The Physics of Matrix-Analytic Algorithms
by Peter Taylor
Abstract: Since Marcel Neuts first showed that Markov chains of GI/M/1 type have a matrix-geometric stationary distribution, the interplay between analyticâ€¨ properties and physical interpretations has played a major part in the development of matrix-analytic methods for stochastic models.
Most performance measures of interest in such models can be expressed in terms of the solutions of matrix or vector polynomial equations, which have to be solved numerically. Over the years, various iterative algorithms have been proposed for doing this. In order to establish convergence, and gain information about the speed of convergence, it is often helpful to think about the physical interpretation of the iterates.
In this talk, I shall discuss the physical interpretation of matrix-analytic algorithms that have been proposed for analyzing block-structured continuous-time Markov chains. If I have time, I shall also say something about algorithms for stochastic fluid models and multitype continuous-time branching processes.
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