Bounding Availability of Repairable Systems
IEEE Transactions on Computers
Computing bounds on steady state availability of repairable computer systems
Journal of the ACM (JACM)
Bounds for quasi-lumpable Markov chains
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
Numerical Analysis of Superposed GSPNs
IEEE Transactions on Software Engineering - Special issue: best papers of the sixth international workshop on Petri nets and performance models (PNPM'95)
Efficient descriptor-vector multiplications in stochastic automata networks
Journal of the ACM (JACM)
Structured analysis approaches for large Markov chains
Applied Numerical Mathematics
Bound Computation of Dependability and Performance Measures
IEEE Transactions on Computers
Refinable Bounds for Large Markov Chains
IEEE Transactions on Computers
Hierarchical Structuring of Superposed GSPNs
IEEE Transactions on Software Engineering
On Bounds for Token Probabilities in a Class of Generalized Stochastic Petri Nets
PNPM '89 The Proceedings of the Third International Workshop on Petri Nets and Performance Models
Analysis of Large Markovian Models by Parts. Applications to Queueing Network Models
Messung, Modellierung und Bewertung von Rechensystemen, 3. GI/NTG-Fachtagung
INFORMS Journal on Computing
An improved method for bounding stationary measures of finite Markov processes
Performance Evaluation - Performance 2005
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
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A method to bound stationary distributions of large Markov chains resulting from networks of stochastic automata is presented. It combines the concepts for bounding the stationary distribution using eigenvector polyhedra with the exploitation of the specific structure of Markov chains resulting from stochastic automata networks. The quality of the bounds depends on the coupling between automata. Three consecutive steps of the method are presented. In the first step bounds are computed using information about single automata in isolation. Bounds for single automata are refined in a second step by considering the environment of an automaton given by the other automata in the network. In a third step, bounds are further improved using a disaggregation step. By means of two small examples it is shown that the method yields tight bounds for loosely coupled automata and that the approach is extremely efficient compared to other bounding methods, let alone compared to an exact numerical analysis.