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- W1540867392 abstract "In this chapter, we restrict ourselves to the computation of the steady-state probability vector of ergodic Markov chains. Most of the literature on solution techniques of Markov chains assumes ergodicity of the underlying model. A comprehensive source on algorithms for steady-state solution techniques is the book by Stewart. To determine the steady-state probabilities of finite Markov chains, three different approaches for the solution of a linear system of the form 0 = xA are commonly used: direct or iterative numerical methods and techniques that yield closed-form results. Both types of numerical, methods have merits of their own. Whereas direct methods yield exact results, iterative methods are generally more efficient, both in time and space. Disadvantages of iterative methods are that for some of these methods no guarantee of convergence can be given in general and that determination of suitable error bounds for termination of the iterations is not always easy. Since iterative methods are considerably more efficient in solving Markov chains, they are commonly used for larger models. For smaller models with fewer than a few thousand states, direct methods are reliable and accurate. Though closed-form results are highly desirable, they can be obtained for only a small class of models that have some structure in their matrix." @default.
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- W1540867392 date "1998-08-31" @default.
- W1540867392 modified "2023-09-30" @default.
- W1540867392 title "Steady‐State Solutions of Markov Chains" @default.
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- W1540867392 doi "https://doi.org/10.1002/0471200581.ch3" @default.
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