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This state of the art discusses the problem of reliability estimation for highly reliable stochastic flow networks. There are algorithms to compute this reliability exactly, but they have exponential complexity, making the problem intractable for large or even medium sized networks. In this case Monte Carlo simulation is a simple and straightforward alternative tool to provide a reliability estimation...
The object under study is a metric associated to each graph, called diameter constrained reliability. The exact evaluation of the diameter constrained reliability belongs to the class of NP-Hard problems, and becomes prohibitive in large graphs. In the literature, several estimation methods have been developed, inspired in statistics, combinatorics, algebra and other branches of knowledge. We are...
A multi-component system is usually defined over a ground set S with m = |S| components that work (or fail) stochastically and independently, ruled by the probability vector p ∊ [0, 1]m, where pi is the probability that component i works. We study systems which can be either in “up” or “down” state, according to their ability to comply with their stated mission given the subset of components under...
Let G = (V,E) be a simple graph with |V| = n nodes and |E| = m links, a subset K ⊆ V of terminals, a vector p = (p1, …, pm) ∈ [0, 1]m and a positive integer d, called diameter. We assume nodes are perfect but links fail stochastically and independently, with probabilities qi = 1 − pi. The diameter-constrained reliability (DCR for short), is the probability that the terminals of the resulting subgraph...
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...
We propose a polynomial-time algorithm for detecting and deleting classes of network edges which are irrelevant in the evaluation of the Source-to-terminal Diameter Constrained Network reliability parameter. As evaluating this parameter is known to be an NP-hard problem, the proposed procedure may lead to important computational gains when combined with an exact method to calculate the reliability...
Given the pervasive nature of computer and communication networks, many paradigms have been used to study their properties and performances. In particular, reliability models based on topological properties can adequately represent the network capacity to survive failures of its components. Classical reliability models are based on the existence of end-to-end paths between network nodes, not taking...
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