Bounding availability of repairable computer systems
SIGMETRICS '89 Proceedings of the 1989 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
An improved method for bounding stationary measures of finite Markov processes
Performance Evaluation - Performance 2005
Mathematics of Operations Research
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
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A method to bound the steady-state solution of large Markov chains is presented. It integrates the concepts of eigenvector polyhedron and of aggregation and is iterative in nature.The bounds are obtained by considering a subset only of the system state space. This makes the method specially attractive for problems which are too large to be dealt with by traditional methods. The quality of the bounds depends on the locality of the system which is studied: when the system spends most of its time in a small subset of states, tight bounds can be obtained by considering this subset only. Finally, the bounds are refinable in the sense that the tightness of the bounds can be improved by enlarging the subset of states which is considered.The method is illustrated on a model of a repairable fault-tolerant system with 16 million states. Tight bounds on its availability are obtained by considering less than 0.1 percent of its state space.