## 3 Improved Multi Mobile Agent Data Fusion Scheme
### Link Stability in Mobile Environments  
In the previous section, the mobile network graph suggests the connectivity concept, which provides the next hop as the migration path of the mobile agent. The choice of the next hop is to find the path of 1- full time connectivity. While implementing this method, we do consider the possibility of setting up a new connection, that is, we consider the stability of newly built link. The sensor nodes in the sensor network model are mobile, composed of randomly moving sensor nodes and very frequent sink nodes. Due to the limited information dissemination, the communication links of special nodes change often. This change not only affects the ongoing node communication, but also hinders the communication of other nodes in the multi hop network. On the study of stable links in mobile environments, [PERSON] et al. introduced the empirical distribution of link lifetime and residual link lifetime [42]. Based on these results, they proposed two types of link stability criteria to classify stable links. Lim names continuous effects, but the shortest path of high density in wireless networks tend to be unstable. Other nodes in the communication area edge form the links, and a small movement of any node is enough to destroy the stability. In studying the link problem in a random mobility model, we assume that there is a link between two nodes at moment \(t_{0}\), and use the model to quantify the probability that the link is still valid after time \(t\). For independent link failures, we use probability to estimate the reliability of the path after the time \(t\). This forms the basis of a dynamic aggregation algorithm, so the network can choose more reliable links to form clusters. However, it may not be realistic to use the standard to select a routing path, because the model is still valid at moment \(t_{0+t}\), even when the link is experiencing one or more faults between \(t_{0}\) and time \(t_{0+t}\). The normal approach should be to find an alternative path when a link is in use, instead of waiting indefinitely for the link to return to normal. [PERSON] overcame this shortcoming by estimating the probability of a continuous link between two nodes in \(T_{p}\) in a period a, where \(T_{p}\) is based on the current activity of the node. Figure 9 shows the transmission area of node 1, which is based on the node as the center of the circle with radius R, where another node 2 moves from point A to point B along the line AB. Figure 8: Abstract interval estimation. Figure 9 shows the transmission area of node 1. Node 2 enters the region from the A point and leaves the area from the B point. The distance \(d_{link}\) of the node 2 in the transmission area of the node 1 is:  
\[d_{link}=|2R\cos(\alpha+\phi)|=2R|\cos(\alpha+\phi)| \tag{32}\]  
where \(R\) is the transmission radius of node 1, which is the angle between the horizontal direction and the direction of point A to node 1, and in turn the angle between the straight-line AB and the horizontal direction. Link life expectancy is:  
\[\overline{T_{link}}(v_{1})=\frac{R}{2b}(\int_{0}^{\pi}\lg\left|\frac{b+\sqrt{ b^{2}-v_{1}^{2}sin^{2}\phi}}{v_{1}+v_{1}\cos\phi}\right|d\phi) \tag{33}\]  
where \(v_{1}\) and \(b\) are the upper and lower bound of node motion rate. Figure 10 shows the relationship between the life expectancy and the speed of the sensor node link, where the speed of nodes in the network is between 0 and 40 m/s. We can see from the curve that the link node life expectancy decreases rapidly with the increase of speed. The time needed for the node to move at 5 m/s speed is two times longer than the time needed for the node to move at a speed of 25 m/s. At the same time, the life expectancy of the link is directly proportional to the node transmission radius R.  
Figure 10: Relationship between the expected life and velocity of the node link (\(a=0\) m/s, \(b=40\) m/s, \(R=250\) m). Figure 9: Simulation diagram of node moving radius.