An efficient algorithm for computing exact system and survival signatures of K-terminal network reliability

An efficient algorithm is presented for computing exact system and survival signatures of K-terminal reliability in undirected networks with unreliable edges. K-terminal reliability is defined as the probability that a subset K of the network nodes can communicate with each other. Signatures have several advantages over direct reliability calculation such as enabling certain stochastic comparisons of reliability between competing network topology designs, extremely fast repeat computation of network reliability for different edge reliabilities and computation of network reliability when failures of edges are exchangeable but not independent. Existing methods for computation of signatures for K-terminal network reliability require derivation of cut-sets or path-sets which is only feasible for small networks due to the computational expense. The new algorithm utilises binary decision diagrams, boundary set partition sets and simple array operations to efficiently compute signatures through a factorisation of the network edges. The performance and advantages of the algorithm are demonstrated through application to a set of benchmark networks and a sensor network from an underground mine

Practical sequential bounds for approximating two-terminal reliability

With increasing emphases on better and more reliable services, network systems have incorporated reliability analysis as an integral part in their planning, design and operation. This article first presents a simple exact decomposition algorithm for computing the NP-hard two-terminal reliability, which measures the probability of successful communication from specified source node to sink node in the network. Then a practical bounding algorithm, which is indispensable for large networks, is presented by modifying the exact algorithm for obtaining sequential lower and upper bounds on two-terminal reliability. Based on randomly generated large networks, computational experiments are conducted to compare the proposed algorithm to the well-known and widely used edge-packing approximation model and to explore the performance of the proposed bounding algorithm. Computational results reveal that the proposed bounding algorithm is superior to the edge-packing model, and the trade-off of accuracy for execution time ensures that an exact difference between upper and lower bounds on two-terminal reliability can be obtained within an acceptable time.Two-terminal reliability Decomposition Sequential bounds Computational experiments