Maximising the Amount of Transmitted Flow through Repairable Flow Networks

Abstract

A fundamental theorem related to maximizing the flow in a repairable flow network with arbitrary topology has been stated and proved. `The flow transmitted through a repairable network with arbitrary topology and a single source and sink can be maximized by (i) determining, all possible flow paths from the start node (the source) to the end node (the sink); (ii) arranging the flow paths in ascending order according to their specific flow path resistance and (iii) setting up the flow in the network by a sequential saturation of the flow paths starting with the one with the smallest specific resistance, until the entire flow network is saturated'. Based on the proved theorem, a new method for maximizing the flow in repairable flow networks has been proposed. The method is based on the new concept `specific resistance of a flow path'. Finally, a new stochastic optimization method has been proposed for determining the network topology combining a maximum flow and minimum cost.