Analysis of cluster damages in network systems

Changes in the functional characteristics of a multicommodity network with cluster architecture of the logical links depending on damages of edges of its physical topology graph are studied. The concept of a cluster damage is defined as a damage that separates at least one vertex from its sinks. The analysis is carried out on the class of minimum cluster damages. The stability of each cluster of logical links is analyzed with respect to the set of damages when the damage is not directly aimed at the source vertex of the cluster. Estimates of the cluster integrity on the whole and in terms of the undamaged (undivided) links remaining in the cluster are obtained. These estimates provide a basis for bi-criteria ranking of clusters depending on their susceptibility to nonrandom damages of the network. Characteristics of the minimum cluster damages and methods for their comparison are proposed. This approach can be used for a quick analysis of vulnerability of large territorially distributed systems, including telecommunication, communication, and control systems.