Quick estimation of rare events in stochastic networks

Lieber, D.; Rubinstein, Reuven Y.; Elmakis, David

doi:10.1109/24.589954

Cited by 26 publications

(15 citation statements)

References 8 publications

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“…Note finally that the redundant parameters, like those labeled 2 and 3 (the parameter of the remaining time distribution in the initial state of the sources and the parameter tol), were eliminated (screened out) automatically at the early stage of the simulation using the Screening Algorithm proposed in Lieber et al (1997).…”

Section: Fig 2 Source States' Synchronicitymentioning

confidence: 99%

A combined splitting—cross entropy method for rare-event probability estimation of queueing networks

Garvels

2009

Ann Oper Res

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We present a fast algorithm for the efficient estimation of rare-event (buffer overflow) probabilities in queueing networks. Our algorithm presents a combined version of two well known methods: the splitting and the cross-entropy (CE) method. We call the new method SPLITCE. In this method, the optimal change of measure (importance sampling) is determined adaptively by using the CE method. Simulation results for a single queue and queueing networks of the ATM-type are presented. Our numerical results demonstrate higher efficiency of the proposed method as compared to the original splitting and CE methods. In particular, for a single server queue example we demonstrate numerically that both the splitting and the SPLITCE methods can handle our buffer overflow example problems with both light and heavy tails efficiently. Further research must show the full potential of the proposed method.

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Section: Fig 2 Source States' Synchronicitymentioning

confidence: 99%

A combined splitting—cross entropy method for rare-event probability estimation of queueing networks

Garvels

2009

Ann Oper Res

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“…Then, the problem of selecting a good g reduces to the problem of selecting a good parameter v. Two well-known methods for choosing such an optimal reference parameter v are the CE method [21,22] and the variance minimization (VM) method [12]. In the latter, the optimal v is determined or estimated from the solution to the variance minimization program…”

Section: Estimation and Optimization Via Monte Carlo Simulationmentioning

confidence: 99%

“…To make (12) easier to handle as an estimation problem, we note that (12) is equivalent to max x∈{0,1} n S(x), where x = (x 1 , . .…”

Section: Combinatorial Optimization Examplementioning

confidence: 99%

An Efficient Algorithm for Rare-event Probability Estimation, Combinatorial Optimization, and Counting

Botev

Kroese

2008

Methodol Comput Appl Probab

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Although importance sampling is an established and effective sampling and estimation technique, it becomes unstable and unreliable for highdimensional problems. The main reason is that the likelihood ratio in the importance sampling estimator degenerates when the dimension of the problem becomes large. Various remedies to this problem have been suggested, including heuristics such as resampling. Even so, the consensus is that for large-dimensional problems, likelihood ratios (and hence importance sampling) should be avoided. In this paper we introduce a new adaptive simulation approach that does away with likelihood ratios, while retaining the multi-level approach of the cross-entropy method. Like the latter, the method can be used for rare-event probability estimation, optimization, and counting. Moreover, the method allows one to sample exactly from the target distribution rather than asymptotically as in Markov chain Monte Carlo. Numerical examples demonstrate the effectiveness of the method for a variety of applications.

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“…where P 1 = {1, 4}, P 2 = {2, 5}, P 3 = {2, 3, 4} and P 4 = {1, 3, 5} are the sets of maximal paths, see (Barlow and Proschan, 1975;Lieber, Rubinstein, and Elmakis, 1997). Suppose the "nominal" parameter vector is u = (0.3, 0.1, 0.8, 0.1, 0.2).…”

Section: Cross-entropy and Crude Monte Carlomentioning

confidence: 99%

“…The method can also be used for solving optimisation problems (Rubinstein, 1999(Rubinstein, , 2001). The Cross-Entropy method has been successfully applied to a wide range of combinatorial and continuous optimisation problems (Dubin, 2002;Lieber, 1998;Margolin, 2002;Rubinstein, 1999), including problems in reliability theory (Lieber, Rubinstein, and Elmakis, 1997), buffer allocation (Alon et al, 2005), telecommunication systems (de Boer, 2000;de Boer, Kroese, and Rubinstein, 2004;de Boer and Nicola, 2002;de Boer, Nicola, and Rubinstein, 2000), neural computation (Dubin, 2002), control and navigation (Helvik and Wittner, 2001;Wittner and Helvik, 2002), DNA sequence alignment (Keith and Kroese, 2002), scheduling (de Mello and Rubinstein, 2002;Margolin, 2002) and Max-Cut and bipartition problems (Rubinstein, 2002). A short review of the basic ideas behind the Cross-Entropy method is given at the end of this section, but for details we refer to the book on Cross-Entropy , and the tutorial in de Boer et al (2005).…”

Section: Fishman Proposedmentioning

confidence: 99%

The Cross-Entropy Method for Network Reliability Estimation

et al. 2005

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Abstract. Consider a network of unreliable links, modelling for example a communication network. Estimating the reliability of the network -expressed as the probability that certain nodes in the network are connected -is a computationally difficult task. In this paper we study how the Cross-Entropy method can be used to obtain more efficient network reliability estimation procedures. Three techniques of estimation are considered: Crude Monte Carlo and the more sophisticated Permutation Monte Carlo and Merge Process. We show that the Cross-Entropy method yields a speed-up over all three techniques.

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Quick estimation of rare events in stochastic networks

Cited by 26 publications

References 8 publications

A combined splitting—cross entropy method for rare-event probability estimation of queueing networks

A combined splitting—cross entropy method for rare-event probability estimation of queueing networks

An Efficient Algorithm for Rare-event Probability Estimation, Combinatorial Optimization, and Counting

The Cross-Entropy Method for Network Reliability Estimation

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