Network Reliability Monte Carlo With Nodes Subject to Failure

We extend the network reliability estimation methodology based on evolution (creation) Monte Carlo into four directions: (i) introducing unreliable nodes; (ii) adjusting the evolution process with merging to "closure" operation suitable for unreliable nodes; (iii) in case of numerical instability in computing convolutions, we suggest a special Monte Carlo algorithm based on importance sampling; (iv) we extend the traditional network terminal connectivity criterion to criteria describing network disintegration into a critical number of clusters, or the critical size of the largest component.