Capacity function-preserving star-delta transformations in flow networks

The concept of pseudo-switching (PS) functions has definite advantages in representing nonbinary discrete random functions, usually encountered in the study of flow networks. That concept is utilized in the development of star-delta and delta-star transformations that preserve the source-to-terminal (s−t) capacity function in a flow network. The usefulness of these transformations in reducing complex networks to equivalent series-parallel ones is illustrated by examples. The resulting series-parallel networks are easily solvable for the networks s−t capacity function, which is a compact expression of the probability mass function (p.m.f.) of the maximum s−t flow.