Conditional steady-state bounds for a subset of states in Markov chains

Authors:
Tuǧrul Dayar;Nihal Pekergin;Sana Younès
Affiliations:
Bilkent University, Ankara, Turkey;Université de Versailles-St.Quentin, Versailles, France and Centre Marin Mersenne Université Paris, Paris, France;Université de Versailles-St.Quentin, Versailles, France
Venue:
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Year:
2006

Citing 3
Cited 2

Bounds for the Positive Eigenvectors of Nonnegative Matrices and for their Approximations by Decomposition

Journal of the ACM (JACM)
Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems

SIAM Review
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)

Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)

Stochastic Bounds for Partially Generated Markov Chains: An Algebraic Approach

EPEW '08 Proceedings of the 5th European Performance Engineering Workshop on Computer Performance Engineering
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

Quantified Score

Hi-index	0.00

Visualization

Abstract

The problem of computing bounds on the conditional steady-state probability vector of a subset of states in finite, ergodic discrete-time Markov chains (DTMCs) is considered. An improved algorithm utilizing the strong stochastic (st-)order is given. On standard benchmarks from the literature and other examples, it is shown that the proposed algorithm performs better than the existing one in the strong stochastic sense. Furthermore, in certain cases the conditional steady-state probability vector of the subset under consideration can be obtained exactly.