## 6 Simulation Evaluation of the Dynamic VWSN
### Adaptivity of the VWSN Topology against Targeted Attacks  
In this section, we evaluate the adaptivity of the VWSN topology against targeted attacks. The simulation time is 10,000 s; after 5000 s have elapsed, one node fails for every 10 s until 30 nodes have failed. Nodes fail in descending order of initial degree in the VWSN topology, without adjusting degrees after each failure and choosing arbitrarily among nodes of equal degree. The values of \(Rrecovery\), average \(Trecovery\) and average \(CPrecovery\) for each method are summarized in Table 6. The number of trials in which the virtual or physical topology becomes fragmented is \begin{table}
\begin{tabular}{l c c c c c} \hline  & \(phy\) & \(phyFrag\) & \(L0 Frag\) & \(L1 Frag\) & \(L2 Frag\) \\ \hline BICM(hh,HH) & \(T1\) & 19 & 17 & 1 & 0 \\ BICM(ll,LL) & \(T1\) & 19 & 17 & 0 & 0 \\ Bio-inspired & \(T1\) & 19 & 46 & 26 & \\ BICM(hh,HH) & \(T2\) & 6 & 18 & 5 & 0 \\ BICM(ll,LL) & \(T2\) & 6 & 18 & 5 & 0 \\ Bio-inspired & \(T2\) & 6 & 62 & 63 & \\ \hline \end{tabular}
\end{table} 
Table 4: Number of trials in which the virtual or physical topology fragments when nodes are removed by random failure. \begin{table}
\begin{tabular}{l l c c c c c c} \hline  & \(phy\) & \(T0 UF\) & \(T1 UF\) & \(L0 Loop\) & \(L1 Loop\) & \(LLLost\) & \(TTL\) & \(ConT^{N}Up\) \\ \hline BICM(hh,HH) & \(T1\) & 0 & 5 & 2 & 0 & 0 & 0 & 2 \\ BICM(ll,LL) & \(T1\) & 0 & 4 & 3 & 0 & 0 & 0 & 2 \\ Bio-inspired & \(T1\) & 11 & 99 & 2 & 0 & 0 & 0 & 2 \\ BICM(hh,HH) & \(T2\) & 0 & 14 & 0 & 0 & 0 & 0 & 1 \\ BICM(ll,LL) & \(T2\) & 3 & 13 & 1 & 0 & 0 & 0 & 2 \\ Bio-inspired & \(T2\) & 10 & 98 & 0 & 0 & 2 & 2 & 7 \\ \hline \end{tabular}
\end{table} 
Table 5: Number of trials in which the data delivery ratio fails to recover due to the inconsistency in tables when nodes are removed by random failure. shown in Table 7, and the number of trials in which the data delivery ratio fails to recover due to the inconsistency in the tables is shown in Table 8. As elsewhere, _phy_ indicates the physical topology. The blanks in Table 6 indicate that the value could not be calculated because the data delivery ratio did not recover. In physical topology _T2_, \(R_{recovery}\) is quite low when using BICM(hh,HH), but \(R_{recovery}\) remains high when using BICM(ll,LL). When using BICM(hh,HH), it is easy to divide a module, and so, the route discovery process must be carried out frequently because high-degree nodes are selected to be connected nodes. This means that many connected nodes fail when nodes are removed by targeted attack. However, the value of \(R_{recovery}\) is zero in BICM(ll,LL) for \(T1\). This is because a zeroth-tier topology in a first-tier module becomes fragmented in all trials, as shown in Table 7. In \(T1\), there is a first-tier module whose central area is densely connected. Because the degree of a node in this area is high, this first-tier module becomes fragmented when all of the nodes in the area fail. From the above, although adaptivity against targeted attack is strongly dependent on physical topology and the method of modular division, the adaptivity of the VWSN constructed by BICM(ll,LL) is the highest in many cases. \begin{table}
\begin{tabular}{l l l l l} \hline  & _phy_ & \(R_{recovery}\) & **Average \(T_{recovery}\)** & **Average \(CP_{recovery}\)** \\ \hline BICM(hh,HH) & \(T1\) & 0.16 & 793.43 & \(16.66\times 10^{4}\) \\ BICM(ll,LL) & \(T1\) & 0.00 & & \\ Bio-inspired & \(T1\) & 0.00 & & \\ BICM(hh,HH) & \(T2\) & 0.07 & 791.87 & \(24.13\times 10^{4}\) \\ BICM(ll,LL) & \(T2\) & 0.83 & 797.07 & \(18.17\times 10^{4}\) \\ Bio-inspired & \(T2\) & 0.00 & & \\ \hline \end{tabular}
\end{table} 
Table 6: The rate of recovering the data delivery ratio \((R_{recovery})\), the average time needed for data delivery ratio to recover to over 99.9% \((T_{recovery})\) and the average number of control packets \((CP_{recovery})\) when nodes are removed by targeted attack.