An adaptive zero-variance importance sampling approximation for static network dependability evaluation

Tuffin, Bruno; Saggadi, Samira; L’Ecuyer, Pierre

doi:10.1016/j.cor.2013.12.011

Cited by 6 publications

(3 citation statements)

References 15 publications

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“…Several Monte Carlo variance-reduction methods have been proposed for network reliability estimation in rare-event situations; see, e.g., [3,5,10,15,19,28,25,31] and the references given there. Most of these methods are for the special case of independent links with binary states and nodes that never fail.…”

Section: The Modelmentioning

confidence: 99%

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Reliability Estimation for Networks with Minimal Flow Demand and Random Link Capacities

Botev¹,

L’Ecuyer²,

Tuffin³

2018

Preprint

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We consider a network whose links have random capacities and in which a certain target amount of flow must be carried from some source nodes to some destination nodes. Each destination node has a fixed demand that must be satisfied and each source node has a given supply. We want to estimate the unreliability of the network, defined as the probability that the network cannot carry the required amount of flow to meet the demand at all destination nodes. When this unreliability is very small, which is our main interest in this paper, standard Monte Carlo estimators become useless because failure to meet the demand is a rare event. We propose and compare two different methods to handle this situation, one based on a conditional Monte Carlo approach and the other based on generalized splitting. We find that the first is more effective when the network is highly reliable and not too large, whereas for a larger network and/or moderate reliability, the second is more effective.

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Section: The Modelmentioning

confidence: 99%

“…In this example we use the well-known dodecahedron network (Figure 3), with 20 nodes and 30 links, often used as a standard benchmark in network reliability estimation [3,9,11,12,31]. Here we took ρ = 0.7, b i = 4 and d net = 5.…”

Section: A Dodecahedron Networkmentioning

confidence: 99%

Reliability Estimation for Networks with Minimal Flow Demand and Random Link Capacities

Botev¹,

L’Ecuyer²,

Tuffin³

2018

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…A third type of application occurs in the setting where we want to estimate the probability of the rare event and to understand under which circumstances the rare event is likely to occur. A popular method to estimate is importance sampling, and the optimal way to do it is to sample under a density f proportional to the original density conditional on the rare event, and then adjust the estimator using a likelihood ratio (Tuffin et al 2014, Botev and Ridder 2014). This also fits our framework.…”

Section: Introductionmentioning

confidence: 99%

Sampling Conditionally on a Rare Event via Generalized Splitting

Botev

L’Ecuyer

2020

INFORMS Journal on Computing

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We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering, and computational statistics. The method uses independent trials starting from a single particle. We exploit this independence to obtain asymptotic and non-asymptotic bounds on the total variation error of the sampler. Our main finding is that the approximation error depends crucially on the relative variability of the number of points produced by the splitting algorithm in one run, and that this relative variability can be readily estimated via simulation. We illustrate the relevance of the proposed method on an application in which one needs to sample (approximately) from an intractable posterior density in Bayesian inference.

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Challenges in Stochastic Binary Systems

Romero

2019

2019 11th International Workshop on Resilient Networks Design and Modeling (RNDM)

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An adaptive zero-variance importance sampling approximation for static network dependability evaluation

Cited by 6 publications

References 15 publications

Reliability Estimation for Networks with Minimal Flow Demand and Random Link Capacities

Reliability Estimation for Networks with Minimal Flow Demand and Random Link Capacities

Sampling Conditionally on a Rare Event via Generalized Splitting

Challenges in Stochastic Binary Systems

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