# Satellite Network Security Routing Technology Based on Deep Learning and Trust Management
## 4 Experimental Simulation and Analysis
### Model Complexity Analysis  
Time complexity analysis: To analyze the time complexity of the algorithm proposed in this paper, we break down the algorithm's operational steps and gradually analyze their  
Figure 8: The effect of a malicious attack on throughput. time complexities. As the D-S evidence theory's time consumption in handling communication data is fixed, its time complexity is \(O(1)\). The VAE network's time consumption in processing trust evidence data is also fixed, resulting in an \(O(1)\) time complexity during processing. In the context of the ant colony algorithm, let us discuss specific results based on the parameters established earlier in this paper. From the previous context, the number of satellite network nodes is \(N_{s}\), the number of ants is \(N\), and the number of iterations for the ant colony is \(e_{\max}\). Considering the worst-case scenario, given the number of \(N_{s}\) satellite network nodes, the lower limit for ants to find the destination node is NP steps. Meanwhile, when ants choose the next hop during their journey, there are \(N_{s}-1\) potential scenarios. This implies that the worst-case scenario involves \(N_{s}*(N_{s}-1)\) operations for a single ant's pathfinding, resulting in a time complexity of \(O(N_{s}^{2})\). Considering that the ant colony comprises \(N\) distinct ants, the time complexity for N ants' pathfinding is \(O(N_{s}^{2}*N)\). Moreover, since a single iteration through the ant colony's pathfinding process might not yield the optimal solution, continuous iterations are necessary to achieve the optimal solution. With \(e_{\max}\) iterations, the overall time complexity of the ant colony algorithm becomes \(O(e_{\max}*N_{s}^{2}*N)\). The above is an analysis of the time complexity of the algorithm proposed in this paper. Additionally, the additional time overhead introduced by the algorithm (TVAE) during practical operation is not significant and falls well within an acceptable timeframe. The specific reasons are as follows: The algorithm (TVAE) proposed in this paper operates in two distinct phases. The first phase involves satellite nodes assessing the security of their neighboring nodes. In the second phase, the satellite network executes the secure ant colony optimization algorithm. These two phases are executed separately, meaning that satellite nodes periodically evaluate the security of their neighboring nodes and store the security assessment factor \(m\) locally. When the secure ant colony algorithm is engaged in pathfinding, it solely requires the prestored local security assessment factor \(m\). Furthermore, this action of accessing the security assessment factor \(m\) is executed with exceptional speed, resulting in minimal time consumption during the secure ant colony algorithm's operation. Moreover, as depicted in Figure 6, when the number of malicious nodes is zero, the TVAE algorithm exhibits slightly higher average end-to-end latency compared to the ACO algorithm but lower than the SLT algorithm. Consequently, its runtime remains within acceptable limits. Further, according to [32], the time complexity of the ACO algorithm is also \(O(e_{\max}*N_{s}^{2}*N)\), which is the same as the time complexity of the TVAE algorithm proposed in this paper. However, because the TVAE algorithm introduces additional time overhead for looking up the security assessment factor \(m\) and combining it with pheromones compared to the ACO algorithm, the TVAE algorithm consumes slightly more time than the ACO algorithm. According to [20], the time complexity of TAODV is \(O(N_{s}^{2}+X)\). Here, \(N_{s}\) represents the number of satellite nodes, and \(X\) denotes the additional time overhead involved in trust calculations. The time complexity of this algorithm is lower than that of the TVAE algorithm, so the average end-to-end delay during the operation of the TVAE algorithm is slightly higher than that of TAODV. Finally, based on [18], the time complexity of the SLT algorithm is \(O(N_{s}^{2}*M)+O(N_{s}*M)\), which is equivalent to \(O(N_{s}^{2}*M)\).