## 5 Performance Evaluation
### Numerical Results
This means that the TD-PSO clustering protocol only involves CH and GW in the routing process, and the control overhead decrease is much less in the scheme with TD-PSO clustering protocol compared with schemes without TD-PSO clustering protocol. On the other hand, the proposed DLSMR  
Figure 11: Packet delivery ratio as a function of node speed. Figure 12: Routing delay as a function of node speed. routing protocol outperforms the MAODV protocol. Thus, the DLSMR+TD-PSO protocol with the RPGM model presented has the best performance which can improve connectivity and provide a stable connection compared to the other schemes regarding control overhead. In Figure 14, we demonstrate the PDR as a function of multicast group size to evaluate the scalability of the DLSMR+TD-PSO protocol. It can be observed that the PDR has a nearly constant value and is unaffected when the multicast group size increases. The reason is that the DLSMR+TD-PSO protocol is capable of delivering packets to multiple destinations at the same time, ensuring consistent PDR even as the size of the multicast group increases. The protocol under the RPGM model shows superior performance compared to the RWP model. This is primarily because nodes in RPGM move in groups, which results in a more predictable and less chaotic network. Consequently, this leads to fewer packet losses and a better PDR, despite an increase in destinations. Furthermore, the DLSMR+TD-PSO protocol accurately predicts the secure next node during the routing process, even in a dynamic network. TD-PSO also helps the optimization of the allocation of network resources, thereby ensuring efficient data delivery. As a result, we can conclude that the DLSMR+TD-PSO protocol with the RPGM model has strong scalability in terms of PDR. Then, we will turn our attention to look at the security performance. Figure 15 illustrates the comparison of the average packet loss ratio and number of packet losses in each session as a function of node speed as shown in Figure 15a and Figure 15b, respectively. Figure 14: PDR as a function of multicast group size. Figure 13: Control overhead as a function of node speed. According to Figure 15a, when the node's speed increases, the ratio of packet loss increases. Furthermore, also in Figure 15b, when the node's speed increases, the average number of packet losses increases. The reason is that, when the node's speed increases, the node's location frequently changes, thus causing packets to be transmitted directly to wormhole nodes. Furthermore, the proposed TD-PSO clustering protocol can reduce the number of links between nodes. Therefore, it can improve the packet loss ratio and the number of packet loss performances. On the other hand, the RPGM model instead of RWP can help the mitigation of the movement issue due to the collective and predictable movement of nodes resulting in fewer route changes and more stable connections, also reducing the likelihood of packet loss. Thus, the proposed DLSMR+TD-PSO protocol with the RPGM model is proven to be secure from a network security perspective. Figure 16 shows the impact of the node density of the proposed DLSMR+TD-PSO protocol on the network metrics. We set the minimum number of nodes at 30, 50, and the maximum of 100. As can be seen in Figure 16a, the PDR decreases when the node speed increases, while the PDR slightly increases when the number of nodes increases. This behavior is influenced by the more predictable movement patterns in the RPGM model, which leads to less frequent route changes and fewer packet losses. Furthermore, we evaluate the routing delay as a function of node speed with different numbers of nodes, as shown in Figure 16b. It is observed that, when the number of nodes and speed of nodes increases, the routing delay increases slightly but not significantly. This means that when the number of nodes and node speed increases, the number of hops also increases, which can cause the routing process to take longer.