A simple MC-based algorithm for evaluating reliability of stochastic-flow network with unreliable nodes

A MP/minimal cutset (MC) is a path/cut set such that if any edge is removed from this path/cut set, then the remaining set is no longer a path/cut set. An intuitive method is proposed to evaluate the reliability in terms of MCs in a stochastic-flow network subject to both edge and node failures under the condition that all of the MCs are given in advance. This is an extension of the best of known algorithms for solving the d-MC (a special MC but formatted in a system-state vector, where d is the lower bound points of the system capacity level) problem from the stochastic-flow network without unreliable nodes to with unreliable nodes by introducing some simple concepts. These concepts were first developed in the literature to implement the proposed algorithm to reduce the number of d-MC candidates. This method is more efficient than the best of known existing algorithms regardless if the network has or does not have unreliable nodes. Two examples are illustrated to show how the reliability is determined using the proposed algorithm in the network with or without unreliable nodes. The computational complexity of the proposed algorithm is analyzed and compared with the existing methods.