Matrix Analytic Methods: Theory and Applications : Proceedings of the Fourth International Conference : Adelaide, Australia, 14-16 July 2002

428 Pages·2002·16.15 MB·English

by  Latouche

MATRIX-ANALYTIC METHODS
THEORY AND APPLICATIONS
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PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE
MATRIX-ANALYTIC METHODS
THEORY AND APPLICATIONS
Adelaide, Australia 14-16 July 2002
edited by
Guy Latouche
Universite Libre de Bruxelles, Belgium
Peter Taylor
The University of Melbourne, Australia
V^fe World Scientific
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V
Preface
Matrix-analytic methods are fundamental to the analysis of a family
of Markov processes rich in structure and of wide applicability. They are ex
tensively 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.
Following the success of three previous conferences held in Flint
(Michigan), Winnipeg (Manitoba) and Leuven (Belgium), the Fourth Interna
tional Conference on Matrix-Analytic Methods in Stochastic Models was held
in Adelaide (Australia) in July 2002. The conference brought together the
top researchers in the field who presented papers dealing with new theoretical
developments and applications. This volume contains a selection of papers
presented at the conference. The papers were subject to a rigorous refereeing
process comparable to that which would be used by an international journal
in the field.
The papers fall into a number of different categories. Approximately
a third deals with various aspects of the theory of block-structured Markov
chains. They demonstrate how the specific structure of transition matrices
can be exploited. Another third of the papers deals with the analysis of
complex queueing models. The final third deals with parameter estimation
and specific applications to such areas as cellular mobile systems, FS-ALOHA,
the Internet and production systems.
Three leading researchers in the field were invited to present a lecture
to the conference: Masakiyo Miyazawa presented a paper on Markov additive
processes in the context of matrix-analytic methods, V. Ramaswami discussed
a number of applications and G.W. Stewart shared his vast experience on
numerical methods for block Hessenberg matrices. A paper based on Masakiyo
Miyazawa's talk is included in this volume.
In order to encourage young researchers to attend the conference,
the organisers implemented a streamlined procedure, accepting submissions
from students long after the general deadline. As a consequence, some late
submissions by students are not included in these proceedings. They were,
nevertheless, part of the official conference programme.
We would like to thank Kathryn Kennedy, David Green, Angela Hoff
mann and Michael Green for their help in preparing the manuscripts for final
publication. We acknowledge with gratitude financial assistance from several
sources, specifically, the Australian Mathematical Society, the Teletraffic Re
search Centre, the Department of Applied Mathematics at the University of
VI
Adelaide and the University of Adelaide itself.
Finally, it is a pleasure to acknowledge that the workshop could not
have been held had it not been for the active involvment of reviewers and the
authors who were all very good at respecting deadlines.
Guy Latouche
Peter Taylor
VII
Contents
Preface v
Author Index xi
Organisers xii
Reviewers xiii
Sponsors xiv
A New Algorithm for Computing the Rate Matrix of GI/M/1 Type
Markov Chains
Attahiru Sule Alfa, Bhaskar Sengupta, Tetsuya Takine and
Jungong Xue 1
Decay Rates of Discrete Phase-Type Distributions with
Infinitely-Many Phases
Nigel Bean and Bo Friis Nielsen 17
Distributions of Reward Functions on Continuous-Time Markov
Chains
Mogens Bladt, Beatrice Meini, Marcel F. Neuts and
Bruno Sericola 39
A Batch Markovian Queue with a Variable Number of Servers and
Group Services
Srinivas R. Chakravarthy and Alexander N. Dudin 63
Further Results on the Similarity Between Fluid Queues and QBDs
Ana da Silva Soares and Guy Latouche 89
Penalised Maximum Likelihood Estimation of the Parameters in a
Coxian Phase-Type Distribution
Malcolm Faddy 107
VIII
MAP/PH/1 Queues with Level-Dependent Feedback and Their
Departure Processes
David Green 115
A Matrix Analytic Model for Machine Maintenance
David Green, Andrew V. Metcalfe and David C. Swailes 133
A Linear Program Approach to Ergodicity of M/G/1 Type Markov
Chains with a Tree Structure
Qi-Ming He and Hui Li 147
Matrix Geometric Solution of Fluid Stochastic Petri Nets
Andrds Horvdth and Marco Gribaudo 163
A Markovian Point Process Exhibiting Multifractal Behavior and
Its Application to Traffic Modeling
Andrds Horvdth and Miklos Telek 183
Convergence of the Ratio "Variance Over Mean" in the IPhP3
Guy Latouche and Marie-Ange Remiche 209
Application of the Factorization Property to the Analysis of
Production Systems with a Non-Renewal Input, Bilevel Threshold
Control, Setup Time and Maintenance
Ho Woo Lee, No Ik Park and Jongwoo Jeon 219
A Constructive Method for Finding ^-Invariant Measures for
Transition Matrices of M/G/1 Type
Quan-Lin Li and Yiqiang Zhao 237
A Paradigm of Markov Additive Processes for Queues and Their
Networks
Masakiyo Miyazawa 265
Spectral Methods for a Tree Structure MAP
Shoichi Nishimura 291
Sojourn and Passage Times in Markov Chains
Claudia Nunes and Antonio Pacheco 311
IX
Matrix-Analytic Analysis of a MAP/PH/1 Queue Fitted to Web
Server Data
Alma Riska, Mark S. Squillante, Shun-Zheng Yu, Zhen Liu
and Li Zhang 333
Analysis of Parallel-Server Queues under Spacesharing and
Timesharing Disciplines
Jay Sethuraman and Mark S. Squillante 357
Robustness of FS-ALOHA
Benny van Houdt and Chris Blondia 381
Accurate Estimate of Spectral Radii of Rate Matrices of GI/M/1
Type Markov Chains
Qiang Ye 403
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