Linear Algebra, Markov Chains, and Queueing Models

1. Front Matter

   Pages i-xvi

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2. Perturbation Theory and Error Analysis

   1. Error Bounds for the Computation of Null Vectors with Applications to Markov Chains

      • Jesse L. Barlow

      Pages 1-12

   2. The Influence of Nonnormality on Matrix Computations

      • Françoise Chatelin

      Pages 13-27

   3. Componentwise Error Analysis for Stationary Iterative Methods

      • Nicholas J. Higham, Philip A. Knight

      Pages 29-46

   4. The Character of a Finite Markov Chain

      • Carl D. Meyer

      Pages 47-58

   5. Gaussian Elimination, Perturbation Theory, and Markov Chains

      • G. W. Stewart

      Pages 59-69

3. Iterative Methods

   1. Algorithms for Periodic Markov Chains

      • François Bonhoure, Yves Dallery, William J. Stewart

      Pages 71-88

   2. Iterative Methods for Queueing Networks with Irregular State-Spaces

      • Raymond H. Chan

      Pages 89-109

   3. Analysis of P-Cyclic Iterations for Markov Chains

      • Apostolos Hadjidimos, Robert J. Plemmons

      Pages 111-124

   4. Iterative Methods for Finding the Stationary Vector for Markov Chains

      • Dianne P. O’leary

      Pages 125-136

   5. Local Convergence of (Exact and Inexact) Iterative Aggregation

      • Daniel B. Szyld

      Pages 137-143

4. Queueing Theory and Applications

   1. Automated Generation and Analysis of Markov Reward Models Using Stochastic Reward Nets

      • Gianfranco Ciardo, Alex Blakemore, Philip F. Chimento Jr., Jogesh K. Muppala, Kishor S. Trivedi

      Pages 145-191

   2. Means and Variances in Markov Reward Systems

      • Winfried K. Grassmann

      Pages 193-204

   3. A Direct Algorithm for Computing the Stationary Distribution of a P-Cyclic Markov Chain

      • Daniel P. Heyman

      Pages 205-209

   4. Approximate Analysis of a Discrete-Time Queueing Model of the Shared Buffer ATM Switch

      • S. Hong, H. G. Perros, H. Yamashita

      Pages 211-229

   5. Algorithms for Infinite Markov Chains with Repeating Columns

      • Guy Latouche

      Pages 231-265

   6. CRAY-2 Memory Organization and Interprocessor Memory Contention

      • Robert W. Numrich

      Pages 267-294

This IMA Volume in Mathematics and its Applications LINEAR ALGEBRA, MARKOV CHAINS, AND QUEUEING MODELS is based on the proceedings of a workshop which was an integral part of the 1991-92 IMA program on "Applied Linear Algebra". We thank Carl Meyer and R.J. Plemmons for editing the proceedings. We also take this opportunity to thank the National Science Founda­ tion, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. xi PREFACE This volume contains some of the lectures given at the workshop Lin­ ear Algebra, Markov Chains, and Queueing Models held January 13-17, 1992, as part of the Year of Applied Linear Algebra at the Institute for Mathematics and its Applications. Markov chains and queueing models play an increasingly important role in the understanding of complex systems such as computer, communi­ cation, and transportation systems. Linear algebra is an indispensable tool in such research, and this volume collects a selection of important papers in this area. The articles contained herein are representative of the underlying purpose of the workshop, which was to bring together practitioners and re­ searchers from the areas of linear algebra, numerical analysis, and queueing theory who share a common interest of analyzing and solving finite state Markov chains. The papers in this volume are grouped into three major categories-perturbation theory and error analysis, iterative methods, and applications regarding queueing models.

• Matrix
• algebra
• linear algebra
• matrix theory

• Mathematics Department, North Carolina State University, Raleigh, USA

  Carl D. Meyer

• Department of Mathematics and Computer Science, Wake Forest University, Winston-Salem, USA

  Robert J. Plemmons

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