``Introduction to the Numerical Solution of Markov Chains''

William J. Stewart

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Preface,   Organization
Table of Contents,   Ordering Information

Acknowledgments

I am indebted to the administration of North Carolina State University and to the faculty and staff of its Computer Science Department for their support of my efforts in writing this book and for providing all the necessary facilities that we all too often take for granted. Also, I am indebted to the administration and staff of IMAG, Informatique et Math\'{e}matiques Appliqu\'{e}es de Grenoble , France. During the 1993--94 academic year, they provided me with the yearlong refuge from teaching and administrative duties that allowed me the time to formulate my classroom notes into a coherent whole. I am most grateful to the National Science Foundation for their generous financial support of my research under a variety of grants dating back to 1979.

Many of my friends and colleagues have contributed to this book through collaborative research efforts, through technical or philosophical discussions of different parts of it, or simply through their encouragement. They will see their influence throughout this book. I am deeply indebted to them and offer them my sincere gratitude.

First, let me begin by expressing my thanks to the many teachers who have influenced me so profoundly throughout the years of my education. I was fortunate in that for a precious few years at St. Thomas's Secondary School, Belfast, I had the privilege of having the renowned Irish novelist, Michael McLaverty, as my mathematics teacher. My great regret is that it was only later in life that I came to understand and appreciate his influence on me. It was he, perhaps more than anyone else, who sent me skipping down the magical yellow brick road that is mathematics.

The influence of my M.Sc. and Ph.D. advisors on the work that is described in this book is second to none. Alan Jennings first introduced me to the matrix eigenvalue problem and to simultaneous iteration methods, while Tony Hoare introduced me to Markov chains and their application to the modelling of computer operating systems. These were the origins for the research in which I have been engaged for some twenty years. It is a pleasure to acknowledge their guidance and to thank them for it.

After completing my Ph.D. degree, I moved to France, where I fell under the influence of Erol Gelenbe, Jacques Lenfant, Jean-Pierre Verjus, and, somewhat later, Raymond Marie. I would like to thank all four for their support and encouragement during those early days. Since then I have had the good fortune to be associated with a large number of friends and colleagues, all of whom have had a profound effect on me and on my research. It would be impossible and perhaps inappropriate to try to list them all. Rather let me just single out a few from among the many. They include Don Bitzer, Pierre-Jacques Courtois, Yves Dallery, David McAllister, Carl Meyer, Arne Nilsson, Harry Perros, Bob Plemmons, Bernard Philippe, Brigitte Plateau, Guy Pujolle, Yousef Saad, Ken Sevcik, Pete Stewart, Sandy Stidham, Kishor Trivedi, and Mladen Vouk. To these, and to all my colleagues who have helped and encouraged me in my research, I offer my sincere thanks.

This book grew out of a graduate-level course on aspects of performance modelling that I taught at irregular intervals at North Carolina State University. It therefore follows, as surely as day follows night, that the students who enrolled in this course contributed significantly to its form and content. I am thankful to all of them for their patience and their input in this endeavor. Some of these students continued on to do M.Sc. or Ph.D. research projects with me and I thank them in particular. The intellectual and philosophical discussions that I have had in working with students everywhere has had a profound effect on the contents and organization of the book. These students include Hassan Allouba, Karim Atif, Francois Bonhoure, Wei-Lu Cao, Munkee Choi, Tugrul Dayar, Steve Dodd, Larry Hodges, Halim Kafeety, Rick Klevans, Kimon Kontovasilis, Bob Koury, Butch Lin, David Lin, David Michael, Blaise Sidje, Patricia Snyder, Wayne Stohs, Abderezak Touzene, and Wei Wu.

Among my students, Tugrul Dayar, Halim Kafeety, and Kimon Kontovasilis were exposed to preliminary versions of this text. They provided many helpful comments on one or more draft chapters. For this, I offer them a special word of gratitude. I also wish to single out Wei-Lu Cao for particular thanks for the wonderful job he did in meticulously reading through a final draft of the entire manuscript, searching for all kinds of errors, and making numerous corrections and suggestions for improvement.

I wish to express my profound thanks to my parents, William and Mary Stewart, for their constant encouragement and the selfless sacrifices that they made in allowing me, the eldest of their eight children, to pursue my education at a time when I would normally have been expected to contribute financially to the family budget. Without their farsightedness, this book would never have seen the light of day.

Last and most of all, I offer a special word of thanks to my wife, Kathie, and to our four children, Nicola, Stephanie, Kathryn, and William. Despite the numerous evenings and weekends devoted to writing this book and excursions near and far devoted to developing the material, they provided the loving family environment that afforded me the tranquility and peace of mind that made writing it possible. This book is dedicated to them.

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