A new importance sampling Monte Carlo method for a flow network reliability problem

Bulteau, Stéphane; Khadiri, Mohamed El

doi:10.1002/nav.10004

Cited by 20 publications

(7 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Monte Carlo simulation relies on repeated random sampling to compute an approximate estimate of reliability. Some studies [4,13] have proposed Monte Carlo simulation approaches to estimate the reliability of network-structured systems using a state-space decomposition methodology. Significantly more research [12,22,[28][29][30][31] has been devoted to evaluating the system reliability of binary-state networks.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Simulation approach to estimate the system reliability of a time-based capacitated flow network susceptible to correlated failures

Lin

Fiondella

Chang

2013

Simulation Modelling Practice and Theory

View full text Add to dashboard Cite

Section: Related Workmentioning

confidence: 99%

“…In addition to numerical techniques, simulation tools have been widely applied for network modeling [4,12,13,22,[24][25][26][28][29][30][31]. Monte Carlo simulation is a common method to evaluate system reliability when exact numerical calculation is computationally complex.…”

Section: Related Workmentioning

confidence: 99%

Simulation approach to estimate the system reliability of a time-based capacitated flow network susceptible to correlated failures

Lin

Fiondella

Chang

2013

Simulation Modelling Practice and Theory

View full text Add to dashboard Cite

“…, X m ) belongs to the space X = ∏ m i=1 X i and has joint pdf p(x) = P(X = x), for x ∈ X . We also make the standard independence assumption (see [1,8,13]) that p(x) = ∏ m i=1 P[X i = x i ] and that the nodes do not fail.…”

Section: The Modelmentioning

confidence: 99%

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

Botev¹,

L’Ecuyer²,

Tuffin³

2018

Preprint

View full text Add to dashboard Cite

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.

show abstract

“…For rare event simulation, i.e., when the failure probability p f is small, crude MCS is inefficient or even infeasible when the LSF is expensive to compute. In such cases, advanced sampling techniques such as subset simulation [12][13][14][15][16][17] and importance sampling (IS) [18][19][20] should be employed to decrease the required number of LSF evaluations for obtaining an accurate estimate of p f . Alternatively, Dehghani et.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Cross Entropy Method for Network Reliability Assessment

Chan¹,

Papaioannou²,

Straub³

2021

Proceedings of the 31st European Safety and Reliability Conference (ESREL 2021)

View full text Add to dashboard Cite

We propose a modification of the improved cross entropy (iCE) method to enhance its performance for network reliability assessment. The iCE method performs a transition from the nominal density to the optimal importance sampling (IS) density via a parametric distribution model whose cross entropy with the optimal IS is minimized. The efficiency and accuracy of the iCE method are largely influenced by the choice of the parametric model. In the context of reliability of systems with independent multi-state components, the obvious choice of the parametric family is the categorical distribution. When updating this distribution model with standard iCE, the probability assigned to a certain category often converges to 0 due to lack of occurrence of samples from this category during the adaptive sampling process, resulting in a poor IS estima tor with a strong negative bias. To circumvent this issue, we propose an algorithm termed Bayesian improved cross entropy method (BiCE). Thereby, the posterior predictive distribution is employed to update the parametric model instead of the weighted maximum likelihood estimation approach employed in the original iCE method. A set of numerical examples illustrate the efficiency and accuracy of the proposed method.

show abstract

A new importance sampling Monte Carlo method for a flow network reliability problem

Cited by 20 publications

References 11 publications

Simulation approach to estimate the system reliability of a time-based capacitated flow network susceptible to correlated failures

Simulation approach to estimate the system reliability of a time-based capacitated flow network susceptible to correlated failures

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

Bayesian Cross Entropy Method for Network Reliability Assessment

Contact Info

Product

Resources

About