A coherent model for reliability of multiprocessor networks

Graph G has perfectly reliable nodes and edges that are subject to stochastic failure. The network reliability R is the probability that the surviving edges induce a spanning connected subgraph of G. Analysis problems concern determining efficient algorithms to calculate R, which is known to be NP-hard for general graphs. Synthesis problems concern determining graphs that are, according to some definition, the most reliable in the class of all graphs having a given number of edges and nodes. In applications where the edges are perfectly reliable and the nodes are subject to failure, another measure (residual node connectedness reliability) is defined as the probability that the surviving nodes induce a connected subgraph of G. Referring to such a subset as an operating state, the measure is not coherent because a superset of an operating state need not be an operating state. This paper proposes a new definition of network reliability that handles the case of node failures; it is coherent. We determine many of its properties, and present several analysis and synthesis results.