# A Vulnerability Assessment Approach for Transportation Networks Subjected to Cyber-Physical Attacks
## 4 Case Study of a Cyber-Physical Transportation Network
### Case Study Analysis and Results  
This section provides the results of the analysis obtained by performing five thousand Monte Carlo simulations using uniformly distributed random number generators and considering mean values as the basic statistical measure [88]. Specifically, based on the constructed BN attack graph (i.e., see example of Figure 5) and the assigned values presented in Tables 4 and 5, Monte Carlo simulations were performed to calculate the PI (i.e., see Equation (2)) and calculate the total probability score of a successful attack for every node. Table 7 presents the results of the overall process and the total probability score for every node (see Equation (1)) in a descending probability-based ranking. The probabilistic ranking indicates which nodes are most vulnerable, an assessment based on the considered level of attacker characteristics and the level of control barriers. Table 7 demonstrates that the existence of higher-level control barriers, both in the physical and cyber space, results in a low probability of success (i.e., see Node 6, \(\text{P}(6)=0.06\)). However, deficient control barriers in the physical and cyber space result in a high probability of success (i.e., see Node 8, \(\text{P}(8)=0.60\)). Indeed, the significant statistical relationship between the level of control barriers and the probability of a node being successfully attacked can be indicated using the correlation coefficient \(r\) (i.e., Pearson correlation coefficient [89]). Specifically, \(r\) is equal to \(-0.63\) when we consider nodes that integrate at least one high-level control barrier, either in physical or cyber space, indicating that nodes with a higher level of protection are probabilistically less vulnerable. A sensitivity analysis was undertaken to demonstrate the importance of level of attacker characteristics in the vulnerability assessment approach, as shown in Table 8. We considered Node 8, which was probabilistically the most vulnerable node, according to Table 7. Specifically, all the inputs of the level of attacker characteristics remain constant, excluding the level of _knowledge_ (i.e., \(X_{\text{KN}}\), set as low level (1) in contrast to high level (2-3) in our case study). The attacker profile has a low level of _knowledge_ (i.e., \(X_{\text{KN}}\) is equal \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Node**} & \multicolumn{1}{c}{**Volnerability State**} & \multicolumn{1}{c}{**PI/Probability Range**} & \multicolumn{1}{c}{**Total Probability Score Based**} \\  & & & **on Equation (1)** \\ \hline \multirow{4}{*}{4} & A & \(\text{PI}_{\text{A}}=1/\text{P}(\text{A})=0.50\) & \\ \cline{2-3}  & C & \(\text{PIC}_{\text{C}}=1/\text{P}(\text{C})=0.50\) & \\ \cline{2-3}  & D & \(2\leq\text{PID}_{\text{D}}\leq 3/\text{P}(\text{D})=0.875\) & \(=0.5*0.5*0.875=0.22\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Example of calculation of PI and total probability score, for Node 4. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Node**} & \multicolumn{1}{c}{**Probability of Successful Attack for Node \(i\), P(i)**} \\ \hline
8 & \(\text{P}(8)=0.60\) \\
1 & \(\text{P}(1)=0.57\) \\
7 & \(\text{P}(7)=0.27\) \\
3 & \(\text{P}(3)=0.22\) \\
4 & \(\text{P}(4)=0.22\) \\
2 & \(\text{P}(2)=0.21\) \\
5 & \(\text{P}(5)=0.12\) \\
6 & \(\text{P}(6)=0.06\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Case study probability-based ranking of successful attack in a descending order. to one), which could potentially indicate a _basic user_. Results taken from performed Monte Carlo simulations indicated a decrease in 50.0% (i.e., from 0.60 to 0.30) in the total probability score when the attacker had a low level of knowledge. These results indicate the importance of including attacker profile, but also of making accurate assessments of potential attackers' knowledge.