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General conditions for bounded relative error in simulations of highly reliable Markovian systems
  • M. Nakayama
  • Mathematics
    Advances in Applied Probability
  • 1 September 1996
We establish a necessary condition for any importance sampling scheme to give bounded relative error when estimating a performance measure of a highly reliable Markovian system. Also, a class of
Confidence Intervals for Quantiles Using Sectioning When Applying Variance-Reduction Techniques
The asymptotic validity of the sectioning CI for importance sampling and control variates is established, and the proofs rely on first showing that the corresponding quantile estimators satisfy a Bahadur representation, which has been done in prior work.
Fast Simulation of Highly Dependable Systems with General Failure and Repair Processes
An approach for simulating models of highly dependable systems with general failure and repair time distribution is described and it is shown how the technique can be applied to systems with redundant components and/or periodic maintenance.
Two-stage multiple-comparison procedures for steady-state simulations
Two-stage procedures for construction of absolute- and relative-width confidence intervals are presented, and the techniques developed here extend to other multiple-comparison procedures such as unconstrained MCB, multiple comparisons with a control, and all-pairwise comparisons.
Statistical analysis of simulation output
We discuss methods for statistically analyzing the output from stochastic discrete-event or Monte Carlo simulations. Terminating and steady-state simulations are considered.
On finite exponential moments for branching processes and busy periods for queues
Using a known fact that a Galton–Watson branching process can be represented as an embedded random walk, together with a result of Heyde (1964), we first derive finite exponential moment results for
Techniques for fast simulation of models of highly dependable systems
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 are reviewed.
Confidence intervals for quantiles when applying variance-reduction techniques
This article develops asymptotically valid confidence intervals for quantiles estimated via simulation using variance-reduction techniques (VRTs) within a general framework for VRTs, which it is shown includes importance sampling, stratified sampling, antithetic variates, and control variates.
A Markovian Dependability Model with Cascading Failures
A recursive algorithm generating all possible trees corresponding to a given transition, along with an experimental study of an implementation of the algorithm on two examples, highlight the effects of cascading on the dependability of the models.
Modeling and analysis of system dependability using the System Availability Estimator
This paper reviews the System Availability Estimator (SAVE) modeling program package and provides software demonstrations using both fast simulation techniques using importance sampling and numerical solution methods.