Bounding Availability of Repairable Systems
IEEE Transactions on Computers
Stochastic Bounds on Execution Times of Parallel Programs
IEEE Transactions on Software Engineering
Bound Computation of Dependability and Performance Measures
IEEE Transactions on Computers
An Algorithmic Approach to Stochastic Bounds
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
CLOSED-FORM STOCHASTIC BOUNDS ON THE STATIONARY DISTRIBUTION OF MARKOV CHAINS
Probability in the Engineering and Informational Sciences
Computing Closed-Form Stochastic Bounds on Transient Distributions of Markov Chains
SAINT-W '05 Proceedings of the 2005 Symposium on Applications and the Internet Workshops
Model Checking of Continuous-Time Markov Chains by Closed-Form Bounding Distributions
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Generalized Class 𝒞 Markov Chains And Computation Of Closed-Form Bounding Distributions
Probability in the Engineering and Informational Sciences
A precedence PEPA model for performance and reliability analysis
EPEW'06 Proceedings of the Third European conference on Formal Methods and Stochastic Models for Performance Evaluation
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We consider a class of Markov chains known for its closed form transient and steady-state distributions. We show that some absorbing chains can be also seen as members of this class and we provide the closed form solution for their absorption time distributions. By constructing upper and lower bounding chains that belong to this particular class one can easily compute both lower and upper bounds for absorption time distribution of an arbitrary absorbing Markov chain. We provide a new algorithm for the construction of bounding chains from this class and we show a possible application of these bounds.