# A Novel Feeder Link Handover Strategy for Backhaul in LEO Satellite Networks
## 4 Problem Analysis and Strategy Design
### Problem Analysis  
As Equation (14) shows, the optimization comprises handover decision variables and traffic distribution variables. Thereby, the optimization is decomposed into the feeder link handover problem and maximum flow problem. The handover decision variables are determined by solving the handover problem. Then, based on the network topology and link constraints, the maximum flow problem is solved to determine the available backhaulcapacity in the satellite network. Note that the order of these two sub-problems cannot be reversed since the network topology depends on the handover results. The Ford-Fulkerson augmenting flow algorithm is widely used to find the maximum flow from a source to a sink in a directed graph. The classic algorithms include Edmonds-Karp and Dinic. These algorithms utilize the BFS-based method to find the augmenting paths to calculate the maximum flow. Although the solution for the maximum flow problem is mature, the maximum flow problem in this optimization problem is quite different. As shown in Equation (10), the outgoing traffic of \(S_{n}\) is composed of the traffic it transmits to neighboring satellites and the traffic to the GSs. The latter is related to the handover decision variables, so the handover strategy would affect the maximum flow calculation. Therefore, it is essential to explore the handover's effects on the maximum flow in the handover decisions. We propose an available backhaul capacity ratio to predict the available backhaul flow. Unlike the achievable transmission rate based on the channel quality represented in [23], the available backhaul capacity ratio is based on the combination of feeder link capacity and inter-satellite network capacity. The available feeder link capacity is expressed by the normalized channel capacity as follows:  
\[r_{n,m}^{g}(t)=\frac{C_{n,m}^{g}(t)}{C_{\max}^{g}} \tag{15}\]  
where \(C_{\max}^{g}\) is a constant representing the maximum channel capacity of feeder links. In addition, the available backhaul capacity also depends on the available satellite capacity, which is related to the traffic the satellite can receive from its neighboring nodes. The available satellite capacity is defined as the sum of the USLs' remaining capacity and the ISLs' remaining capacity. Since the traffic generally transmits through multiple satellites, the available capacity of these satellites should be updated after each handover decision. The calculation process of the available satellite capacity is described as follows: (1) At the beginning of each time slot \(t\), the available satellite capacity of each visible satellite is initialized to the sum capacity of its adjacent ISLs and USLs. (2) Then, the handover decisions are figured out in sequence. After each handover decision, the available satellite capacity of each visible satellite is updated based on the hops to the connecting satellite and the available feeder link capacity of the connecting satellite. Figure 2 illustrates the capacity update strategy. The GS \(G_{m}\) establishes a feeder link with the satellite \(S_{n}\), whose available link capacity is \(C^{g}n,m\). The available satellite capacity of the directed connected satellite \(S_{n}\) would decrease \(C^{g}n,m\). The available satellite capacity of the adjacent satellites of \(S_{n}\) would decrease \(\frac{C^{g}n,m}{4}\). Moreover, there are eight satellites that are two hops away from \(S_{n}\), so their available satellite capacity would decrease \(\frac{C^{g}n,m}{8}\). In the scenario, the available satellite capacity of a satellite that is \(h\) hops away from the access satellite would decrease \(\frac{C^{g}n,m}{4h}\). The shade of the satellite nodes shown in the figure represents the influence of the feeder link on the satellites' capacity.