Evaluation of all one-to-many reliabilities for acyclic multistate-node distributed computing system under cost and capacity constraints

A novel problem is proposed in this study by considering all one-to-many acyclic multistate-node distributed computing system (AMNDCS) reliabilities with limited cost (budget) and memory capacity. The AMNDCS is an extension of the multistate network without satisfying the flow conservation law. A very straightforward and simply programmed exact algorithm is developed for this problem using the universal generating function method (UGFM) and a generalized multiplication operator. The correctness and computational complexity of the proposed algorithm will be analyzed and proven. An illustrative example is presented to demonstrate how this problem is solved using the proposed UGFM.