Survival Signature Estimation Using Optimization and Monte-Carlo Simulation for \u3ci\u3eK\u3c/i\u3e ≥ 3 Classes of Nodes on Two-Terminal Networks

Abstract

This research develops an efficient approach to estimating survival signatures for two-terminal networks with more than two classes of components. Recently, the survival signature has gained substantial attention in the literature on network reliability estimation due to its unique separability property, which enables passing the network topology information independent of the failure distribution of the components. Following recent results from the literature, estimating the two-terminal survival signature by Monte Carlo simulation entails solving a multi-objective maximum capacity path problem on a two-terminal network in each replication. We adapt a multi-objective Dijkstra’s algorithm from the literature to construct the set of non-dominated paths solving the multi-objective maximum capacity path problem for each replication of the Monte-Carlo simulation. We have carried out experiments on random two-terminal networks and grid networks with three, four, and five classes of components. In these experiments, our version of the multi-objective Dijkstra’s algorithm was compared against four benchmark algorithms and an improvement technique that prunes some paths to be explored in the multi-objective Dijkstra’s algorithm setting lower bounds on capacities. We compared the run-time of our approach with all these benchmark approaches and found that the multi-objective Dijkstra’s algorithm performs significantly better in most instances