Contributions to applied probability : a thesis presented for the degree of Doctor of Science at Massey University, Albany, New Zealand

Abstract

This thesis covers a selection of published research papers, manuscripts and book chapters of the contributions that the author has made in the field of applied probability. The overall themes focus on the development of the theory and applications of Markov renewal processes, Markov chains, generalized matrix inverses, queueing models, and two dimensional renewal processes. The presentation highlights some strong interconnections between many of the topics including Markov renewal theory and Markov chains to queueing models; generalized matrix inverses to Markov chains and Markov renewal processes; and correlated bivariate processes as two-dimensional renewal processes and arrival processes to queueing models. Many of the research papers have appeared in the "Advances in Applied Probability" or in "Linear Algebra and its Applications" highlighting the strong interdisciplinary links and contributions that the author has made to the both the fields of Applied Probability and Linear Algebra.