## 6 Simulation Evaluation of the Dynamic VWSN
### Adaptivity of the VWSN Topology against Random Failure
In Figure 5, \(CP_{recovery}\) is mapped on the horizontal axis, and the cumulative number of trials in which the data delivery ratio recovers before \(CP_{recovery}\) has elapsed is mapped on the vertical axis. Similarly, in Figure 6, the horizontal axis reflects \(T_{recovery}\), and the vertical axis reflects the cumulative distribution of the number of trials in which the data delivery ratio recovers before \(T_{recovery}\) has elapsed. Although the difference according to the method is small for the cumulative distribution of \(CP_{recovery}\) or \(T_{recovery}\) against random failure, when a VWSN is constructed by BICM(hh,HH), there are some trials whose \(CP_{recovery}\) and \(T_{recovery}\) are smaller (i.e., better) than those for topologies constructed by other methods. This is because when a node with a high degree is selected as a connected node in BICM(hh,HH), the endpoints of virtual links between modules tend to be concentrated to a small number of nodes. Therefore, the probability that a connected node fails in random failure is low, allowing the recovery of the zeroth-tier routing table unless a connected node fails. The number of trials in which either the virtual or physical topology fragments is shown in Table 4, and the number of trials in which the data delivery ratio does not recover because of the inconsistency in tables is shown in Table 5. In this, _phy_ identifies the physical topology. Blank entries in Table 4 reflect that the VWSN topology constructed by the bio-inspired method does not have tiers higher than the first tier. Figure 5: Cumulative distribution of the number of control packets \((CP_{recovery})\) when nodes are removed by random failure. Figure 6: Cumulative distribution of the time needed for the data delivery ratio to recover to over 99.9% \((T_{recovery})\) when nodes are removed by random failure. The values of \(phyFrag\) are the same in each physical topology, because we use the same node failure patterns. The value of \(L0 Frag\) for BICM(hh,HH) and BICM(ll,LL) is the same because the results of modular division by the Newman algorithm are almost identical between the cases. Whether the value of \(L1 Frag\) is high or low depends on the physical topology. For topologies constructed according to our proposed method, it is easy to fragment the first-tier virtual topology into physical topology \(T2\). There are two main reasons for this. One is that there is a first-tier module with a small number of nodes, and the other is that there is a first-tier module whose degree in the first tier is one. The point in common between these is that some first-tier modules contain few connected nodes. Therefore, the failure of a few connected nodes in a first-tier module that either has few nodes or has degree one in the first tier results in the fragmentation of the module. When we use the bio-inspired method, few connected nodes exist in their respective first-tier modules, and each module is small. Therefore, fragmentation of the topology is more likely than with our proposed method. In Table 5, \(T1 UF\) has the highest value for each method. This is because it is comparatively difficult to find an alternative route in the upper tier. Particularly when using the bio-inspired method, \(T1 UF\) is nearly the same as the number of trials. This near parity results from the congestion and loss of control packets around the connected nodes, which attract a large number of links. From the above, the adaptivity of VWSN topologies constructed by our proposal is not markedly different. However, in a few trials, \(Trecovery\) is notably smaller in the topology constructed by BICM(hh,HH). This suggests that the adaptivity to random failure of a VWSN topology constructed by BICM(hh,HH) is comparatively high.