A simple minimal path method for estimating the weighted multi-commodity multistate unreliable networks reliability

The weighted multicommodity multistate unreliable network (WMMUN) is a novel network composed of multistate unreliable components (arcs and nodes) capable of transmitting different types of commodities in which capacity weight varies with components. It is an extension of the multistate network. The current method for evaluating the directed WMMUN reliability has been derived from minimal cut (MC) based algorithm. The existing best-known method needed extensive comparison and verification, and failed to find the real directed WMMUN reliability. A very simple algorithm based on minimal paths (MPs) is developed for the WMMUN reliability problem. The correctness and computational complexity of the proposed algorithm will be analyzed and proven. An example is given to illustrate how the WMMUN reliability is evaluated using the proposed algorithm. The relationships among all different versions of MPs are also clarified.