## 5 Simulations, Results, and Discussions
### Attack Scenario  
In this scenario, we assume an excessive data rate is received as a result of an attack. In this scenario:  
* We fix the resources used in the LTE system with 3 PRB (\(C=3\)).
* We increase the average arrival rate of \(R_{R}\) to be (\(\lambda_{1}=3\)).
* We keep using the same average arrival rate of \(M_{R}\) (\(\lambda_{2}=2\)).
* We decrease the service rate of \(R_{R}\) to be (\(\mu_{1}=1\)).
* In addition, we decrease the service rate of \(M_{R}\) to be (\(\mu_{2}=1\)).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**State** & **Steady-State Probability** & **Probability Value** & **Phase** \\ \hline S(0,0) & \(\pi(0,0)\) & \(6/38=15.78\%\) & Initial \\ S(0,1) & \(\pi(0,1)\) & \(6/38=15.78\%\) & Authentic \\ S(0,2) & \(\pi(0,2)\) & \(3/38=7.9\%\) & Authentic \\ S(0,3) & \(\pi(0,3)\) & \(1/38=2.63\%\) & Suspicious \\ S(1,0) & \(\pi(1,0)\) & \(6/38=15.78\%\) & Authentic \\ S(1,1) & \(\pi(1,1)\) & \(6/38=15.78\%\) & Authentic \\ S(1,2) & \(\pi(1,2)\) & \(3/38=7.9\%\) & Suspicious \\ S(2,0) & \(\pi(2,0)\) & \(3/38=7.9\%\) & Authentic \\ S(2,1) & \(\pi(2,1)\) & \(3/38=7.9\%\) & Suspicious \\ S(3,0) & \(\pi(3,0)\) & \(1/38=2.63\%\) & Suspicious \\ \hline \hline \end{tabular}
\end{table}
Table 3: The probability values for each state S(_i,j_) in the Suspicious scenario, where “S(_i,j_)” represents different states, \(\pi(i,j)\) is the steady-state probability, “\(i\)” is the number of ongoing services for Read Requests (\(R_{R}\)), and “\(j\)” is the number of ongoing services for Modify Requests (\(M_{R}\)).  
Figure 9: The probability values for each state S(_i,j_) in the normal cycle, where “S(_i,j_)” represents different states, \(\pi(i,j)\) is the steady-state probability, “\(i\)” is the number of ongoing services for Read Requests (\(R_{R}\)), and “\(j\)” is the number of ongoing services for Modify Requests (\(M_{R}\)).  
The results of the attack scenario are shown in Table 4.  
The probability values for each state S(\(i\),\(j\)) in the attack scenario, where \"S(\(i\),\(j\))\" represents different states, \(\pi\)(\(i\),\(j\)) is the steady-state probability, \"\(i\)\" is the number of ongoing services for Read Requests (\(R_{R}\)), and \"\(j\)\" is the number of ongoing services for Modify Requests (\(M_{R}\)).  
Figure 11 shows the results and percentages of different phases the attack scenario.  
\begin{table}
\begin{tabular}{c c c c} \hline
**State** & **Steady-State Probability** & **Probability Value** & **Phase** \\ \hline S(0,0) & \(\pi\)(0,0) & \(6/236=2.54\%\) & Initial \\ S(0,1) & \(\pi\)(0,1) & \(12/236=5.08\%\) & Authentic \\ S(0,2) & \(\pi\)(0,2) & \(12/236=5.08\%\) & Authentic \\ S(0,3) & \(\pi\)(0,3) & \(8/236=3.4\%\) & Suspicious \\ S(1,0) & \(\pi\)(1,0) & \(18/236=7.62\%\) & Authentic \\ S(1,1) & \(\pi\)(1,1) & \(36/236=15.25\%\) & Authentic \\ S(1,2) & \(\pi\)(1,2) & \(36/236=15.25\%\) & Suspicious \\ S(2,0) & \(\pi\)(2,0) & \(27/236=11.44\%\) & Authentic \\ S(2,1) & \(\pi\)(2,1) & \(54/236=22.88\%\) & Suspicious \\ S(3,0) & \(\pi\)(3,0) & \(27/236=11.44\%\) & Suspicious \\ \hline \end{tabular}
\end{table}
Table 4: The probability values for each state S(\(i\),\(j\)) in the attack scenario, where “S(\(i\),\(j\))” represents different states, \(\pi\)(\(i\),\(j\)) is the steady-state probability, “\(i\)” is the number of ongoing services for Read Requests (\(R_{R}\)), and “\(j\)” is the number of ongoing services for Modify Requests (\(M_{R}\)).  
Figure 10: The probability values for each state S(\(i\),\(j\)) in the Suspicious scenario, where “S(\(i\),\(j\))” represents different states, \(\pi\)(\(i\),\(j\)) is the steady-state probability, “\(i\)” is the number of ongoing services for Read Requests (\(R_{R}\)), and “\(j\)” is the number of ongoing services for Modify Requests (\(M_{R}\)).  
* Initial phase probability = \(\pi_{(0,0)}=3\%\).
* Authentic phase probability = \(\pi_{(0,1)}+\pi_{(1,0)}+\pi_{(0,2)}+\pi_{(1,1)}+\pi_{(2,0)}=44\%\).
* Suspicious phase probability = \(\pi_{(0,3)}+\pi_{(1,2)}+\pi_{(2,1)}+\pi_{(3,0)}=53\%\).