Bounding Availability of Repairable Systems
IEEE Transactions on Computers
Computing bounds on steady state availability of repairable computer systems
Journal of the ACM (JACM)
Bounding steady-state availability models with group repair and phase type repair distributions
IPDS '98 Proceedings of the third IEEE international performance and dependability symposium on International performance and dependability symposium
An Algorithmic Approach to Stochastic Bounds
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
Storage Alternatives for Large Structured State Spaces
Proceedings of the 9th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
Bounding asymptotic dependability and performance measures
IPDS '96 Proceedings of the 2nd International Computer Performance and Dependability Symposium (IPDS '96)
Bounding transient and steady-state dependability measures through algorithmic stochastic comparison
ACM SIGMETRICS Performance Evaluation Review
Bounds based on lumpable matrices for partially ordered state space
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Perfect simulation and monotone stochastic bounds
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Stochastic Bounds for Partially Generated Markov Chains: An Algebraic Approach
EPEW '08 Proceedings of the 5th European Performance Engineering Workshop on Computer Performance Engineering
Analysis and Optimization of Aggregation in a Reconfigurable Optical ADD/DROP Multiplexer
NEW2AN '09 and ruSMART '09 Proceedings of the 9th International Conference on Smart Spaces and Next Generation Wired/Wireless Networking and Second Conference on Smart Spaces
Censoring Markov chains and stochastic bounds
EPEW'07 Proceedings of the 4th European performance engineering conference on Formal methods and stochastic models for performance evaluation
Approximate aggregation of Markovian models using alternating least squares
Performance Evaluation
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Markov chains and rewards have been widely used to evaluate performance, dependability and performability characteristics of computer systems and networks. Despite considerable works, the numerical analysis of Markov chains to obtain transient or steady-state distribution is still a difficult problem when the chain is large or the eigenvalues badly distributed. Thus bounding techniques have been proposed for long to analyze steady-state distribution. Here, we show how to bound some dependability characteristics such as steady-state and point availability using an algorithmic approach. The bound is based on stochastic comparison of Markov chains but it does not use sample-path arguments. The algorithm builds a lumped Markov chain whose steady-state or transient distributions are upper bounds in the strong stochastic sense of the exact distributions. In this paper, the implementation of algorithm is detailed and we show some numerical results. We also show how we can avoid the generation of the state space and the transition matrix to model chains with more than 1010 states.