Reliability Evaluation of Stochastic-flow Network through Two Minimal Intersecting Paths under Budget and Time Constraints

A stochastic flow network (SFN) is more suitable than a general network to describe some real systems as it is composed of multistate links as well as multistate nodes. As the nodes and the links have different capacities at different time, the minimum transmission time through a stochastic flow network is not fixed. In order to shorten the transmission time, in this paper the data are allowed to be transmitted through two intersecting minimal paths. Reliability of the stochastic flow network is evaluated in term of the transmission of a given amount of data through a specified pair of intersecting minimal paths simultaneously under both time and budget constraint. An efficient algorithm is proposed which generates the capacity vectors from the source node to the sink node for a specified demand under both time and budget constraints. The reliability is evaluated by sum-ofdisjoint product technique related to these generated capacity vectors. The proposed method is well illustrated through a simple network. Further, the reliability of some bench mark networks are evaluated by using the proposed method.