An Improved Method for Multistate Flow Network Reliability With Unreliable Nodes and a Budget Constraint Based on Path Set

Evaluating multistate flow network reliability and reducing system cost are important tasks when planning and designing systems. Existing methods are based on (
d
,
c
)-minimal paths ((
d
,
c
)-MP), which are vectors, such that
d
units of flow transmit between two specified nodes with a total cost that does not exceed
c
. However, these methods only work for directed networks. This correspondence paper finds all (
d
,
c
) -MPs before calculating network reliability under budget constraints using a novel method. The proposed algorithm is easier to understand and implement and is superior to existing algorithms. This correspondence paper analyzes and proves the correctness of the proposed algorithm, using two examples to demonstrate how to generate, verify, and implement all (
d
,
c
)-MPs to solve multistate flow network reliabilities under budget constraints using the proposed algorithm.