# Reliable Design for a Network of Networks with Inspiration from Brain Functional Networks
## 4 Evaluation
### Evaluation Results  
#### 4.3.1 Comparing the Availability of the Three Types of PV-NoN Model  
First, we compare the performance regarding the availability of the type-SD, type-UD, and type-DD versions of the PV-NoN model. We set \(V=2\) as the number of VNs, \(N^{P}=100\) and \(N^{V_{k}}=0.9N^{P}\) (\(k\in\mathcal{V}\)) for the number of nodes, and \(L^{P}=3N^{P}\) and \(L^{V_{k}}=3N^{V_{k}}\) (\(k\in\mathcal{V}\)) for the number of links. The ER model is used to construct the PN topology, while both the ER and BA models are used for the VNs. In this evaluation, the inter/intranetwork connectivity is determined randomly without considering the assortativity. The packet buffer size for the P-interfaces is set to \(\forall\mathcal{B}^{P}_{r,s}=20\), and the bandwidth for the P-interfaces is set to \(W=1\); This means that each P-interface can send \(W\) packets from the network I/O every time unit, \(\forall\mathcal{B}^{P}_{r,s}\) is determined assuming a TCP/IP environment, where in general packet size is set to 1.5 KB and buffer size is set to 8-256 KB. We simulate two types of traffic conditions based on the arrival rate \(\lambda\): (i) an equal amount of traffic flows on each VN and (ii) traffic is biased toward one of the two VNs. For (i), \(\lambda\) for both VNs is changed in the range \([0.1,1.6]\), while for (ii) \(\lambda\) is fixed at 0.2 on VN1 and varied in the range \([0.2,3.2]\) on VN2. We use the _giant component size_ (GCS) and the _packet delay_ as evaluation metrics to investigate NoN reliability from the perspectives of availability and communication performance. When a network topology is fixed, the evaluation on availability and communication performance is correlated with a given traffic fluctuation, i.e., availability increases when communication performance is high. However, when configuring a network topology, there can be a trade-off of availability and communication performance. If we configure a network topology to distribute the communication path, the network diameter can increase. This is the reason why we introduced communication performance in addition to availability as the evaluation metrics for evaluating reliability. The GCS denotes the largest connected component on each VN consisting of available V-interfaces (i.e., \(\sigma^{V_{k}}_{r,s}(t)=1\)), which we use to evaluate the availability of the entire network for each VN. The GCSis often used as a metric for complex networks [31; 37]. The packet delay denotes the average time required for a packet to be transmitted from its source to its destination, which is a more practical performance metric in communication networks. To see the impact of packet delay, we set the number of packet retransmissions to \(R=100\). In a realistic TCP/IP implementation, a much smaller number of around 10 would be used for the number of retransmissions. However, with such small values, only those packets whose source and destination are near each other can be transmitted successfully and longer routes do not work on the VN, thereby making it difficult to evaluate the impact of packet delay appropriately. Instead, we used \(R=100\) for the number of retransmissions. To evaluate the GCS, packets are created on the VN over 100 time steps and the GCS is measured at the 100 th step, which is when the availability state of the V-interfaces is assumed to have converged and the simulation is finished. Regarding the packet delay, we create packets for the first 20 time steps and then continue the simulation until all the packets are either transmitted or removed from the VN. The packet delay is then counted for all the packets that were transmitted successfully during the simulation. Each result shown is the mean value from 50 simulations. The simulation results for the GCS are shown in Figure 4. Each subfigure shows that type-DD gives the best availability of the three types of PV-NoN model.