On the robustness of fishman's bound-based method for the network reliability problem

International audienceStatic network unreliability computation is an NP-hard problem, leading to the use of Monte Carlo techniques to estimate it. The latter, in turn, suffer from the rare event problem, in the frequent situation where the system's unreliability is a very small value. As a consequence, specific rare event event simulation techniques are relevant tools to provide this estimation. We focus here on a method proposed by Fishman making use of bounds on the structure function of the model. The bounds are based on the computation of (disjoint) mincuts disconnecting the set of nodes and (disjoint) minpaths ensuring that they are connected. We analyze the robustness of the method when the unreliability of links goes to zero. We show that the conditions provided by Fishman, based on a bound, are only sufficient, and we provide more insight and examples on the behavior of the method

A new simulation method based on the RVR principle for the rare event K - network reliability problem

In this paper we consider the evaluation of a well Known K-network unreliability parameter by means of a new RVR Monte-Carlo method. It is based on seres-parellel reductions and a conditioning procedure using pathsets and cutsets for recursively changing the original problem into the unreliability problem for a smaller network. We illustrate by experimental results that the proposed method has good behavior in rare event cases and offers significant speed-ups over other state-of-the art variance-reduction techniques

A Monte Carlo method based on antithetic variates for network reliability computations

The exact evaluation of usual reliability measures of communication networks is seriously limited because of the excessive computational time usually needed to obtain them. In the general case, the computation of almost all the interesting reliability metrics are NP-hard problems. An alternative approach is to estimate them by means of a Monte Carlo simulation. This allows to deal with larger models than those that can be evaluated exactly. In this paper, we propose an algorithm much more performant in time and in precision that the standard Monte Carlo technique. Moreover, it is particularly efficient in the case of highly reliable systems. It will be shown that it behaves much better than the so called dagger sampling plan on which good results have been reported in the literature. We will also show that the applicability of the dagger method depends on the reliabilities of the components of the network while this is not the case of the method proposed here

A Monte Carlo Simulation of the Flow Network Reliability using Importance and Stratified Sampling

We consider the evaluation of the flow network reliability parameter. Because the exact evaluation of this parameter has exponential time complexity- , simulation methods are used to derive an estimate. In this paper, we use the state space decomposition methodology of Doulliez and Jamoulle for constructing a new simulation method which combines the importance and the stratified Monte Carlo principles. We show that the related estimator belongs to the variance-reduction family. By numerical comparisons, we illustrate the interest of our method when compared to the previous simulation methods based on the same decomposition

Estimation of network reliability on a parallel machine by means of a Monte Carlo technique

Disponible dans les fichiers attachés à ce documen

Rare events analysis by Monte Carlo techniques in static models

International audienc