## 5 Simulation and Analysis
### The Defensive Ability of an ACD Network
Hence when these two technologies are adopted in combination appropriately, they can protect the system with better defensive efficiency. To make the conclusion more obvious, we simulate the resource consumption of different systems when they are used to guarantee the same level of security. The attack time (i.e., \(MTTA\) or \(MTTR\)) is taken as the metric of security in this simulation. As mentioned above, the parametric configuration is simulated in two typical scenarios: ordinary and worse-case scenarios. In general, ordinary defenses guarantee a certain level of security with low consumption of resources (i.e., \(\omega<\mu/(\mu+1)\)). In worst-case scenarios, defenders pay more cost (i.e., \(\omega>\mu/(\mu+1)\)) for anti-attacking in exchange for stronger security due to the detected attacks. We calculate the number of reshuffled SCVs \(N_{\textit{reshuffled}}\) in each \(T_{P}\) time period as the metric of the defensive cost. \[N_{\textit{reshuffled}}=\omega\times L\times N\times\frac{T_{P}}{T}. \tag{36}\]  
\(N_{\textit{reshuffled}}\) is related to three values: the migrating period \(T\), migrating range \(\omega\), and the number \(N\) of online SCVs in each node. The \(T\) value can be selected according to the system requirement. For example, we set \(T\) as 12 h representing that VM migration is executed each half day. According to Equations (31) and (32), the migrating range \(\omega\) is obtained. \[\omega= \begin{cases}\frac{1-e^{-Tp_{A}}-LT/E[T_{A}]}{2-e^{-Tp_{A}}}&E[T_{A}] =MTTA>L*T/\mu,\\ \frac{1-e^{-Tp_{A}}+LT/E[T_{A}]}{2-e^{-Tp_{A}}}&E[T_{A}]=MTTR>L*T.\end{cases}  \tag{37}\]  
where \(E[T_{A}]\) is the expected time until the attacker moves to the next or previous \(L^{th}\) node. In the ordinary scenario, \(E[T_{A}]\) represents the value of \(MTTA\), and in the worst-case scenario, \(E[T_{A}]\) represents the value of \(MTTR\). After obtaining the analysis formula, upon their design requirements \(E[T_{A}]\), the system can flexibly adjust the \(\omega\) value indicating the different number of reshuffled SCVs. For example, in an ordinary scenario, the aim of attack time is set as \(2*10^{5}\) h; and in the worst-case scenario, the aim of driving the attacker back to the previous \(L_{th}\) node is set as \(4*10^{4}\) h. We select 6 systems as examples from Table 7, including \(Baseline_{4}(BL)\), (\(N=4\), \(M=3\)), (\(N=8\), \(M=5\)), (\(N=8\), \(M=6\)), (\(N=8\), \(M=7\)), and (\(N=8\), \(M=8\)). Then, according to the value from Table 7, \(N_{\textit{reshuffled}}\)s of different ACD system are obtained, as shown in Table 8 (\(T_{P}=100\) h, \(T=12\) h). \begin{table}
\begin{tabular}{c c c c c c c c}  & & \(BL\) & **(4,3)** & **(8,5)** & **(8,6)** & **(8,7)** & **(8,8)** \\ \hline \multirow{2}{*}{\(N_{\textit{reshuffled}}\)} & \(MTTA=2*10^{5}\) & 36.45 & 50.84 & 60.38 & 9.02 & 0 & 0 \\ \cline{2-9}  & \(MTTR=4*10^{4}\) & 38.76 & 61.08 & 81.29 & 30.49 & 19.37 & 18.07 \\ \end{tabular}
\end{table} 
Table 8: The number of reshuffled SCVs in each 100 h.  
In Table 8, \(BL\) represents the system which only adopts VM migration, which can be described as \((N=1,M=1)\). When \(MTTA=2*10^{5}\), the reshuffle number of SCVs in (8,7) and (8,8) systems are 0. Because, in such two scenarios, each ACD node presents a strong defensive ability. Even though only one SCV is migrated in each migration period, the whole ACD network guarantees enough security (i.e., a \(MTTA\) value much larger than \(2*10^{5}\)). Comparing (4,3) and \(BL\), (4,3) guarantees the same security level with a higher cost than \(BL\), although its ACD node is more secure. In the (4,3) scenario, the redundancy overhead brought by NVP technology is more evident than the security gain, so the defensive efficiency of the whole network is lower than the BL system that only adopts VM migration. However, as for (8,6), (8,7), and (8,8) systems, there is an apparent discount of overhead compared with the BL system.