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.