# A Matrix-Based Proactive Data Relay Algorithm for Large Distributed Sensor Networks
## 5 Model Maintenance Algorithm
### Updating the Data Distribution Matrix D
Then we compare the performance of CDU with the other three related algorithms mentioned above in default settings with the progress of simulations. After that we compare these algorithms while independently changing the following environmental factors: the size of the field to test if CDU is scalable; the ratio of moved sensors to test if CDU can adapt to dynamic networks; and the threshold of fused targets. Finally, since GRAB is one of the routing protocols, we compare the final energy distribution between CDU and that of GRAB. ### Different \(\beta\) and Different Length of Path

The value of \(\beta\) is a parameter used by CDU to balance forwarding data and minimizing energy consumption, which is defined in Equation (1). The path is a data structure used in CDU to store the sensor visited in each data. The length of path affects rich degree of the local matrix model. To understand how \(\beta\) and the length of path affect efficient data relay, we varied \(\beta\) from 0 to 4, and varied the length also from 1 to 4. Experimental results of a number of fused information, energy cost on communication, and efficiency are illustrated in Figure 3. As we can see, the higher the value of \(\beta\), the definition of useless data becomes more strict, and more data will be stopped from broadcasting especially those data with lower confidence or well known by neighbors. To some degree, it affects the number of fused information. As shown in Figure 3a,b, the number of fused information is proportional to \(\beta\) and the energy cost decreases as \(\beta\) increases. When \(\beta=0\), any data received will be broadcast and all the information can be fused. Figure 3c shows the efficiency for different \(\beta\). When \(\beta=2.0\), the efficiency reaches a high position. The balance of data relay and saving energy is good. When \(\beta>2.0\), the efficiency still keeps a high value. However, the information fused is much less. Figure 3: Experimental results with different \(\beta\) and different length of path. (**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. In the next simulations, the default value of \(\beta\) is 2.0. We notice that the performance of CDU is slightly affected by the length of the path. Regardless of the value of \(\beta\), when the length of path is longer than 1, it performs better than when the length is 1. While the other values work almost the same for sensors, broadcast decisions can only affect their neighbors, and neighbors' neighbors have higher probabilities to be neighbors than nodes far away with sensors moving around. However, the longer the path, the more storage space needed to store these matrices. Therefore in the following simulation, the default length of a path is 2. ### Different Algorithms

In this experiment, we compared the performance of our data relay algorithm CDU, with the Flooding algorithm, SBA and GRAB. 100 events about targets randomly occurred during 10 th-95 th time steps. The results are shown in Figure 4. At the first 10 time steps, no events exist, and no information is fused as Figure 4a shows. During this period, sensors in SBA broadcast hello messages to maintain 2-hop neighbor knowledge [16] and sensors in GRAB maintain their cost field. Therefore, in Figure 4b the cost of these two algorithms is more than 0. In the next 90 time steps, as time goes by, information is fused as more and more energy is consumed on data relay. In general, Flooding and SBA can fuse almost all the information. Correspondingly, their energy cost is higher than CDU because of flooding's no limitations on broadcast and SBA's purpose to cover all sensors with all data until it is possible to fuse them. GRAB fuse less information than CDU while consuming more for the long path to relay data to the fixed sink node. The efficiency of CDU is the highest of these algorithms for its effective constraining broadcast of the useless data.