# Reliable Design for a Network of Networks with Inspiration from Brain Functional Networks
## 5 Discussion and Conclusions  
With the growing use of network slicing to implement the IoT network environment, it has been pointed out that traffic fluctuation in a sliced network could propagate to other networks [10; 11]. It has therefore become necessary to consider reliable design for not just single networks and interconnected networks but also interdependent networks, i.e., NoN. The existing NoN models [12; 13] describe the availability state of the NoN while considering the interdependence among the component networks, but are yet to be applied to practical systems of information networks. A contribution of the present work is that we considered layered VNs with network slicing as an NoN. We then proposed the PV-NoN model that expresses the availability state of an NoN that comprises a PN and VNs. The most notable aspect of our proposed model is that it considers traffic conditions and interdependence among the VNs. In this model, there are three types of interdependence according to the strategy used to divide the physical resources. With type-SD, the interface buffer on the physical nodes is divided statically. With type-UD, the buffer is undivided and the traffic among the VNs interferes with itself in a logical AND-like way, as seen in the C-NoN model. With type-DD, the buffer is usually undivided but is divided when there is congestion, in which case interference occurs in a logical OR-like way similarly to the B-NoN model. To investigate a reliable NoN design in the assumed network virtualization environment, in our simulation experiments we measured the GCS and packet delay on an NoN to evaluate the availability and communication performance. In the first experiment, we compared the performance of the three types of PV-NoN model, and we confirmed that in every case type-DD achieves the highest availability and communication performance. This superiority of type-DD arises from combining the guaranteed resource utilization of type-SD and the utilization efficiency of type-UD. Furthermore, we confirmed that type-DD prevents the cascading of performance degradation even though it shares physical resources on P-interfaces similarly to type-UD. In that aspect, even when dealing with interdependent network systems other than those based on network slicing, there appears to be potential for improving the availability of the system by adopting the complementary dependence inspired by the B-NoN model. Regarding the application of brain functional networks, it is also the case that type-DD appears to be highly resilient to network failures, which is one of the most notable characteristics of brain networks [52; 53]. We also conducted simulation experiments in which we configured the intra/internetwork assortativity of network influencers. The evaluation results confirmed that when the internetwork connectivity is disassortative (i.e., \(\theta<0\)), both the availability and communication performance are improved because influential nodes are not shared among the VNs, thereby avoiding interference among those nodes. When the intranetwork connectivity is assortative (i.e., \(\theta>0\)), the availability is improved while the communication performance is degraded. Although the internetwork connectivity  
Figure 7: Packet delay with changes in assortativity. Now, in contrast to the GCS, higher values indicate low performance (dark colors). affects only the interdependence among the VNs, the intranetwork connectivity also influences the structural performance of each VN in addition to the aforementioned interdependence. In detail, assortative connectivity within VNs localizes the area of physical resource sharing, thereby decreasing the interference among the VNs. At the same time, the assortative connectivity creates a long and narrow topology for each VN, thereby increasing the delay for packet communication. In a more practical scenario assuming the IoT environment, a larger-scale NoN must be considered, wherein the number of VNs or network components increases greatly.