## 3 Satellite Network Model  
The mapping method of virtual networks oriented towards the ground model is inadequate for dynamic and changeable satellite networks. For example, the dynamic movement of satellite nodes will lead to service interruption, causing the established satellite network links to squander resources and increase waiting time. Therefore, establishing the network model according to the particularity of satellite network is of great significance which support virtual network mapping method research. In this paper, the satellite network model is established for the dynamic and changeable special satellite network environment, and \(G^{S}=\{N^{S},L^{S},W^{S}_{N},W^{S}_{L}\}\) stands for satellite physical network which is the directed graph, where \(N^{S}\) stands for the satellite network nodes, \(L^{S}\) represents the satellite network link set, the node attribute set \(W^{S}_{N}\) represents the satellite network, which includes the available CPU resources \(CPU(n^{s})\) and the delay \(Delay(n^{s})\), and \(W^{S}_{L}\) represents the satellite network link attribute set, which includes bandwidth remaining resources \(BW(l^{s})\) and transmission delay of links \(Delay(l^{s})\). In this paper, virtual network \(G^{VR}=\{N^{VR},L^{VR},C^{V}_{NR},C^{VR}_{L}\}\) will be established for virtual network requests, where \(N^{VR}\) stands for the virtual node set, \(C^{VR}_{N}\) represents the constraint of \(N^{VR}\), that is, the demand of satellite nodes, \(L^{VR}\) stands for virtual link set, and \(C^{VR}_{L}\) represents the constraint of \(L^{VR}\), that is, the demand of inter-satellite links. We mainly investigate the resource allocation of satellite network under cloud network convergence. To achieve this, in order to optimize resource allocation, we introduce VNE. The node mapping result is shown as the following formula:  
\[\varphi_{ij}=\left\{ \begin{array}{l}1,\ if\ n_{i}^{vr}\to n_{j}^{s}\\ 0,\ else\end{array} \right.. \tag{1}\]  
The mapping process of virtual nodes can be expressed as \(n_{i}^{vr}\to n_{j}^{s}\), where \(n_{i}^{vr}\) represents the virtual node that need to be mapped and \(n_{j}^{s}\) represents the physical node. The CPU resources constraint are defined as the following formula:  
\[\mathbb{C}^{CPU}_{n_{i}^{vr}\to n_{j}^{s}}:CPU(n_{j}^{s})\geq CPU(n_{i}^{vr}). \tag{2}\]  
The CPU resources of \(n_{j}^{s}\) must meet the \(n_{i}^{vr}\) resource requirement, which is an essential condition for successful mapping. In addition, during the virtual node mapping process, a physical node can only host one virtual node at most, so the following calculation should be satisfied:  
\[\sum_{n_{i}^{vr}\in N^{VR},n_{j}^{s}}\varphi_{ij}=1. \tag{3}\]After the node mapping is completed, it is necessary to map the virtual link to the physical link. The link mapping process is shown in the following formula:  
\[\phi_{ij}=\left\{ \begin{array}{l}1,\ if\ l_{i}^{vr}\to l_{j}^{s}\\ 0,\ else\end{array} \right.. \tag{4}\]  
Similar to \(n_{i}^{vr}\to n_{j}^{s}\), the expression of \(l_{i}^{vr}\to l_{j}^{s}\) is used to describe virtual link mapping, where \(l_{i}^{vr}\) represents the virtual link and \(l_{j}^{s}\) represents the physical link. Whether \(l_{i}^{vr}\) can successfully map to \(l_{j}^{s}\) depends on whether the bandwidth resources meet the conditions. The judgment conditions are as follows:  
\[\mathbb{C}_{l_{i}^{vr}\to l_{j}^{s}}^{BW}:BW(l_{j}^{s})\geq BW(l_{i}^{vr}). \tag{5}\]  
Besides, the link mapping should meet the following constraints:  
\[\sum_{l_{i}^{vr}\in LV^{\prime}R_{j}^{s}}\phi_{ij}\geq 1. \tag{6}\]  
In the VNE problem, a virtual link can be mapped to multiple physical links, and the mapping to multiple physical links is called path splitting.