An Efficient Evaluation for the Reliability Upper Bound of Distributed Systems with Unreliable Nodes and Edges

The distributed systems in which nodes and/or edges may fail with certain probabilities have been modelled by a probabilistic network or a graph G. Computing the residual connectedness reliability (RCR), denoted by R(G), of probabilistic networks under the fault model with both node and edge faults is very useful, but is an NP-hard problem. Since it may need exponential time of the network size to compute the exact value of R(G), it is important to calculate its tight approximate value. In this paper, we present a new approach with an efficient algorithm for evaluating the upper bound of R(G) of distributed systems with unreliable nodes and edges. We also apply our algorithm to some typical classes of networks to evaluate the upper bounds and show the effectiveness and the efficiency of the new algorithm. Numerical results are presented. Keywordsdistributed system; residual connectedness reliability; node and edge faults; upper bound