The Analysis of Multiuser Network Systems under Uncertainty: 7.the Problem of Standard Vulnerability analysis of a Multicommodity flow Network

摘要

The problem of analyzing the efficiency of multiuser network systems that may be exposed to nonrandom external factors which decrease the capacity of arcs of the network physical graph is considered. The demand vector is supposed to be known (it is considered as a given standard-for example, the initial flow in the network). The problem of standard vulnerability analysis is posed, i.e., the finding of guaranteed estimates of quality of network functioning if this quality is described by the supply diagram of demands of communicating pairs, i.e., by the distribution of functions of all demands according to supply levels. This problem is represented as a multi-criteria minimax problem with a diagram criterion. The decision-making is formalized and, for a number of model networks, explicit solutions were obtained. This gives us an opportunity to compare three types of network structures (linear, circular and starshaped) in terms of the vulnerability criterion and to obtain nontrivial results even for the simplest examples.