Modeling and analysis of computer system availability
IBM Journal of Research and Development
Importance sampling for stochastic simulations
Management Science
A Unified Framework for Simulating Markovian Models of Highly Dependable Systems
IEEE Transactions on Computers
Importance sampling for the simulation of highly reliable Markovian systems
Management Science
Variance reduction in mean time to failure simulations
WSC '88 Proceedings of the 20th conference on Winter simulation
Stochastic approximation for Monte Carlo optimization
WSC '86 Proceedings of the 18th conference on Winter simulation
Simulation and analysis of highly reliable systems
Simulation and analysis of highly reliable systems
Bounded relative error in estimating transient measures of highly dependable non-Markovian systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficiency improvement and variance reduction
WSC '94 Proceedings of the 26th conference on Winter simulation
Fast simulation methods for highly dependable systems
WSC '94 Proceedings of the 26th conference on Winter simulation
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Probability in the Engineering and Informational Sciences
ANSS '06 Proceedings of the 39th annual Symposium on Simulation
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Simple failure biasing is an importance-sampling technique used to reduce the variance of estimates of performance measures and their gradients in simulations of highly reliable Markovian systems. Although simple failure biasing yields bounded relative error for the performance measure estimate when the system is balanced, it may not provide bounded relative error when the system is unbalanced.In this article, we provide a characterization of when the simple failure-biasing method produces estimators of a performance measure and its derivatives with bounded relative error. We derive a necessary and sufficient condition on the structure of the system for when the performance measure can be estimated with bounded relative error when using simple failure biasing. Furthermore, a similar condition for the derivative estimators is established. One interesting aspect of the conditions is that it shows that to obtain bounded relative error, not only the most likely paths to system failure must be examined but also some secondary paths leading to failure as well. We also show by example that the necessary and sufficient conditions for a derivative estimator do not imply those for the performance measure estimator; i.e., it is possible to estimate a derivative more efficiently than the performance measure when using simple failure biasing.