## 3 Dynamic Traffic Grooming Based on Virtualization-Plane-Aided Optimization
### EOSNV-ETL-PE Algorithm  
Design path evaluation indicators in optical satellite networks evaluate node busyness and link load in the path by quantifying business traffic. Node betweenness \(C_{n}(t)\) represents the degree to which the node \(n\) acts as an intermediary in the satellite network, that is, the frequency with which it appears on the shortest path between other nodes. The shortest path between any two node pairs is calculated on the basis of the connection situation of the optical satellite network. The total number is denoted as \(g_{st}(t)\). The number of the shortest paths passing through node \(n\) as \(g^{n}_{st}(t)\), at time \(t\), the calculation formula for node betweenness \(C_{n}(t)\) is as Equation (2) [27]. \[C_{n}(t)=\sum_{s\
eq n\
eq t}\frac{g^{n}_{st}(t)}{g_{st}(t)} \tag{2}\]  
Figure 3: The correlation between the time points of request \(r\). The calculation mode of optical link cost is given. \(Q_{nj}(t)\) represents the generation value of optical link \(l_{nj}\) at time \(t\), which mainly consists of transmission delay and link congestion. Therefore, \(Q_{nj}(t)\) is expressed as Equation (3). \[Q_{nj}(t)=\frac{U_{nj}(t)}{U_{max}}+\frac{D_{nj}(t)}{D_{max}} \tag{3}\]  
where \(D_{max}\) and \(U_{max}\) indicate the maximum transmission delay and maximum link congestion of optical links in the entire network, respectively. \(U_{nj}(t)\) shows the wavelength usage of the optical link \(l_{nj}\) at time \(t\). \(D_{nj}(t)\) represents the transmission delay from satellite \(n\) to the next node \(j\) at time \(t\), mainly including the propagation delay of services through optical link \(l_{nj}\) and the processing delay of intermediate node forwarding, respectively represented by \(D_{nj}^{prop}(t)\) and \(D_{nj}^{proc}(t)\). \(D_{nj}(t)\) is shown in Equation (4). \[D_{nj}(t)=\ D_{nj}^{prop}(t)+D_{nj}^{proc}(t) \tag{4}\]  
As shown in Figure 4a, the busyness degree of satellite nodes can be divided into three types: high, medium, and low. A correction index is introduced to facilitate the traffic through satellite nodes reasonably. The correction index reflects the busyness degree of satellite nodes, which can increase the generation value of the path when passing through the node with a high busyness degree, make the traffic pass through the node with a low busy degree, and channel the traffic to the appropriate link. The correction index \(f_{nj}(t)\) of the link \(l_{nj}\) is defined as Equation (5). \[f_{nj}(t)= \begin{cases}\begin{array}{c}a,&0<C_{n}(t)<3\\ 1,&3\leq C_{n}(t)<6\\ 1+lg(C_{n}(t)-5),&C_{n}(t)\geq 6\end{array}\end{cases}  \tag{5}\]  
As shown in Figure 4b, when the node busyness \(C_{n}(t)\) of satellite node \(n\) at time \(t\) is \(\{C_{n}(t)|0<C_{n}(t)<3\}\), the node busyness is low, and the generation value of an optical link depends on the constant \(a(0<a<1)\) make corrections to divert traffic to links and nodes that are not busy; When the node busyness is \(\{C_{n}(t)|3\leq C_{n}(t)<6\}\), the node busyness is moderate, and the generation value of the optical link remains the same as before. When the node busyness degree is \(\{C_{n}(t)|C_{n}(t)\geq 6\}\), the node busyness degree is high, and the generation value of a link is related to the node busyness degree and is a monotonically increasing function. Finally, define the path evaluation index \(P_{assess}(t)\). \(P_{assess}(t)\) represents the total generation value of the optical path \(P(s,d)\) at time \(t\), and its value is expressed as Equation (6). \[P_{assess}(t)=\sum_{n\in P(s,d)}f_{nj}(t)Q_{nj}(t) \tag{6}\]  
Figure 4: The relationship between the node betweenness and correction index. (**a**) Node betweenness. (**b**) Correction index. When the request arrives, determine whether the \(s_{r}\) and \(d_{r}\) of request \(r\) exist in the virtual topology \(G^{V}\). If so, calculate \(K\) feasible paths between the \(s_{r}\) and \(d_{r}\) and figure the \(P_{assess}\) of these possible paths in \(G^{V}\).