## 2 System Model
### Position and Mobility Description  
As illustrated in Figure 2, BS1 and BS2 are denoted as the BS to which an AUV is currently connected and the new BS to which the AUV will move through handover (i.e., the target BS), respectively. The communication ranges of the two BSs are overlapped, leading to handover execution when the AUV moves through the overlapping region. The positions and motion of the two BSs are modeled as follows:  
* The positions of BS1 and BS2 are represented in an x-y-z coordinate system. As shown in Figure 2, their initial positions are expressed as \((r,-r,0)\) and \((r+L,-r,0)\), respectively.
* The positions of the BSs vary over time along the x-, y-, and z-axes due to BS motion.
* The BS has a buoy-shaped structure and is moored to the seafloor with the help of the mooring line.
* The two BSs are separated by the distance of \(L\) on the water surface, and the width of the overlapping region (i.e., \(2r-L\)) is determined based on the overlapping rate (\(\delta\)). As illustrated in Figure 2, \(\delta\) is defined as \(\frac{2r-L}{2r}\). According to the value of \(L\), \(\delta\) is given as \(\delta=\left\{\begin{array}{ll}0,&L=2r\\ 0.5,&L=r\end{array}\right.\). For instance, \(\delta=0\) implies that the two cells are not overlapped at all. In this paper, while the overlapping rate is simply determined by the width of the overlapping region, it is possible to define the overlapping rate more precisely by considering the overlapping region in three dimensions.
* The AUV generally moves underwater with respect to a scheduled path plan with a consistent direction and speed [45]. By considering these characteristics of the AUV, we can define \(T_{O}\), i.e., the time the AUV spends in the overlapping region. By using the moving speed of the AUV (i.e., \(v_{A}\)) and the width of the overlapping region (i.e., \(2r-L\)), \(T_{O}\) can be defined as \(\frac{2r-L}{v_{A}}=\frac{2r\delta}{v_{A}}\). This parameter can be utilized to determine the handover expiration time concerning AUV movement.
* The location and mobility of an AUV are modeled as follows:  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Parameters** & **Description** \\ \hline \(d_{A}\) & The operational depth of an AUV \\ \(v_{A}\) & The moving speed of an AUV \\ \(R\) & The communication range \\ \(r\) & The network radius of a BS on the water surface \\ \(L\) & The straight-line distance between the two BSs on the water surface \\ \(\delta\) & The rate of the overlapping region between two BSs \\ \(T_{O}\) & The time during which an AUV stays in the overlapping region \\ \(D_{BA}\) & The distance between a BS and an AUV \\ \hline \hline \end{tabular}
\end{table}
Table 1: The definitions of parameters to describe the system model.  
* The position of an AUV is also expressed in an x-y-z coordinate system. As depicted in Figure 2, its initial position is given as \((0,-r,-d_{A})\), which is at the network edge of BS1.
* The AUV is programmed to move from the network edge of BS1 to that of BS2 (in the positive x-axis direction) at a constant speed. In the system model, the AUV is considered to move along a planned one-way path from the edge of BS1 to the edge of BS2.