Physical Interpretations for Quasi-Birth-and-Death Process Algorithms
Keywords:
Matrix quadratic equations, matrix-analytic methods, quasi-birth-and-death processes, Newton's iterations.Abstract
The solution of polynomial matrix equations lies at the heart of the analysis of quasi-birth-and-death processes (QBDs), fluid queues and other random walks on a strip in the plane. Many algorithms have been proposed (and are still being proposed) to solve these equations. In order to improve upon one algorithm, or to understand the qualities which make one better than another, it often helps to use our physical understanding of the behaviour of the process. We illustrate this here by considering algorithms for the solution of the basic quadratic equation for QBDs, with a particular reference to Newton's Method.
