## 6 Simulation Evaluation of the Dynamic VWSN
### Adaptivity of the VWSN Topology against Random Failure  
In this section, we evaluate the adaptivity of the VWSN topology against random failure. The simulation time is 10,000 s; after 5000 s have elapsed, one node fails every 10 s until 30 nodes have failed. We use one hundred patterns of node failure, each corresponding to a trial. In each pattern, 30 nodes are randomly selected to fail, and the order of failure is random. To compare the adaptivity of a physical topology with that of a VWSN topology, we try to evaluate the adaptivity of a physical topology in which we apply shortest-path routing to the topology. However, the simulation cannot be finished. Because all nodes have routing table entries to all other nodes, several nodes generate more than one hundred route request packets after failure of a single node. This leads to frequent packet collision and high packet loss. When a Hello packet is lost, neighboring nodes erroneously detect the failure of the sending node and generate many unnecessary route request packets. From this result, the division of a physical topology into small sub-topologies is an effective method for avoiding this type of problem. Table 3 shows the rate of recovering the data delivery ratio in each combination of a physical topology and a method of constructing a VWSN topology. The recovery rate is the ratio between the number of trials in which all of the flows can reach the destination node and the total number of trials. In the simulation, _phy_ indicates the physical topology. We use \(R_{recovery}\) to denote the rate of recovering the data delivery ratio. Table 3 shows that \(R_{recovery}\) for the bio-inspired topology is zero. There are some connected centroid nodes with a high degree in the virtual topology constructed by the bio-inspired method. The failure of a few of these is fatal because they are essential for connectivity. Note that the routing algorithm mentioned in Section 5 restricts the communication between modules because we keep nodes' overheads low by reducing their managing information on tables. A data packet must pass through the connected node of the module if the destination node of the data packet belongs to the different module. This means that, in the bio-inspired method, the virtual link connecting different modules is ignored when an endpoint node is neither a centroid node nor a peripheral node. Therefore, a VWSN topology constructed by the bio-inspired method seems to fragment easily into subnetworks because of the routing algorithm, even though it is highly robust on connectivity against random failure, as discussed in our previous work [13]. Moreover, these topologies generate many control packets as part of the route recovery mechanism in upper tiers. This results in congestion and the loss of control packets. In the topologies created according to our proposal, the physical topology determines whether \(R_{recovery}\) is high or low. As an example, when there are some sparse areas in the physical topology, it is difficult to find an alternative path by flooding because of collisions among control packets or isolation in the physical or virtual topology. When we compare values of \(R_{recovery}\) among different physical topologies, the differences are small between methods. We investigate the cumulative distributions of \(CP_{recovery}\) and \(T_{recovery}\) against random failure; however, few differences can be seen among the strategies for _inter_ in each topology. Examples of the cumulative distributions of \(CP_{recovery}\) and \(T_{recovery}\) are shown in Figures 5 and 6, respectively. \begin{table}
\begin{tabular}{l c c} \hline  & _phy_ & \(R_{recovery}\) \\ \hline BICM(hh,HH) & \(T1\) & 0.80 \\ BICM(ll,LL) & \(T1\) & 0.81 \\ Bio-inspired & \(T1\) & 0.00 \\ BICM(hh,HH) & \(T2\) & 0.69 \\ BICM(ll,LL) & \(T2\) & 0.67 \\ Bio-inspired & \(T2\) & 0.00 \\ \hline \end{tabular}
\end{table} 
Table 3: Rate of recovering the data delivery ratio (\(R_{recovery}\)) against random failure.