Cybernetics and Systems Analysis
Fast Simulation of Unavailability of a Repairable System with a Bounded Relative Error of Estimate
Cybernetics and Systems Analysis
Fast Simulation of Unavailability of a Repairable System with a Bounded Relative Error of Estimate
Cybernetics and Systems Analysis
Combining importance sampling and temporal difference control variates to simulate Markov Chains
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Estimation of Stationary Loss Probability in a Queuing System with Recurrent Input Flows
Cybernetics and Systems Analysis
Probability in the Engineering and Informational Sciences
Alignment graph analysis of embedded discrete-time Markov Chains
CompSysTech '04 Proceedings of the 5th international conference on Computer systems and technologies
ANSS '06 Proceedings of the 39th annual Symposium on Simulation
Importance sampling in Markovian settings
WSC '05 Proceedings of the 37th conference on Winter simulation
Perwez Shahabuddin, 1962--2005: A professional appreciation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Rare events, splitting, and quasi-Monte Carlo
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Rare event simulation for highly dependable systems with fast repairs
Performance Evaluation
Hi-index | 0.01 |
Consider a finite-state Markov chain where the transition probabilities differ by orders of magnitude. This Markov chain has an "attractor state," i.e., from any state of the Markov chain there exists a sample path ofsignificant probability to the attractor state. There also exists a "rare set," which is accessible from the attractor state only by sample paths of very small probability. The problem is to estimate the probability that starting from the attractor state, the Markov chain hits the rare set before returning to the attractor state. Examples of this setting arise in the case of reliability models with highly reliable components as well as in the case of queueing networks with low traffic. Importance-sampling is a commonly used simulation technique for the fast estimation of rare-event probabilities. It involves simulating the Markov chain under a new probability measure that emphasizes the most likely paths to the rare set. Previous research focused on developing importance-sampling schemes for a special case of Markov chains that did not include "high-probability cycles." We show through examples that the Markov chains used to model many commonly encountered systems do have high-probability cycles, and existing importance-sampling schemes can lead to infinite variance in simulating such systems. We then develop the insight that in the presence of high-probability cycles care should be taken in allocating the new transition probabilities so that the variance accumulated over these cycles does not increase without bounds. Based on this observation we develop two importance-sampling techniques that have the bounded relative error property, i.e., the simulation run-length required to estimate the rare-event probability to a fixed degree of accuracy remains bounded as the event of interest becomes more rare.