Importance Sampling Simulations of Markovian Reliability Systems Using Cross-Entropy

Ridder, Ad

doi:10.1007/s10479-005-5727-9

Cited by 36 publications

(40 citation statements)

References 16 publications

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“…For each simple command in the system, an importance sampling parameter taking strictly positive values is introduced to bias the rates. To test the performance of PLASMA's paramterised importance sampling engine we applied it to repair models from [5] that have previously been considered in the context of state dependent tilting and which may be verified by PRISM's numerical algorithm. We have found that our state independent tilting scheme is nevertheless capable of achieving dramatic increases in performance.…”

Section: Rare Properties and Importance Samplingmentioning

confidence: 99%

“…We have found that our state independent tilting scheme is nevertheless capable of achieving dramatic increases in performance. For instance, example 1 of [5] considers a property with probability 1.17 × 10 −7 , requiring an expected 10 8 simulation runs to see a few examples. Using just six parameters PLASMA is able to make a 10 6 -fold increase in the frequency of observing the rare event.…”

Section: Rare Properties and Importance Samplingmentioning

confidence: 99%

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A Platform for High Performance Statistical Model Checking – PLASMA

Jégourel

Legay

Sedwards

2012

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Statistical model checking offers the potential to decide and quantify dynamical properties of models with intractably large state space, opening up the possibility to verify the performance of complex real-world systems. Rare properties and long simulations pose a challenge to this approach, so here we present a fast and compact statistical model checking platform, PLASMA, that incorporates an efficient simulation engine and uses importance sampling to reduce the number and length of simulations when properties are rare. For increased flexibility and efficiency PLASMA compiles both model and property into bytecode that is executed on an in-built memory-efficient virtual machine.

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Section: Rare Properties and Importance Samplingmentioning

confidence: 99%

Section: Rare Properties and Importance Samplingmentioning

confidence: 99%

A Platform for High Performance Statistical Model Checking – PLASMA

Jégourel

Legay

Sedwards

2012

Tools and Algorithms for the Construction and Analysis of Systems

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“…Applications to classical combinatorial optimization problems including the max-cut, traveling salesman, and Hamiltonian cycle problems are given in [7,17,42,43,44]. Various CE estimation and noisy optimization problems for reliability systems and network design can be found in [6,22,25,26,35,36,37,39]. Parallel implementations of the CE method are discussed in [18,19], and recent generalizations and advances are explored in [51].…”

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confidence: 99%

A Tutorial on the Cross-Entropy Method

et al. 2005

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Abstract:The cross-entropy method is a recent versatile Monte Carlo technique. This article provides a brief introduction to the cross-entropy method and discusses how it can be used for rare-event probability estimation and for solving combinatorial, continuous, constrained and noisy optimization problems. A comprehensive list of references on cross-entropy methods and applications is included.Keywords: cross-entropy, Kullback-Leibler divergence, rare events, importance sampling, stochastic search.The cross-entropy (CE) method is a recent generic Monte Carlo technique for solving complicated simulation and optimization problems. The approach was introduced by R.Y. Rubinstein in [41,42], extending his earlier work on variance minimization methods for rare-event probability estimation [40].The CE method can be applied to two types of problem:, where X is a random variable or vector taking values in some set X and H is function on X . An important special case is the estimation of a probability = P(S(X) γ), where S is another function on X .2. Optimization: Optimize (that is, maximize or minimize) S(x) over all x ∈ X , where S is some objective function on X . S can be either a known or a noisy function. In the latter case the objective function needs to be estimated, e.g., via simulation.In the estimation setting, the CE method can be viewed as an adaptive importance sampling procedure that uses the cross-entropy or Kullback-Leibler divergence as a measure of closeness between two sampling distributions, as is explained further in Section 1. In the optimization setting, the optimization problem is first translated into a rare-event estimation problem, and then the CE method for estimation is used as an adaptive algorithm to locate the optimum, as is explained further in Section 2.An easy tutorial on the CE method is given in [15]. A more comprehensive treatment can be found in [45]; see also [46, Chapter 8]. The CE method homepage can be found at www.cemethod.org .The CE method has been successfully applied to a diverse range of estimation and optimization problems, including buffer allocation [1], queueing models of telecommunication systems [14,16], optimal control of HIV/AIDS spread [48,49], signal detection [30], combinatorial auctions [9], DNA sequence alignment [24,38], scheduling and vehicle routing [3,8,11,20,23,53], neural and reinforcement learning [31,32,34,52,54], project management [12], rare-event simulation with light-and heavy-tail distributions [2,10,21,28], clustering analysis [4,5,29]. Applications to classical combinatorial optimization problems including the max-cut, traveling salesman, and Hamiltonian cycle 1

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“…Repair Model We first apply our cross-entropy minimisation algorithm to a repair model from [23], using N = 10000 simulations per iteration. The system comprises six types of subsystems containing (5,4,6,3,7,5) components that may fail independently.…”

Section: Importance Sampling Resultsmentioning

confidence: 99%