# Modeling and Performance Analysis of Satellite Network Moving Target Defense System with Petri Nets
## 5 Model Simulation and Experiments  
In order to verify the impact of MTD technology on satellite network performance, and to explore the variation of average delay, average throughput, and on-star bandwidth resource utilization with different parameters, in this section, simulations are performed for proposed models and a large number of experiments are carried out for the performance analysis work. First, the two proposed SPN models are simulated separately based on PIPE (Platform Independent Petri Net Editor), one of the simulation tools for Petri Nets, which can draw Petri Net models, simulate the dynamic effects of Petri Nets, and can verify the correctness and usability of the models. The initial reference values of each model are set as shown in Table 6.  
Figures 10 and 11 show the reachable graphs obtained from the simulation of the two SPN models, respectively. By replacing each transition with its corresponding average firing time rate, the same isomorphic Markov Chain as in the theoretical analysis can be obtained, as shown in Figures 6 and 9, where \(S_{i}\) corresponds to \(M_{i}\), thus verifying the correctness of the theoretical inference results. Furthermore, based on the initial parameter values in Table 6, the simulation results of the steady-state probabilities of each marking are shown in Table 7. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Values** & **Parameters** & **Values** \\ \hline \(\lambda_{1}\) & 2 & \(\lambda_{5}\) & 2 \\ \(\lambda_{2}\) & 1 & \(\lambda_{6}\) & 0.6 \\ \(\lambda_{3}\) & 0.4 & \(\lambda_{7}\) & 0.8 \\ \(\lambda_{4}\) & 2 & \(\lambda_{8}\) & 0.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Initial parameters’ values. We use the data obtained from the above simulations and the formulas in Section 4 to calculate the average delay \(T\), average throughput \(O\), and bandwidth utilization \(U\) of the network under each scenario. The results are shown in Table 8. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Steady-State Probabilities** & **SPN Model 1** & **SPN Model 2** \\ \hline \(P(M_{0})\) & 0.12371 & 0.04878 \\ \(P(M_{1})\) & 0.30928 & 0.09756 \\ \(P(M_{2})\) & 0.20619 & 0.2439 \\ \(P(M_{3})\) & 0.15464 & 0.1626 \\ \(P(M_{4})\) & 0.20619 & 0.1626 \\ \(P(M_{5})\) & — & 0.12195 \\ \(P(M_{6})\) & — & 0.1626 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Steady-state probabilities of each marking. Figure 11: Reachability diagram of SPN model 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Indicators** & **SPN Model 1** & **SPN Model 2** \\ \hline \(T\) (Average Time Delay) & 12.250 & 14.417 \\ \(O\) (Average Throughput) & 0.124 & 0.098 \\ \(U\) (Utilization of Bandwidth) & 0.361 & 0.447 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of performance indicators. Figure 10: Reachability diagram of SPN model 1. We can see from Table 8 that the introduction of the MTD mechanism has led to a decline in the performance of the satellite network system, which is consistent with the theoretical reasoning results. More specifically, the average delay and bandwidth resource utilization have increased by 17% and 23%, respectively, while the average throughput of the system has decreased by about 20%. To illustrate the influence relationship of parameters on the selected three performance metrics more clearly and quantitatively, further experiments are conducted by varying values of parameters. **Experiment 1**. : _With the other parameters fixed, the changes of the average delay of the whole network with the increase of synchronization rate, hopping rate, and migration efficiency are investigated, respectively. The results are shown in Figure 12. The horizontal coordinate represents the change rate, and the vertical coordinate represents the average delay._  
**Experiment 2**. : _Under the condition of Experiment 1, the variation of the average throughput of the whole network is examined.