# Reliable Design for a Network of Networks with Inspiration from Brain Functional Networks
## 1 Introduction  
The Internet-of-Things (IoT) has seen an increasing number of practical implementations in recent years, regarding not only traditional Internet services but also other services of extreme societal importance, such as infrastructure (e.g., electricity grids, vehicular traffic) and life-critical services (security, medical treatment, etc.) [1, 2]. This situation is leading to the emergence of interconnected networks with mutual dependencies, known as a _network of networks_ (NoN) [3]. Network slicing based on network virtualization technology can be regarded as an NoN case and has been attractingmuch attention as a way to realize the assumed IoT network environment [4; 5]. In this architecture, sliced networks, i.e., virtual networks (VNs), are created by service providers to offer specific services on physical networks (PNs) provided by the infrastructure providers. To enhance the flexibility and efficiency of resource utilization, recent studies have investigated new methods for reallocating resources dynamically between VNs according to traffic fluctuations instead of dividing the PN resources statically [6; 7; 8; 9]. However, although the above methods have several advantages, traffic fluctuations in one VN can be propagated to other VNs because of the mutual dependences between the VNs sharing the same PN resources [10; 11]. In the upcoming IoT network scenario, environmental changes in service networks will exert an increasing influence on society and human life. Consequently, an urgent issue is to establish a method for designing an NoN with high reliability, namely, the ability to sustain network services under traffic fluctuation, assuming the network-slicing environment. The Catastrophic NoN (C-NoN) was presented as a model expressing NoN availability based on actual interconnected networks comprising infrastructure networks in Italy, namely, a power network and a control network [12]. The functional availability of each infrastructure network depends on that of the other network: the power network must be operated by the control network, while the control network must be supplied with electricity by the power network. The C-NoN model reproduces the dependence between both networks, revealing how partial fluctuations spread their influence over the entire NoN. On the other hand, [PERSON] et al. argued that not all complex networks existing in nature are vulnerable to fluctuations [13]. Brain functional networks comprise a number of mutually connected network modules (i.e., regions) of neural cells. The regions are interdependent to complement their functionalities. Advances in neuroimaging technology, such as functional magnetic resonance imaging (fMRI), now make it possible to identify the interregional dependence of brain functional networks, for which [PERSON] et al. proposed the Brain NoN (B-NoN) model [13]. The B-NoN model reproduces the complementary interregional dependence and elucidates the mechanisms that suppress the propagation of local fluctuations. However, insights from studying NoN models are yet to be applied to practical systems of information networks including the aforementioned network-slicing environment. As an NoN system, we consider herein layered VNs with slicing, and we propose the _Physical-Virtual NoN_ (PV-NoN) model based on existing NoN models. To deal with traffic conditions and interdependence among a PN and VNs, this model describes NoN availability, focusing on the states of the node interfaces. Here, availability denotes the ability for a network to transmit packets without loss from the source to the destination. For the PV-NoN model, we assume three different types of interdependence according to how the resources (e.g., packet buffer, network I/O) are assigned on the physical interfaces. To investigate NoN reliability, we measured availability and communication performance through simulation experiments.