# A Hybrid Trust Model against Insider Packet Drop Attacks in Wireless Sensor Networks
## 5 Performance Evaluation
### Simulation Results
#### 5.2.2 Multiple Attackers  
We examine how each routing algorithm performs in the presence of multiple attackers. We assume that attackers are not colluding. To deploy multiple attackers in the network, we randomly choose 5, 8, and 10 relay nodes as attackers, which correspond to 5%, 10%, and 15% of total nodes, respectively. We use three attack rates of 30%, 60%, and 100%. For the trust threshold, we use 0.7. We compare all performance evaluation metrics recorded at the maximum simulation time (three hours). Since we thoroughly examined the detection speed of each routing in the single attacker case, we do not provide \(DCT\) here. In summary, the results in the multiple attacker case are similar with the results in the single attacker case. The results are as follows. First, we report \(DR\) and \(FAR\). As in the single attacker case shown in Figure 12, our hybrid trust model based on consecutive drops has a very high \(DR\) in all simulation setups. Meanwhile, the beta GRP has a low \(DR\) in the presence of multiple grayhole attackers with  
Figure 11: Energy efficiency es. (**a**) TH = 0.6. (**b**) TH = 0.7. (**c**) TH = 0.8.  
a 30% attack rate. Our hybrid trust model also has a slightly higher _FAR_ than the beta trust model (see Figure 13). However, as we will show regarding the _PDR_ below, this small FAR (due to nodes in bad links) does not degrade the packet delivery performance of our hybrid GRP but improves the packet delivery performance of our hybrid GRP. Second, we consider \(N_{A}\), \(N_{NA}\), and _PDR_. In summary, as shown in Figures 14-16, our hybrid GRP has the least \(N_{A}\) and \(N_{NA}\) and the highest _PDR_ among the three routing algorithms in the presence of multiple attackers. As shown in Figure 14, it is not surprising that as the number of attackers grows, \(N_{A}\) also grows. In the case of the pure GRP, we can see that multiple attackers (especially when they are blackhole attackers) drop a very large number of packets since the pure GRP does not have any defensive mechanism, such as a trust mechanism, against multiple attackers. Meanwhile, both our hybrid GRP and the beta GRP have much less \(N_{A}\) than the pure GRP since their trust mechanisms can defend against the multiple attackers. In addition, thanks to the trust evaluation scheme using consecutive drops, our hybrid GRP is able to further decrease \(N_{A}\) compared with the beta GRP. On the other hand, \(N_{NA}\) does not significantly change as the number of attackers grows as shown in Figure 15. As in the single attacker case, our hybrid GRP has the least \(N_{NA}\) because some normal nodes (non-attackers) with many transmission errors are detected (as false alarms) by our hybrid trust model. Finally, our hybrid GRP has the highest PDR, as shown in Figure 16. We clearly see that our hybrid GRP can deliver most packets to the BS very reliably, even in the presence of multiple attackers with various attack rates. It is particularly impressive that our hybrid GRP can deliver approximately 92% of data packets from source nodes to the BS successfully, even when 15% of nodes in the network are grayhole attackers that are randomly dropping 30% of packets, while the pure GRP and the beta GRP can deliver only 71% and 78% of data packets to the BS, respectively. In other words, when compared with the pure GRP, the beta GRP, which does not consider consecutive drops, can only improve _PDR_ by 7%, but our hybrid GRP, which considers consecutive drops, can significantly improve _PDR_ by 21%. Figure 12: Detection rate DR (sultiple attackers). (**a**) 3 Attackers (5%). (**b**) 5 Attackers (10%). (**c**) 8 Attackers (15%). Figure 13: False alarm rate FAR (multiple attackers). (**a**) Three attackers (5%). (**b**) Five attackers (10%). (**c**) Eight attackers (15%). Finally, we report \(e_{5}\). Our hybrid GRP has the least \(e_{5}\) among the three routing algorithms, as shown in Figure 17. As in the single attacker case, our hybrid GRP consumes the smallest amount of energy to deliver a data packet to the BS.