New Measures of Robustness in Rare Event Simulation

Cancela, Héctor; Rubino, Gerardo; Tuffin, Bruno

doi:10.1109/wsc.2005.1574290

Cited by 9 publications

(7 citation statements)

References 11 publications

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“…Sufficient conditions for getting the BRE property for the above conditional Monte Carlo method were derived in Cancela et al (2005). When additionally using zero-variance approximation, we obtain the stronger property that BRE is always verified, and even VRE can be obtained in some cases.…”

Section: Proofmentioning

confidence: 85%

Combination of conditional Monte Carlo and approximate zero-variance importance sampling for network reliability estimation

Cancela¹,

L’Ecuyer²,

Rubino³

et al. 2010

Proceedings of the 2010 Winter Simulation Conference

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We study the combination of two efficient rare event Monte Carlo simulation techniques for the estimation of the connectivity probability of a given set of nodes in a graph when links can fail: approximate zero-variance importance sampling and a conditional Monte Carlo method which conditions on the event that a prespecified set of disjoint minpaths linking the set of nodes fails. Those two methods have been applied separately. Here we show how their combination can be defined and implemented, we derive asymptotic robustness properties of the resulting estimator when reliabilities of individual links go arbitrarily close to one, and we illustrate numerically the efficiency gain that can be obtained.

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Section: Proofmentioning

confidence: 85%

Combination of conditional Monte Carlo and approximate zero-variance importance sampling for network reliability estimation

Cancela¹,

L’Ecuyer²,

Rubino³

et al. 2010

Proceedings of the 2010 Winter Simulation Conference

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“…Concerning future work, one of the topics to highlight is the theoretical study of robustness measures, such as those discussed by Cancela et al (2005). The idea is to explore the conceptual frame of the results obtained in the present article about the behavior of the Splitting method for these static reliability models.…”

Section: Discussionmentioning

confidence: 99%

A splitting algorithm for network reliability estimation

2013

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“…The basic result presented in Subsection 3.1 can also be extended to other algorithms such as the one proposed in (Khadiri and Rubino 1996) and used in (Cancela, Rubino, and Tuffin 2005) for illustrating new propositions in the analysis of the properties of rare events estimators, so that a detailed analysis of those extensions is the object of current efforts.…”

Section: Discussionmentioning

confidence: 99%

Sensitivity analysis for robust parameter design experiments

Litko¹

2005

Proceedings of the Winter Simulation Conference, 2005.

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We analyze the computation of sensitivities in network reliability analysis. The associated models are graphs whose components are weighted by probabilities (their reliabilities) and they are widely used, for instance, in the design of communication networks. The paper deals with the sensitivities of usual reliability network metrics, with respect to the reliabilities of the components. The importance of sensitivities in this context is discussed and it is shown how to efficiently estmate the vector of sensitivities using Monte Carlo procedures. A first result allows to evaluate sensitivities using the standard Monte Carlo approach. A second method is then presented to deal efficiently with the rare event case. The ideas presented here can be applied to other classes of reliability problems and/or methods. INTRODUCTION The ModelStochastic graphs are widely used models for representing complex multi-component systems subject to component failures. They consist of graphs whose elements (nodes and arcs or edges) are weighted by probabilities. The output usually obtained from this type of structure is the probability of events representing a desired behavior of the system modeled. In this paper we consider the problem of the computation of reliability measures and we focus on a fundamental family of metrics, called K-terminal reliability, in the following version: the input is a stochastic undirected graph G = (V, E) where V is the set of vertices and E is the set of edges. We denote by E the number of edges: E = |E|. The graph may represent, for instance, a communication network. In this case, the vertices correspond to nodes sending and receiving information and the edges model communication lines. This application is used as a reference in the paper. For instance, the terms vertex and node are used as synonymous, and the same with edge or line or link. At a fixed time τ , each line is in one of two states: either working (operational) or completely down (unoperational, behaving as if it did not exist in the network). To simplify the presentation, we assume that nodes are perfect and that only lines can fail, but this is not critical since we are using Monte Carlo techniques. The graph is also assumed to be undirected, that is, the lines of the modeled communication network are bi-directional (messages can pass in both directions.) Finally, we assume that the graph is connected and without loops.The state of line or edge e at time τ is a binary random variable X e with value 1 if the line is working or 0 if it does not work. A basic assumption now is that (X e , e ∈ E) is a family of independent random variables. The K-terminal problem is the following: Given the probability r e of the event {X e = 1} for each line e of the network and a subset K of the set of vertices V, compute the probability R that, at time τ , the nodes can communicate with each other. In other words, if the first graph G = (V, E) is fixed, the set E of operational lines at time τ defines a subgraph G = (V, E ) of the previous one.The number R...

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New Measures of Robustness in Rare Event Simulation

Cited by 9 publications

References 11 publications

Combination of conditional Monte Carlo and approximate zero-variance importance sampling for network reliability estimation

Combination of conditional Monte Carlo and approximate zero-variance importance sampling for network reliability estimation

A splitting algorithm for network reliability estimation

Sensitivity analysis for robust parameter design experiments

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