SPECTRAL APPROACH TO RELIABILITY EVALUATION OF FLOW NETWORKS

In this paper we consider flow networks, which is an important class of networks, and which includes, for example, communication networks, transportation and supply networks, oil and power supply systems, etc. In our model, the edges are subject to failure, which may be caused by "enemy attack", earthquakes, disruption of communication channels etc. Each edge is characterized by its failure probability and flow capacity. The network reliability is defined as the probability that the flow between the source node and sink node is not less than some given threshold. Our approach to flow network reliability evaluation is based on estimating by means of an efficient Monte Carlo simulation, the network topological invariant called network destruction spectrum (D-spectrum). We consider also a design problem on flow network, namely its edge reinforcement in order to increase in an "optimal" way the network reliability.