Reliability Evaluation of Flow Networks Using Delta-Star Transformations

A new approach based on delta-star and/or star-delta transformations is presented for calculating the maximum network flow between a pair of nodes. The procedure consists of simplifying complex structures by converting them into equivalent series parallel configurations and successively reducing the network until a single arc in obtained. The capacity of the single arc is the maximum flow between the pair of nodes. Given the pmf´s of the network arcs, the pmf of the maximum flow can be obtained using these transformations. The system reliability can be determined from this pmf.