Multistate-node acyclic network reliability evaluation

Many real-world systems (such as cellular telephones, transportation, etc.) are multistate-node acyclic network (MNAN) composed of multistate-nodes. Such network has a source node (position) where the signal source is located, a number of sink nodes that only receive the signal, and a number of intermediate nodes that retransmit the received signal to some other nodes. The non-sink node has different states determined by a set of nodes receiving the signal directly from it. The reliability of MNAN can be computed in terms of minimal trees (MTs). Based on the Branch-and-Bound algorithm, we developed an intuitive algorithm that is simpler than the best-known existing method. The computational complexity of the proposed algorithm is also analyzed. One example is illustrated to show how all MTs are generated by the proposed algorithm. The reliability of this example is then computed.