# Teletraffic Analysis of DoS and Malware Cyber Attacks on P2P Networks under Exponential Assumptions
## 7 Numerical Results
### P2P System with a Malware Attack  
For these results, we used the following set of parameters: \(c\) = 0.002 (files/s), \(\lambda\) = 1 (arrival rate, users/s), \(\mu\) = 0.05 (files/s), \(\theta\) = 0.005 (leecher departures per sec), \(\gamma\) = 0.3 (seed departures per sec), \(\eta\) = 0.85, and \(K\) = 1/10 (chunk length), and now, we also use an initial number of infected seeds of \(N_{i}=10\). In this case, the evaluation time was significantly increased due to the increased complexity of the system, as shown in Table 5. The results shown in Figure 9 clearly show that the system also reaches a stable state after a transitory phase. This includes the number of infected peers. Indeed, for this initial number of malicious nodes sharing the malware in their chunks, not all of the system gets infected; it is much less than half of the leechers and half of the number of seeds. These are essential results because, using this model, the system administrator can estimate the number of malicious nodes attacking the system by only observing the resulting number of infected peers in time.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Average in 100,000 Iterations**} \\ \hline
**Leechers** & **Seeds** \\ \hline
100 \(\pm\) 15 & 16 \(\pm\) 3 \\ \hline \multicolumn{2}{c}{Approximate running time: 25 min} \\ \hline \hline \end{tabular}
\end{table}
Table 4: Averages and simulation time of the simple Markov chain for each type of peer.  
Figure 8: Evolution in time of one realization of the number of leechers and seeds in the system.  
To further study the system performance of the system under a malware attack, we vary many of the system parameters, such as \(\gamma\), \(\theta\), \(\lambda\), and \(N_{i}\) see as Figure 10. From these results, we can see that the value of \(\gamma\) has no important impact on the malware process since both healthy and infected peers vary in the same proportion for any value of the initial numerous malicious nodes. However, for the case of \(\theta\), we can see that for variations in the departure rate of leechers, the system becomes very sensitive to the number of initial malicious nodes, i.e., an increasing \(N_{i}\) entails a higher number of infected nodes, which did not occur when varying \(\gamma\). In the case of the arrival rate, we case see an expected increase in the number of infected peers as the leecher arrival rate increases. This occurs simply because there are more peers in the system sharing their resources, which makes it easier for nodes to get infected.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Average in 100,000 Iterations**} \\ \hline
**Healthy** & **Healthy** & **Infected** & **Infected** \\
**Leechers** & **Seeds** & **Leechers** & **Seeds** \\ \hline \(33\pm 8\) & \(2\pm 1\) & \(10\pm 5\) & \(2\pm 2\) \\ \hline \multicolumn{4}{c}{Approximate time: 37 min} \\ \hline \hline \end{tabular}
\end{table}
Table 5: Average results for each type of peer in the network together with the simulation time of the Markov chain with malicious nodes.  
Figure 9: Evaluation in time of one realization of the number of healthy and infected leechers and seeds.