A Monte Carlo simulation of the flow network reliability using importance and stratified sampling

Bulteau, Stéphane; Khadiri, Mohamed El

doi:10.1051/ro/1998320302711

Cited by 6 publications

(7 citation statements)

References 10 publications

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“…Links can be in one of two possible conditions, fully operational, i.e., able to transport flow up to the value M i , or absolutely failed and not able to transport any flow. A broader range of failure values is offered by the state space used in [7] and [6], where…”

Section: Network Modelingmentioning

confidence: 99%

“…It has been studied for the stochastic flow network problem by Botev et al [5]. The methods based on bounds derive from a well-known technique due to George S. Fishman, which was widely applied in the context of Monte Carlo simulation and it is successfully adapted to stochastic flow networks in [6] and [7].…”

Section: Introductionmentioning

confidence: 99%

“…Two other methods proposed in the field of stochastic flow networks, [7] and [6], are based on changing the probability distributions of the individual links' capacities. The objective is that under the new probability distributions the reliability estimator is still unbiased with respect to the real value, but has less variance than the standard one.…”

Section: Introductionmentioning

confidence: 99%

“…The objective is that under the new probability distributions the reliability estimator is still unbiased with respect to the real value, but has less variance than the standard one. In [7] and [6] the change of the probability distributions is based on bounds that come from a decomposition of the state space due to Doulliez and Jamoulle [8].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Efficient Estimation of Stochastic Flow Network Reliability

2019

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The Creation Process is an algorithm that transforms a static network model into a dynamic one. It is the basis of different variance reduction methods designed to make efficient reliability estimations on highly reliable networks in which links can only assume two possible values, operational or failed. In this article the Creation Process is extended to let it operate on network models in which links can assume more than two values. The proposed algorithm, called here Multi-Level Creation Process, is the basis of a method, also introduced here, to make efficient reliability estimations of highly reliable stochastic flow networks. The method proposed, which consists in an application of Splitting over the Multi-Level Creation Process, is empirically shown to be accurate, efficient, and robust.

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Section: Network Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient Estimation of Stochastic Flow Network Reliability

2019

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“…In comparison, the efficiency and accuracy of PrPm (Tong and Tien 2019) and dPrPm as described in this paper are not limited by the ability to assess low-probability events. In Bulteau and El Khadiri (1998) and Zuev et al (2015), the result of a sampling point depends on an indicator function, e.g., by comparison with MLS or MCS, which can be expensive to evaluate. One advantage of the proposed directed probability propagation method is the absence of an indicator function or need to identify the MLS or MCS of a system.…”

Section: Background and Related Workmentioning

confidence: 99%

Probability Propagation Method for Reliability Assessment of Acyclic Directed Networks

Tong

Tien

2019

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

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Many civil infrastructure systems that deliver resources from source points to sinks, e.g., power distribution and gas pipeline networks, can be described as acyclic directed networks comprising nodes and links. Reliability assessment of these systems can be challenging, particularly for systems of increasing size and complexity and if the probabilities of rare events are of interest. This paper proposes a new analytical probability propagation method for reliability assessment of acyclic directed networks called the directed probability propagation method (dPrPm). Through a link-adding sequence to propagate a message consisting of the marginal and pairwise node reliabilities from source nodes to sink nodes, the method results in the upper and lower bounds of all sink node reliabilities. Reliability of a sink node is measured by the probability of reaching that node from a source node. Compared with previous methods, dPrPm addresses the case of multiple-sink networks, results in guaranteed reliability bounds, and analyzes acyclic directed networks as relevant for infrastructure systems. Proofs are provided guaranteeing the accuracy of dPrPm, and computation time is significantly reduced from typical exponential increases with system size to a polynomial increase. To assess performance, the proposed method was applied to three test applications: a directed grid network, a power distribution network, and a more complex gas pipeline network under seismic hazard. Results were compared with the exact solution and Monte Carlo simulations to evaluate accuracy and computational cost. Results showed that dPrPm performs equally well in terms of accuracy across network reliabilities and achieved order-of-magnitude increases in computational efficiency to obtain exact bounds on reliability assessments at all system sink nodes.

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Distribution and reliability evaluation of max-flow in dynamic multi-state flow networks

Jane

Laih

2017

European Journal of Operational Research

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A Monte Carlo simulation of the flow network reliability using importance and stratified sampling

Cited by 6 publications

References 10 publications

Efficient Estimation of Stochastic Flow Network Reliability

Efficient Estimation of Stochastic Flow Network Reliability

Probability Propagation Method for Reliability Assessment of Acyclic Directed Networks

Distribution and reliability evaluation of max-flow in dynamic multi-state flow networks

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