# Delay-Sensitive Service Provisioning in Software-Defined Low-Earth-Orbit Satellite Networks
## 6 Experimental Result
### Comparison Algorithm  
The benchmark algorithm used in this paper is designed based on the DE algorithm, which is an efficient and general problem solving framework. In this paper, we optimize the design of parameters and strategy selection based on the original DE algorithm to better adapt to the problem in this paper. The DE-based algorithm searches the solution space extensively according to certain strategies, thereby obtaining a good solution. Therefore, we use the DE based algorithm to solve the routing optimization problem and use it as a benchmark algorithm. Based on the original DE algorithm framework, there have been many improved algorithms, which adopt different parameter control and strategy selection methods. In this paper, we adopt the linear population size reduction--success history-based adaptive DE (LSHADE) algorithm [29] to solve the problem. To adapt to our problem, we build a population model and design a fitness function.  
In the path-based ILP formulation, the routing of a flow \(f_{j}\) in a time slot \(i\) can be represented as \(z^{j_{i}}=\{0,1,2,\cdots,|P_{j_{i}}|\}\). \(z^{j_{j}}\) represents that flow \(f_{j}\) chooses the \(z^{j_{i}j}\)-th path for transmission in time slot \(\mathcal{T}_{i}\). During the topology cycle of the network, the routing of flow \(f_{j}\) can be represented by a vector \(Z^{j}=(z^{j_{1},z^{j_{2}},\cdots,z^{j_{i}|\mathcal{T}|}})\), which contains the routing paths for flow \(f_{j}\) in each time slot. The dimension of the vector is equal to the total number of time slots of the satellite network, denoted as \(|\mathcal{T}|\). Therefore, a population individual can be represented by the vector \(POP=(Z^{1},Z^{2},\cdots,Z^{|\mathcal{F}|})\), which contains the routing decisions for each flow on the given path in each time slot. Hence, the problem dimension is \(D=|\mathcal{T}||F|\). The fitness function used in the LSHADE algorithm can be nonlinear, so we can directly use the optimization objective without linearization. Meanwhile, in the LSHADE algorithm, the mutation process can generate decimal numbers. To ensure that the variables \(z^{j_{i}}\) are integers, we round off the decimal results generated during the mutation operation.  
The LCP algorithm and the LSHADE algorithm proposed in this paper are two approaches to solving the ILP formulation. These algorithms aim to efficiently obtain approximate optimal solutions. We convert the solutions obtained by these three algorithms for the same problem into routing schemes for each individual TS flow. These routing schemes are then tested on the satellite experiment testbed to compare the performance of different algorithms.  
For the other two comparison algorithm, TGM [30] focuses on finding the shortest path in each time slot as the routing result, while discrete-time dynamic virtual topology routing (DT-DVTR) [17] aims to find the path with the fewest path handovers in each time slot.  
\begin{table}
\begin{tabular}{l l} \hline
**Software and Hardware** & **Configuration Information** \\ \hline OS & Ubuntu 20.04.4 LTS \\ CPU & Intel(R) Xeon(R) Gold 6133 CPU @ 2.50 GHz \\ OpenVSwitch & 2.16.0+ \\ DPDK & 20.11.3 \\ ONOS & 2.8.0 \\ Redis & 6.2.6 \\ Docker & 23.0.3 \\ \hline \end{tabular}
\end{table}
Table 2: Basic configuration.