Hybrid reliability modeling of fault-tolerant computer systems
Computers and Electrical Engineering - Special issue: reliability and verification of computing systems
Calculating Cumulative Operational Time Distributions of Repairable Computer Systems
IEEE Transactions on Computers - The MIT Press scientific computation series
Simple bounds for queueing systems with breakdowns
Performance Evaluation
Journal of the ACM (JACM)
Bounding availability of repairable computer systems
SIGMETRICS '89 Proceedings of the 1989 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Probabilistic Verification of Communication Protocols
Proceedings of the IFIP WG6.1 Seventh International Conference on Protocol Specification, Testing and Verification VII
Efficient exploration of availability models guided by failure distances
Proceedings of the 1996 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Bound Computation of Dependability and Performance Measures
IEEE Transactions on Computers
An iterative bounding method for stochastic automata networks
Performance Evaluation
Computing Performance Bounds of Fork-Join Parallel Programs Under a Multiprocessing Environment
IEEE Transactions on Parallel and Distributed Systems
An Eclectic Survey of Bounding Methods for Markov Chain Models
MASCOTS '95 Proceedings of the 3rd International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems
MASCOTS '96 Proceedings of the 4th International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems
An improved method for bounding stationary measures of finite Markov processes
Performance Evaluation - Performance 2005
Bounding stationary results of Tandem networks with MAP input and PH service time distributions
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
A component-level path-based simulation approach for efficient analysis of large Markov models
WSC '05 Proceedings of the 37th conference on Winter simulation
Modeling, analysis, measurement and experimentation with the Tangram-II integrated environment
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Bounds based on lumpable matrices for partially ordered state space
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Generalized Class 𝒞 Markov Chains And Computation Of Closed-Form Bounding Distributions
Probability in the Engineering and Informational Sciences
On the Numerical Analysis of Inhomogeneous Continuous-Time Markov Chains
INFORMS Journal on Computing
EPEW'05/WS-FM'05 Proceedings of the 2005 international conference on European Performance Engineering, and Web Services and Formal Methods, international conference on Formal Techniques for Computer Systems and Business Processes
Mathematics of Operations Research
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One of the most important performance measures for computer system designers is system availability. Most often, Markov models are used in representing systems for dependability/availability analysis. Due to complex interactions between components and complex repair policies, the Markov model often has an irregular structure, and closed-form solutions are extremely difficult to obtain. Also, a realistic system model often has an unmanageably large state space and it quickly becomes impractical to even generate the entire transition rate matrix. In this paper, we present a methodology that can (i) bound the system steady state availability and at the same time, (ii) drastically reduce the state space of the model that must be solved. The bounding algorithm is iterative and generates a part of the transition matrix at each step. At each step, tighter bounds on system availability are obtained. The algorithm also allows the size of the submodel, to be solved at each step, to be chosen so as to accommodate memory limitations. This general bounding methodology provides an efficient way to evaluate dependability models with very large state spaces without ever generating the entire transition rate matrix.