Modeling and analysis of computer system availability
IBM Journal of Research and Development
Importance sampling for stochastic simulations
Management Science
Bounding Availability of Repairable Systems
IEEE Transactions on Computers
Analytical and simulation estimates of reliability for regenerative models
Systems Analysis Modelling Simulation
A Unified Framework for Simulating Markovian Models of Highly Dependable Systems
IEEE Transactions on Computers
Fast Simulation of Highly Dependable Systems with General Failure and Repair Processes
IEEE Transactions on Computers
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Bounded relative error in estimating transient measures of highly dependable non-Markovian systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Importance sampling for the simulation of highly reliable Markovian systems
Management Science
Fast simulation methods for highly dependable systems
WSC '94 Proceedings of the 26th conference on Winter simulation
Fast transient simulation of Markovian models of highly dependable systems
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Estimation of reliability and its derivatives for large time horizons in Markovian systems
WSC '93 Proceedings of the 25th conference on Winter simulation
Optimal importance sampling for quick simulation of highly reliable Markovian systems
WSC '93 Proceedings of the 25th conference on Winter simulation
Fast Simulation of Markov Chains with Small Transition Probabilities
Management Science
Perwez Shahabuddin, 1962--2005: A professional appreciation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Estimating the probability of a rare event over a finite time horizon
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Considerations of point-to-multipoint qos based route optimization using PCEMP
EUC'05 Proceedings of the 2005 international conference on Embedded and Ubiquitous Computing
Rare event simulation for highly dependable systems with fast repairs
Performance Evaluation
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We investigate fast simulation techniques for estimating the unreliability in large Markovian models of highly reliable systems for which analytical/numerical techniques are difficult to apply. We first show mathematically that for “small” time horizons, the relative simulation error, when using the importance sampling techniques of failure biasing and forcing, remains bounded as component failure rates tend to zero. This is in contrast to naive simulation where the relative error tends to infinity. For “large” time horizons where these techniques are not efficient, we use the approach of first bounding the unreliability in terms of regenerative-cycle-based measures and then estimating the regenerative-cycle-based measures using importance sampling; the latter can be done very efficiently. We first use bounds developed in the literature for the asymptotic distribution of the time to hitting a rare set in regenerative systems. However, these bounds are “close” to the unreliability only for a certain range of time horizons. We develop new bounds that make use of the special structure of the systems that we consider and are “close” to the unreliability for a much wider range of time horizons. These techniques extend to non-Markovian, highly reliable systems as long as the regenerative structure is preserved.