Article

Techniques for fast simulation of models of highly dependable systems

Dept. of Electr. Eng., Twente Univ., Enschede
IEEE Transactions on Reliability (Impact Factor: 2.29). 10/2001; DOI: 10.1109/24.974122
Source: IEEE Xplore

ABSTRACT With the ever-increasing complexity and requirements of highly
dependable systems, their evaluation during design and operation is
becoming more crucial. Realistic models of such systems are often not
amenable to analysis using conventional analytic or numerical methods.
Therefore, analysts and designers turn to simulation to evaluate these
models. However, accurate estimation of dependability measures of these
models requires that the simulation frequently observes system failures,
which are rare events in highly dependable systems. This renders
ordinary Simulation impractical for evaluating such systems. To overcome
this problem, simulation techniques based on importance sampling have
been developed, and are very effective in certain settings. When
importance sampling works well, simulation run lengths can be reduced by
several orders of magnitude when estimating transient as well as
steady-state dependability measures. This paper reviews some of the
importance-sampling techniques that have been developed in recent years
to estimate dependability measures efficiently in Markov and nonMarkov
models of highly dependable systems

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    ABSTRACT: Markov chains with small transition probabilities occur while modeling the reliability of systems where the individual components are highly reliable and quickly repairable. Complex inter-component dependencies can exist and the state space involved can be huge, making these models analytically and numerically intractable. Naive simulation is also difficult because the event of interest (system failure) is rare, so that a prohibitively large amount of computation is needed to obtain samples of these events. An earlier paper (Juneja et al., 2001) proposed an importance sampling scheme that provides large efficiency increases over naive simulation for a very general class of models including reliability models with general repair policies such as deferred and group repairs. However, there is a statistical penalty associated with this scheme when the corresponding Markov chain has high probability cycles as may be the case with reliability models with general repair policies. This paper develops a splitting-based importance-sampling technique that avoids this statistical penalty by splitting paths at high probability cycles and thus achieves bounded relative-error in a stronger sense than in previous attempts
    IEEE Transactions on Reliability 10/2001; · 2.29 Impact Factor
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    ABSTRACT: RESTART is a widely applied accelerated simulation technique that allows the evaluation of very low probabilities. In this method a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of the rare event is higher. Formulas for evaluating the optimal number of regions and retrials have been provided in previous papers. Guidelines were also provided for obtaining a suitable function, the importance function, used to define the regions. This paper provides a simple importance function that can be useful for RESTART simulation of models of many highly dependable systems. Some eXamples from the literature illustrate the application of this importance function. Steady-state unavailability of balanced systems is accurately estimated within short computational times, and also the unavailability of an unbalanced system but with much more computational effort.
    SIMULATION: Transactions of The Society for Modeling and Simulation International 01/2007; 83:821-828. · 0.69 Impact Factor
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    ABSTRACT: This paper is a tutorial on RESTART, a widely applicable accelerated simulation technique for estimating rare event probabilities. The method is based on performing a number of simulation retrials when the process enters regions of the state space where the chance of occurrence of the rare event is higher. The paper analyzes its efficiency, showing formulas for the variance of the estimator and for the gain obtained with respect to crude simulation, as well as for the parameter values that maximize this gain. It also provides guidelines for achieving a high efficiency when it is applied. Emphasis is placed on the choice of the importance function, i.e., the function of the system state used for determining when retrials are made. Several examples on queuing networks and ultra reliable systems are exposed to illustrate the application of the guidelines and the efficiency achieved. KeywordsRare Event–Splitting–RESTART–Simulation–Performance–Reliability
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