Matrix-analytic methods : theory and applications : proceedings of the fourth international conference : Adelaide, Australia, 14-16 July 2002 / edited by Guy Latouche, Peter Taylor.

Includes bibliographical references.

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Matrix-analytic methods are fundamental to the analysis of a family of Markov processes rich in structure and of wide applicability. They are extensively used in the modelling and performance analysis of computer systems, telecommunication networks, network protocols and many other stochastic systems of current commercial and engineering interest. This volume deals with: (1) various aspects of the theory of block-structured Markov chains; (2) analysis of complex queueing models; and (3) parameter estimation and specific applications to such areas as cellular mobile systems, FS-ALOHA, the Internet and production systems.

Preface; Contents; Author Index; Organisers; Reviewers; Sponsors; A New Algorithm for Computing the Rate Matrix of GI/M/1 Type Markov Chains; 1 Introduction; 2 The Non-linear Programming Problem; 3 The New Algorithm; 4 Numerical Examples; References; Decay Rates of Discrete Phase-Type Distributions with Infinitely-Many Phases; 1 Introduction; 2 Phase-Type Distributions on a Finite Phase Space; 3 Phase-Type Distributions on a Countably-Infinite Phase Space; 4 Transition Matrices that represent Level Dependent QBDs; 5 Processes with Block Upper-Triangular Matrices.

6 Transition Matrices that represent Level Independent QBDs7 Transition Matrices that represent Level Independent Birth-and-Death Processes; 8 Examples; 9 Summary; Appendix A The Decay Rate Bound is Exact; References; Distributions of Reward Functions on Continuous-Time Markov Chains; 1 Introduction; 2 The Main Theorem; 3 Moment Formulas; 4 The Total Continuous Reward Distribution; References; A Batch Markovian Queue with a Variable Number of Servers and Group Services; 1 INTRODUCTION; 2 THE MATHEMATICAL MODEL; 3 THE STEADY STATE PROBABILITY VECTOR AT AN ARBITRARY EPOCH.

4 System Performance Measures5 The Stationary Waiting Time Distribution; 6 Numerical Examples; References; Further Results on the Similarity Between Fluid Queues and QBDs; 1 Introduction; 2 Background; 3 First Passage Probabilities; 4 Discretization and Interpretation; 5 Phase-type Representation; References; Penalised Maximum Likelihood Estimation of the Parameters in a Coxian Phase-Type Distribution; 1 Introduction; 2 The Distributions; 3 Examples; 4 Concluding Remarks; References; MAP/PH/1 Queues with Level-Dependent Feedback and Their Departure Processes; 1 Introduction.

2 Notation for the MAP/PH/1 feedback queue3 Approximating the departure process from a MAP/PH/1 feedback queue; 4 Some numerical examples; 5 Summary; Appendix A Tandem queue processes; References; A Matrix Analytic Model for Machine Maintenance; 1 Introduction; 2 Matrix analytic models for one and two production lines; 3 Numerical examples; 4 Discussion and Conclusions; References; A Linear Program Approach to Ergodicity of M/G/1 Type Markov Chains with a Tree Structure; 1 Introduction; 2 Markov Chain of Matrix M/G/l Type with a Tree Structure; 3 Three Existing Approaches to Ergodicity.

4 Linear Programs for Ergodicity Conditions5 Computational Details; 6 Numerical Examples; References; Matrix Geometric Solution of Fluid Stochastic Petri Nets; 1 Introduction; 2 Definitions and Notations; 3 Analysis; 4 Matrix geometric solution techniques; 5 A numerical example; 6 Conclusions; References; A Markovian Point Process Exhibiting Multifractal Behavior and Its Application to Traffic Modeling; 1 Introduction; 2 Multiscale analysis; 3 The proposed MAP structure; 4 Numerical analysis; 5 Conclusion; References; Convergence of the Ratio ""Variance Over Mean"" in the IPhP3.

English.

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