Consider a set of terminal nodes K that belong to a network whose nodes areconnected by links that fail independently with known probabilities. Weintroduce a method for estimating any performability measure that depends onthe hop distance between terminal nodes. It generalises previously introducedMonte Carlo methods for estimation of the K-reliability of networks withvariance reduction compared to crude Monte Carlo. They are based on using setsof edges named d-pathsets and d-cutsets for reducing the variance of theestimator. These sets of edges, considered as a priori known in previousliterature, heaviliy affect the attained performance; we hereby introduce andcompare a family of heuristics for their selection. Numerical examples arepresented, showing the significant efficiency improvements that can be obtainedby chaining the edge set selection heuristics to the proposed Monte Carlosampling plan.
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