 to 8; (**d**) introduces the comparisons of the number of fused information with minifusedNum from 0.4 to 0.85; (**e**) introduces the comparisons of the energy cost on communication with minifusedNum from 0.4 to 0.85; (**f**) introduces the comparisons of the fusion efficiency with minifusedNum from 0.4 to 0.85.