A5001888075- Simulation Techniques and Applications
- Probability and Risk Models
- Statistical Methods and Inference
- Advanced Queuing Theory Analysis
- Statistical Distribution Estimation and Applications
- Probabilistic and Robust Engineering Design
- Advanced Statistical Process Monitoring
- Reliability and Maintenance Optimization
- Software Reliability and Analysis Research
- Statistical Methods and Bayesian Inference
- Financial Risk and Volatility Modeling
- Risk and Safety Analysis
- Insurance, Mortality, Demography, Risk Management
- Markov Chains and Monte Carlo Methods
- Mathematical Approximation and Integration
- Risk and Portfolio Optimization
- Bayesian Methods and Mixture Models
- Stochastic processes and statistical mechanics
- Nuclear reactor physics and engineering
- Statistical Methods in Clinical Trials
- Advanced Mathematical Physics Problems
- Nonlinear Waves and Solitons
- Credit Risk and Financial Regulations
- Spreadsheets and End-User Computing
- Advanced Database Systems and Queries
New Jersey Institute of Technology
2015-2024
IBM Research - Thomas J. Watson Research Center
1992-2005
IBM (United States)
1993-2002
Stanford University
2002
University of the Witwatersrand
1991-1999
Cascading failures present severe threats to power grid security, and thus vulnerability assessment of grids is significant importance. Focusing on analytic methods, this paper reviews the state art methods in context cascading failures. These are based steady-state modeling or high-level probabilistic modeling. The impact emerging technologies including phasor technology, high-performance computing techniques, visualization techniques then addressed, future research directions presented.
Quantiles, which are also known as values-at-risk in finance, frequently arise practice measures of risk. This article develops asymptotically valid confidence intervals for quantiles estimated via simulation using variance-reduction techniques (VRTs). We establish our results within a general framework VRTs, we show includes importance sampling, stratified antithetic variates, and control variates. Our method verifying asymptotic validity is to first demonstrate that quantile estimator...
With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design operation is becoming more crucial. Realistic models such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts designers turn simulation evaluate these models. However, accurate estimation dependability measures requires that frequently observes system failures, which rare events in systems. This renders ordinary...
We develop confidence intervals (CIs) for quantiles when applying variance-reduction techniques (VRTs) and sectioning. Similar to batching, sectioning partitions the independent identically distributed (i.i.d.) outputs into nonoverlapping batches computes a quantile estimator from each batch. But rather than centering CI at average of estimators across batches, as in centers overall based on all outputs. A similar modification is made sample variance, which used determine width CI. establish...
Quantiles are often used to measure risk of stochastic systems. We examine quantile estimators obtained using simulation with Latin hypercube sampling (LHS), a variance-reduction technique that efficiently extends stratified higher dimensions and produces negatively correlated outputs. consider single-sample LHS (ssLHS), which minimizes the variance can be from LHS, also replicated (rLHS). develop consistent estimator asymptotic ssLHS estimator’s central limit theorem, enabling us provide...
Necessary conditions for the existence of compressive solitary-wave solutions a partial differential equation derived by Scott and Stevenson (1986) which describes two-phase fluid flow in medium compacting under gravity are derived. It is shown that to exist satisfy certain boundary it necessary n=m>1 where n m exponents power laws relating permeability viscosity solid matrix, respectively, voidage. The effect value on shape solitary wave investigated using existing analytical new numerical...
We develop a continuous-time Markov chain model of dependability system operating in randomly changing environment and subject to probabilistic cascading failures. A failure can be thought as rooted tree. The root is the component whose triggers cascade, its children are those components that root's immediately caused, next generation failures were caused by children, so on. amount unlimited. consider sense type i causes j fail simultaneously with given probability, all cascade being...
We establish a necessary condition for any importance sampling scheme to give bounded relative error when estimating performance measure of highly reliable Markovian system. Also, class methods is defined which we prove and sufficient the estimator. This probability measures includes all currently existing failure biasing in literature. Similar conditions derivative estimators are established.
An approach for simulating models of highly dependable systems with general failure and repair time distribution is described. The combines importance sampling event rescheduling in order to obtain variance reductions such rare simulations. nature allows a variety features commonly arising dependability modeling be simulated effectively. It shown how the technique can applied redundant components and/or periodic maintenance. For different distributions, effect maintenance period on...
Procedures for multiple comparisons with the best are investigated in context of steady-state simulation, whereby a number k different systems (stochastic processes) compared based upon their (asymptotic) means μ i ( = 1,2,…, ). The variances these (asymptotically stationary) processes assumed to be unknown and possibly unequal. We consider problem constructing simultaneous confidence intervals -max j≠i j i=1,2,…,k) which is known as (MCB). Our constrained contain 0, so called MCB intervals....
Suppose that there are $k \geq 2$ different systems (i.e., stochastic processes), where each system has an unknown steady-state mean performance and asymptotic variance. We allow for the variances to be unequal distributions of k different. consider problem running independent, single-stage simulations make multiple comparisons means systems. derive asymptotically valid (as run lengths tend infinity) simultaneous confidence intervals following problems: all pairwise means, contrasts, with a...
This paper discusses the application of likelihood ratio gradient estimator to simulations large Markovian models highly dependable systems. Extensive empirical work, as well some mathematical analysis small dependability models, suggests that (in this model setting) estimators are not significantly more noisy than estimates performance measures themselves. The also implementation issues associated with estimation, theoretical complements technique continuous-time Markov chains.
Randomized quasi-Monte Carlo methods have been introduced with the main purpose of yielding a computable measure error for approximations through implicit application central limit theorem over independent randomizations. But to increase precision given computational budget, number randomizations is usually set small value so that large points are used from each randomized low-discrepancy sequence benefit fast convergence rate Carlo. While has previously established specific but...
An approach to simulating models of highly dependable systems with general failure and repair time distributions is described. The combines importance sampling event rescheduling in order obtain variance reduction such rare simulations. nature allows effective simulation a variety features commonly arising dependability modeling. For example, it shown how the technique can be applied periodic maintenance. effects on steady-state availability maintenance period different are explored. Some...
Simple failure biasing is an importance-sampling technique used to reduce the variance of estimates performance measures and their gradients in simulations highly reliable Markovian systems. Although simple yields bounded relative error for measure estimate when system balanced, it may not provide unbalanced. In this article, we a characterization failure-biasing method produces estimators its derivatives with error. We derive necessary sufficient condition on structure can be estimated...
We establish a necessary condition for any importance sampling scheme to give bounded relative error when estimating performance measure of highly reliable Markovian system. Also, class methods is defined which we prove and sufficient the estimator. This probability measures includes all currently existing failure biasing in literature. Similar conditions derivative estimators are established.
We propose some new two-stage stopping procedures to construct absolute-width and relative-width confidence intervals for a simulation estimator of the steady-state mean stochastic process. The are based on method standardized time series proposed by Schruben Stein's sampling scheme. prove that our give rise asymptotically valid (as prescribed length interval approaches zero size first stage grows infinity). sole assumption required is process satisfy functional central limit theorem.
We discuss the estimation of derivatives a performance measure using likelihood ratio method in simulations highly reliable Markovian systems. compare difficulties estimating and its partial with respect to component failure rates as tend 0 repair remain fixed. first consider case when quantities are estimated naive simulation; i.e., no variance reduction technique is used. In particular, we prove that limit, some can be accurately itself. This result particular interest light somewhat...
This paper reviews the System Availability Estimator (SAVE) modeling program package. SAVE is used to construct and analyze models of computer communication systems dependability. The language consists a few constructs for describing components in system, their failure repair characteristics, interdependencies between components, conditions on individual system be considered available. parses an input file creates Markov chain model. For small numerical solution methods can used, but larger...
We discuss methods for statistically analyzing the output from stochastic discrete-event or Monte Carlo simulations. Terminating and steady-state simulations are considered.
Using a known fact that Galton–Watson branching process can be represented as an embedded random walk, together with result of Heyde (1964), we first derive finite exponential moment results for the total number descendants individual. We use this basic and simple to prove analogous population size at time t by in age-dependent process. This has applications justifying interchange expectation derivative operators simulation-based estimation generalized semi-Markov processes. Next, using show...
We describe an extension procedure for constructing new standardized time series procedures from existing ones. The approach is based on averaging over sample paths obtained by permuting path segments. Analytical and empirical results indicate that improves methods. compare to alternative known as batching. demonstrate the method applying it estimators maximum area of a normalized path.