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

0 0
 · 
0 Bookmarks
 · 
43 Views
  • Source
    [show abstract] [hide abstract]
    ABSTRACT: We consider a class of Markov chain models that includes the highly reliable Markovian systems (HRMS) often used to represent the evolution of multicomponent systems in reliability settings. We are interested in the design of efficient importance sampling (IS) schemes to estimate the reliability of such systems by simulation. For these models, there is in fact a zero-variance IS scheme that can be written exactly in terms of a value function that gives the expected cost-to-go (the exact reliability, in our case) from any state of the chain. This IS scheme is impractical to implement exactly, but it can be approximated by approximating this value function. We examine how this can be effectively used to estimate the reliability of a highly-reliable multicomponent system with Markovian behavior. In our implementation, we start with a simple crude approximation of the value function, we use it in a first-order IS scheme to obtain a better approximation at a few selected states, then we interpolate in between and use this interpolation in our final (second-order) IS scheme. In numerical illustrations, our approach outperforms the popular IS heuristics previously proposed for this class of problems. We also perform an asymptotic analysis in which the HRMS model is parameterized in a standard way by a rarity parameter ε, so that the relative error (or relative variance) of the crude Monte Carlo estimator is unbounded when ε→0. We show that with our approximation, the IS estimator has bounded relative error (BRE) under very mild conditions, and vanishing relative error (VRE), which means that the relative error converges to 0 when ε→0, under slightly stronger conditions.
    Annals of Operations Research 01/2011; 189:277-297. · 1.03 Impact Factor
  • Source
    [show abstract] [hide abstract]
    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
    12/2011: pages 509-547;
  • Source
    01/2010;

Full-text (2 Sources)

View
8 Downloads
Available from
Oct 16, 2013