Cascading Failure Model in Two-Level Network Systems

Modern networks are becoming increasingly dependent on each other. We can observe that several networks merge into a single interdependent network structure in which, along with connections between elements of a single network, there is also inter-level interaction. This complicates the management of such multi-level networks and creates the risk of cascading failures. As a result of cascading failure, the failure of one or more nodes in a single network can lead to complete fragmentation of the entire multi-level system. An example of such a cascading failure is the power outage in Italy on 28 September 2003: the shutdown of a power plant led to the failure of nodes in the Internet network, which in turn caused further power plant failures. In this study we focus on the case of a two-level network. To describe the network itself and its operations, we use a mathematical model which is able to capable to indicate cascading failures. The model is based on following two main principles: 1. Description of nodes: Each node is described as a time series of values of an indicator characterizing its performance. For each of these indicators, we set an acceptable range of values, outside of which the corresponding node is considered to have failed and it is excluded from the network. Thus the level of risk is determined by the value of the indicator. 2. Types of connections between nodes: We distinguish between functional and correlation connections of nodes among each other. If the failure of one node leads to the immediate failure of another node, we consider them as functionally connected. For all other cases, we consider the correlation of the nodes to describe their effect on each other. Using the two principles above, the model allows us to examine the reliability of the network system and monitor it to prevent a cascade of failures. We will demonstrate how such a model can be created and applied on real systems within several scientific spheres.