A Monte Carlo sampling plan for estimating diameter-dependent network parameters

When analyzing networks with failing components, certain performance parameters cannot be computed based just upon a binary division in “working” and “failed” network states. Parameters like perceived quality associated with delay times or costs per link usage are usually better expressed via several discrete categories (e.g. service levels ranging from “poor” or even “useless” to “excellent”). The classical reliability model assigns the network a binary state based on connectedness of a given set of distinguished nodes. A vast literature exists for computing and estimating the reliability defined as the expected value of the binary structure function associated with such states. Recent research has also considered diameter constraints yet keeping the binary character of the network state. This paper introduces a model for estimating non-binary discrete network parameters that depend on “distances” defined in terms of path lengths. The model considers an arbitrary number of states associated with such distances. It generalizes previously introduced Monte Carlo simulation methods for reliability estimation to consider other-than-binary distance-dependent states. The suggested method and efficiency improvements relative to crude Monte Carlo are illustrated with a numerical example.