# A Dynamic Service Reconfiguration Method for Satellite-Terrestrial Integrated Networks
## 3 Problem Descriptions
### Optimal Objective  
In order to obtain the optimal location and migration path of service migration, the selection of service target location and migration path optimization are modeled as an ILP model for network shortest path optimization. Considering that the user end-to-end delay in STINs is one of the most important performance indicators affecting the service experience, and the service migration will generate extra delay based on the original end-to-end delay, this needs to be considered as the migration cost. Therefore, the optimization objective of service migration and reconfiguration in STINs is defined as minimizing end-to-end delay and migration cost while ensuring service continuity. The following gives the formal definition of end-to-end delay and migration cost, as well as the optimization objectives and constraints of service migration and reconfiguration. \begin{table}
\begin{tabular}{c l} \hline \hline
**Notation** & **Definition** \\ \hline \(G_{\text{sn}}\Big{(}N_{sn}^{\text{tl,l}\text{o}\text{o}\text{o}},L_{\text{snr}},A_{ sn}^{\text{rr,tl}\text{l}}\Big{)}\) & Substrate ground node\(N_{sn}^{\text{lr}\text{l}\text{o}\text{o}}\), satellite node \(N_{sn}^{\text{l}\text{o}\text{o}}\) and substrate link \(L_{sn}\), and their corresponding attributes\(A_{sn}^{\text{rr}\text{l}\text{o}\text{o}}\) and \(A_{sn}^{\text{l}\text{o}\text{o}}\). \\ \hline \(G_{s}\Big{(}F_{s},L_{s},A_{s}^{f},A_{s}^{f}\Big{)}\) & Ordered VNF sequence \(F_{s}\), virtual links between VNF \(L_{s}\), the VNF attributes \(A_{s}^{\text{rr}\text{l}}\) and virtual link attributes \(A_{s}^{l}\). \\ \hline \(\text{Am}_{f,f_{s},f_{v}}\), \(\text{Dis}(f_{k},f_{v})\) & The amount of data \(\text{Am}_{f_{s},f_{v}}\), and physical distance transmitted \(\text{Dis}(f_{k},f_{v})\)between the service request node \(f_{k}\) and \(f_{v}\). \\ \hline \(d_{p}^{f_{k},f_{v}}(t)\), \(d_{td}^{f_{k},f_{v}}(t)\) & Processing delay \(d_{p}^{f_{k},f_{v}}(t)\) and propagation delay \(d_{td}^{f_{k},f_{v}}(t)\)between service request nodes \(f_{k}\) and \(f_{v}\). \\ \hline \(D(t),D_{p}(t),D_{tr}(t),D_{pr}(t)\) & End-to-end total delay \(D(t)\), propagation delay \(D_{p}(t)\), transmission delay \(D_{tr}(t)\), and processing delay \(D_{pr}(t)\). \\ \hline \(\text{Cpu}_{snr}^{i},\text{Cpu}_{s}^{f_{k}}\) & The CPU capacity \(\text{Cpu}_{sn}^{i}\) of the substrate node \(n_{i}\) and the CPU requirements \(\text{Cpu}_{s}^{f_{k}}\) of the service request node \(f_{k}\). \\ \hline \(\text{Bw}_{snr}^{i,j},\text{Bw}_{s}^{f_{v},f_{v}}\) & The bandwidth capacity \(\text{Bw}_{si}^{i,j}\) of the substrate link \(l_{sn}^{i,j}\) and the bandwidth requirements \(\text{Bw}_{s}^{f_{v},f_{v}}\) of the service request link \(l_{s}^{f_{v},f_{v}}\). \\ \hline \(M_{s_{s}}(n_{i},f_{k})\) & The deployment relationship between the substrate node \(n_{i}\) and the service request node \(f_{k}\), where \(1\) represents deployment, while \(0\) is not. \\ \hline \(M_{s_{u}}\Big{(}l_{sn}^{i,j}l_{s}^{f_{k},f_{v}}\Big{)}\) & The mapping relationship between the substrate link \(l_{sn}^{i,j}\) and the service request link \(l_{s}^{f_{v},f_{v}}\), where \(1\) represents mapped, while \(0\) is not. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main notation and definition. (2) Migration Cost  
The migration cost refers to extra operation cost and overhead caused by the migration in the course of the service migration of the STIN. Since our study concentrates on the service migration caused by the mobility of users and satellite nodes, only a single VNF is considered here. For each service migration, the migration cost mainly includes the cost of instantiating a new VNF at the migration node and the extra delay caused by migration path selection. The more routing nodes the service migration passes through and the more inadequate the available bandwidth of the path, the higher the migration cost and the longer the service interruption time caused by the migration, which is not conducive to the user service experience.