Updating the inverse of a matrix
SIAM Review
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
Bound Computation of Dependability and Performance Measures
IEEE Transactions on Computers
An iterative bounding method for stochastic automata networks
Performance Evaluation
Stochastic Well-Formed Colored Nets and Symmetric Modeling Applications
IEEE Transactions on Computers
Refinable Bounds for Large Markov Chains
IEEE Transactions on Computers
Reduced base model construction methods for stochastic activity networks
IEEE Journal on Selected Areas in Communications
Worst case analysis of batch arrivals with the increasing convex ordering
EPEW'06 Proceedings of the Third European conference on Formal Methods and Stochastic Models for Performance Evaluation
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A new method to compute bounds on stationary results of finite Markov processes in discrete or continuous time is introduced. The method extends previously published approaches using polyhedra of eigenvectors for stochastic matrices with a known lower and upper bound of their elements. Known techniques compute bounds for the elements of the stationary vector with respect to the lower bounds of the matrix elements and another set of bounds with respect to the upper bounds of matrix elements. The resulting bounds are usually not sharp, if lower and upper bounds for the elements are known. The new approach combines lower and upper bounds resulting in sharp bounds which are often much tighter than bounds computed using only one bounding value for the matrix elements.