Reliability of a computer network in case capacity weight varying with arcs, nodes and types of commodity

The computer network can be modeled as a capacitated-flow network. This paper concentrates on a two-commodity capacitated-flow network with three characters: (1) nodes as well as arcs have multiple possible capacities and may fail, (2) each component (arc/node) has both capacity and cost attributes; and (3) the capacity weight varies with arcs, nodes and types of commodity (or named file). We study the possibility that a given quantity of two types of files can be transmitted through this network simultaneously under the budget constraint. Such a possibility is named the system reliability which is a performance index to measure the quality level of supply demand systems such as computer, telecommunication, electric-power transmission and transportation systems. The approach of minimal paths is applied to describe the relationship among flow assignments and capacity vectors. A simple algorithm in terms of minimal paths is proposed to evaluate the system reliability.