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