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

We propose an adaptive parameterized method to approximate the zero-variance change of measure for the evaluation of static network reliability models, with links subject to failures. The method uses two rough approximations of the unreliability function, conditional on the states of any subset of l...

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Bibliographic Details
Published in:Computers & operations research Vol. 45; pp. 51 - 59
Main Authors: Tuffin, Bruno, Saggadi, Samira, L'Ecuyer, Pierre
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.05.2014
Elsevier
Pergamon Press Inc
Subjects:
Applied sciences
Approximation
Asymptotic methods
Asymptotic properties
Computer Science
Exact sciences and technology
Failure
Importance sampling
Links
Mathematical analysis
Mathematical models
Mathematics
Monte Carlo simulation
Network flow problem
Networks
Operational research and scientific management
Operational research. Management science
Operations Research
Optimization algorithms
Probability and statistics
Reliability
Reliability theory. Replacement problems
Sampling techniques
Sampling theory, sample surveys
Sciences and techniques of general use
Statistics
Studies
Reliability
Monte Carlo simulation
Pilot
Monte Carlo method
Dependability
Roughness
Approximation algorithm
Failures
Modeling
Adaptive method
Network reliability
Linear combination
Static model
Variance reduction
Asymptotic approximation
Interconnected system
Importance sampling
ISSN:0305-0548, 1873-765X, 0305-0548
Online Access:Get full text
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Summary:We propose an adaptive parameterized method to approximate the zero-variance change of measure for the evaluation of static network reliability models, with links subject to failures. The method uses two rough approximations of the unreliability function, conditional on the states of any subset of links being fixed. One of these approximations, based on mincuts, under-estimates the true unknown unreliability, whereas the other one, based on minpaths, over-estimates it. Our proposed change of measure takes a convex linear combination of the two, estimates the optimal (graph-dependent) coefficient in this combination from pilot runs, and uses the resulting conditional unreliability approximation at each step of a dynamic importance sampling algorithm. This new scheme is more general and more flexible than a previously proposed zero-variance approximation scheme, based on mincuts only, and which was shown to be robust asymptotically when unreliabilities of individual links decrease toward zero. Our numerical examples show that the new scheme is often more efficient when low unreliability comes from a large number of possible paths connecting the considered nodes rather than from small failure probabilities of the links.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2013.12.011