## 2 Node Mobility Model  
Predicting the next-stage motion state of nodes based on historical data involves numerous challenges, such as instantaneous disturbances from ocean waves and abrupt shifts in long-term trends. Nevertheless, link estimation necessitates that node motion adheres to certain patterns rather than being entirely random. In the context of MASS communication scenarios, ships and vessels can acquire positions through various devices, such as the Global Navigation Satellite System, enabling effective prediction of network topology based on node movement patterns [22]. Because one of the most distinctive characteristics of wide-area maritime communication compared to terrestrial communication is sparsity, which means that the probability of a ship appearing per unit time and per unit area in the vast expanse of the ocean is relatively low, and because the traffic of ships at sea is relatively stable, this paper employs the Poisson Distribution to describe the distribution of maritime communication nodes [23; 24]. Consequently, the breakdown of communication links also occurs independently. The term R is used to denote the maximum radius of radio coverage for a mobile node. When one node falls within the transmission range of the other node, a two-way link is established between them. It should be noted that one-way communication is not taken into account. Within a given time interval, each node moves linearly at a constant speed and in a constant direction until the beginning of the next time interval. These time intervals are of equal length and are independently distributed, with a mean value of \(1/\lambda\). At the start of each time interval, the speed and direction of the node's movement are randomly and independently altered. As the speed is influenced by factors such as waves, winds, ship performance, and loading conditions, when there are numerous influencing factors and a sufficient number of ships, the speed distribution approximates a Gaussian distribution, according to the Central Limit Theorem. Gaussian distribution with a mean of \(\mu\) and a variance of \(\sigma^{2}\) is employed to describe the speed distribution of nodes over the entire time period. The direction distribution is uniformly distributed over \([0,2\pi]\) with a fluctuation range of less than \(\pi/2\). On an abstracted two-dimensional plane, the starting positions and destinations of the mobile nodes are random. Let \(\overrightarrow{s_{\mathrm{t}}}\) and \(\overrightarrow{s}(\mathrm{t})\) denote the displacement vector of the node in epoch i and the total time t, respectively, \(\overrightarrow{s}(\mathrm{t})=\sum_{i=1}^{N(\mathrm{t})}\overrightarrow{s _{\mathrm{i}}}\). Here, \(N(\mathrm{t})\) denotes the number of epochs simulated within time t. The magnitude equals the distance from \((X(\mathrm{t}_{0}),\ Y(\mathrm{t}_{0}))\) to \((X(\mathrm{t}_{0}+\mathrm{t}),\ Y(\mathrm{t}_{0}+\mathrm{t}))\) which can be resolved into displacement components in the X and Y directions. As the direction is uniformly distributed, the displacement components in the X and Y directions are symmetric and independent. By the Central Limit Theorem, when the direction is random, the displacement components in the X and Y directions approximate zero-mean Gaussian distributions with identical variances. Consequently, the magnitude conforms to a Rayleigh distribution with parameters of \(\alpha=\)\(\left(\frac{2\pi}{\lambda}\right)\times\left(\mu^{2}+\sigma^{2}\right)\). Therefore, the mobility characteristics of the node can be described by the parameter set \(\left\{\lambda,\ \mu,\ \sigma^{2}\right\}\).