Keywords: networks, graph theory, clustering, hierarchy, risk analysis.

The socioeconomic growth of modern societies is supported on a large number of interconnected components (physical, social, economic), which can be modeled as networks. Infrastructure networks (transportation, water supply), in particular, are essential to modern life and their reliability is paramount to enhance life quality and guarantee sustainable development. As networks become larger, the complexity of the interaction between components, the nature of that interaction and their size make it almost impossible to compute most performance indicators related with connectivity or flow accurately (e.g. overall connectivity, network reliability). For the particular case of connectivity, several approximate solutions and boundaries to failure probability can be found in the literature but the computational cost of these calculations for mid to large network systems is still extremely high. This document presents an approach to estimate network reliability by describing networks hierarchically through a successive clustering process. The hierarchical description can be translated into a set of fictitious networks, one for each level. Then, the analysis is carried out over these fictitious networks, which are smaller and easy to handle. As the analysis moves towards the bottom of the hierarchy, fictitious networks become closer to the actual network.

In this document, the problem is looked at from the perspective of decision makers by taking into account the actual need of information required at the time of the decision. Handling information at different definition levels can be used to support decisions regarding, for instance, new investments, retrofitting and expansions. The approach proposed facilitates the analysis by focussing on feasible scenarios and discarding scenarios that are unlikely and add a lot to the computational burden. The model can be used to make reliability estimations as well as to identify critical scenarios and draw important evidence for decision making. The proposed approach cannot be used as a surrogate measure of failure probability calculation but as a way to model and understand the performance of networks at different levels of description. The model is supported on the idea that in cases of incomplete or partial information risk analysis and reliability estimates can still be made within a coherent theoretical and conceptual framework. The proposed model is illustrated with a fictitious network where connectivity reliability is computed based on a hierarchical representation of the system. The example uses the Markov Clustering Algorithm (MCL) method [1] to develop the hierarchy description of the network and focuses on computing the systems failure probability. Results show the implementation of the procedure and its applicability in practice for decision making.

[1]

S. van Dongen, "Graph Clustering by Flow Simulation", PhD thesis, University of Utrecht, May 2000.

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