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Speaker: Professor Peter Taylor, The University of Melbourne Date: Thursday, February 6 2025 Time: 22:00 Italian time (!!) Title: The Role of Physical Understanding in Matrix-Analytic Methods

Abstract: Since Marcel Neuts first showed that Markov chains of GI/M/1 type have a matrix-geometric stationary distribution in the 1970s and 1980s, the interplay between analytic properties and physical interpretation 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 equations involving matrix power series, 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. I shall discuss the physical interpretation of matrix-analytic algorithms that have been proposed for analysing block-structured Markov additive models.