Performance of Communication Systems: A Model-Based Approach with Matrix-Geometric Methods

298 Pages·2001·7.155 MB·English

by  Alexander Ost (auth.)

Performance of Communication Systems
Springer-Verlag Berlin Heidelberg GmbH
ONLINE LIBRARY
Engineering
http://www.springer.de/engine/
Alexander Ost
Performance of
Communication Systems
A Model-Based Approach
with Matrix-Geometric Methods
, Springer
Alexander Ost
Ericsson Eurolab Germany
Ericsson Allee 1
52134 Herzogenrath
Germany
e-mail: [email protected]
D 82 (Diss. RWTH Aachen)
ISBN 978-3-642-07470-7
Cataloging-in-Publication Data applied for
Ost, Alexander:
Performance of communication systems : a model based evaluation with
matrix geometric methods / Alexander Ost.
Zugl.: Aachen, Techn. Hochsch., Diss. 2000
ISBN 978-3-642-07470-7 ISBN 978-3-662-04421-6 (eBook)
DOI 10.1007/978-3-662-04421-6
This work is subject to copyright. All rights are reserved, whether the whole or part oft he material is concemed,
specifically the rights oft ranslation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on
microfilm or in other ways, and storage in data banks. Duplication oft his publication or parts thereofis permitted
onlyunderthe provisions ofthe German Copyright Law ofSeptember 9, 1965, in its current version, and permission
for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under German
Copyright Law.
http.//www.springer.de
© Springer-Verlag Berlin Heidelberg 2001
Originally published by Springer-Verlag Berlin Heidelberg New York in 2001
Softcover reprint of the hardcover lst edition 2001
The use of general descriptive nanIes, registered names, trademarks,etc. in this publication does not imply, even
in the absence ofa specific statement, that such names are exempt from the relevant protective laws and regulations
and therefore free for general use.
Coverdesign: medio Technologies AG, Berlin
Typesetting: Camera- ready copy by author
°
SPIN: 10792251 62/3020 Printed on acid-free paper - 5 4 3 2 1
Abstract
This work aims at providing approaches to guide the design of modern com
munication networks. During the last decades, the size and the complexity
of communication networks increased substantially. Communication facilities
have become a major infrastructural factor, and the performance offered by
a network is of central interest. However, the evaluation of the performance
of today's communication networks is very difficult due to their size and
complexity. Although it is clearly possible to measure the performance of
one particular configuration, this provides no guidance in choosing among
alternative configurations prior to their actual deployment.
In this work, we therefore advocate a model-based approach, where math
ematical models of actual networks are analyzed to predict the performance
of a large number of different design alternatives. Clearly, these models must
be able to account for the key properties of the networks under investigation.
Our assessment of the modeling requirements is based on both theoretical
considerations and on practical experiences made in an industrial collabo
ration. The computational effort for investigating models that account for
all relevant network properties becomes quickly prohibitive, being the reason
why most approaches in this area resort to a very high level of abstraction.
This work aims to tackle this situation by employing a special class of
stochastic processes, so called quasi-birth-and-death (QBD) processes, for
modeling network nodes. While QBDs are related to conventional queueing
theoretic modeling approaches, they provide the flexibility to account for a
large amount of additional detail. Still, a number of very efficient, so-called
matrix-geometric solution methods for the analysis of these models exist, and
a thorough comparison of these approaches is performed in this work.
While QBDs combine a large degree of modeling expressiveness with effi
cient solution algorithms, their direct and manual specification is cumbersome
and error-prone. In this work, we therefore adopt a high-level modeling tech
nique which is based on the well-established stochastic Petri net formalism.
Our Petri net class, called infinite-state SPNs (iSPNs), is specifically tailored
towards generating QBDs; the equivalence of an iSPN-based specification
to the direct specification of QBDs is formally proven, and a suitable tool
environment is presented.
The applicability of the iSPN-based performance modeling framework
is then illustrated by performing several case studies in the areas of World
Wide-Web and TCP lIP interaction, ATM connection management, and mod
eling systems subject to self-similar traffic.
The last part of this work is dedicated to the development of a framework
for the analysis of a large number of interacting network nodes (each modeled
by an iSPN), thereby allowing to investigate models that are directly related
to the structure of modern communication networks. This is accomplished
by embedding the iSPN approach in a parametric decomposition framework.
Acknowledgements
This book is the result of my PhD studies at the Laboratory for Performance
Evaluation and Distributed Systems at the Aachen University of Technology
(RWTH Aachen), Germany.
In the first place I would like to thank my advisor Prof. Boudewijn
Haverkort for supervising this work. Without his excellent and broad back
ground in the performance evaluation area, this work would not have been
possible. His guiding and careful advice was the important foundation of my
work; with his open-minded and sound attitude, he created a research envi
ronment that can hardly be surpassed. I also thank Prof. Bernhard Walke
(RWTH Aachen, Communication Networks) for taking the co-advisorship
and providing valuable comments on this thesis.
Many thanks go to my colleague Henrik Bohnenkamp for being a pleasant
roommate over several years and for reviewing large parts of this work. I am
indebted to him and my colleagues Ramin Sadre and Rachid El Abdouni for
creating a cooperative and competent atmosphere that made the Department
for Performance Evaluation and Distributed Systems an enjoyable place to
be. Furthermore, I would like to thank Aad van Moorsel for hosting me during
my stay at Bell Labs and for providing valuable and detailed feedback on the
manuscript of this book. Thanks also go to Prof. lsi Mitrani (University of
Newcastle upon Tyne, UK) for reviewing parts of my work.
I gratefully acknowledge the German Research Council (DFG) for funding
large parts of my research by granting a scholarship in the graduate college
"Computer Science and Technology" at the RWTH Aachen; thanks also go to
the college's chairman Prof. Otto Spaniol (RWTH Aachen, Communication
and Distributed Systems).
Finally, I would like to thank my parents, who always encouraged me on
my way. I dedicate this work to them.
Table of Contents
Part I. Introduction and Motivation
1. Introduction.............................................. 3
2. Modern Telecommunication Networks.................... 9
2.1 Common Channel Signaling. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10
2.1.1 CCSN Objectives ................................. 11
2.1.2 Signaling System Number 7. . . . . . . . . . . . . . . . . . . . . . .. 11
2.2 Intelligent Networks .................................... 12
2.2.1 Service Provision. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13
2.2.2 The IN Conceptual Model. . . . . . . . . . . . . . . . . . . . . . . .. 15
2.2.3 Discussion....................................... 15
2.3 The TINA Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17
2.3.1 TINA and the IN Concept.. .. .... . . .. .. .. .. .. . . . .. 18
2.3.2 The TINA Computing Architecture. . . . . . . . . . . . . . . .. 19
2.3.3 Discussion....................................... 21
2.4 Guiding the Network Design Process. . . . . . . . . . . . . . . . . . . . .. 22
2.4.1 Impact of Network Architectures on Performance
Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23
2.4.2 Requirements.................................... 24
2.5 Summary and Concluding Remarks. . . . . . . . . . . . . . . . . . . . . .. 26
3. The View from Industry: First Modeling Approaches. . . .. 27
3.1 Modeling and Evaluation Requirements:
The Practitioner's View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28
3.2 A First Modeling Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 30
3.2.1 Model Description. . . . . . . . . . . ... . . . . . . . . . . . . . . . . .. 30
3.2.2 Model Evaluation. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. 32
3.3 Application Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35
3.3.1 System Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35
3.3.2 Analysis......................................... 38
3.4 Relation to Other Approaches. . . . . . . . . . . . . . . . . . . . . . . . . . .. 44
3.4.1 Single System Evaluation Approaches. . . . . . . . . . . . . .. 44
3.4.2 Approaches Dealing with the Mapping Problem. . . . .. 46
3.4.3 Discussion....................................... 47
X Table of Contents
3.5 Summary and Concluding Remarks. . . . . . . . . . . . . . . . . . . . . .. 47
Part II. Node Analysis
4. Quasi-Birth-and-Death Processes. . . . . . . . . . . . . . . . . . . . . . . .. 51
4.1 Definition............................................. 52
4.1.1 State Space and Transition Structure. . . . . . . . . . . . . .. 52
4.1.2 Generator Matrix and Steady-State Characterization 53
4.2 Matrix-Geometric Solution Methods ....... . . . . . . . . . . . . . .. 56
4.2.1 Preliminaries.................................... 56
4.2.2 The Successive Substitution (SS) Method. . . . . . . . . . .. 58
4.2.3 The Logarithmic Reduction (LR) Approach. . . . . . . . .. 59
4.2.4 Naoumov's Improved LR Algorithm ................ 61
4.3 Transform Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 63
4.3.1 The Cyclic Reduction Method ..................... 63
4.3.2 The Invariant Subspace Approach . . . . . . . . . . . . . . . . .. 64
4.3.3 The Spectral Expansion Method ................... 66
4.4 Non-Skip-Free QBDs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 72
4.4.1 Reduction to Standard QBD Processes. . . . . . . . . . . . .. 72
4.4.2 Approaches for Direct Solution. . . . . . . . . . . . . . . . . . . .. 75
4.5 Numerical Comparison of Solution Methods. . . . . . . . . . . . . . .. 76
4.5.1 Candidate Solution Algorithms. . . . . . . . . . . . . . . . . . . .. 77
4.5.2 The Model under Investigation. . . . . . . . . . . . . . . . . . . .. 78
4.5.3 Numerical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 79
4.5.4 Conclusion...................................... 93
4.6 QBD Extensions ....................................... 94
4.6.1 Approximate Analysis ............................ 94
4.6.2 Buffer Resets ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 96
4.6.3 Quasi-Stationary Solution . . . . . . . . . . . . . . . . . . . . . . . .. 98
4.6.4 Multi-Dimensional QBD Processes.. . . . . . . . . . . . . . . .. 99
4.7 Summary and Concluding Remarks ....................... 100
5. High-Level System Specification with iSPNs .............. 103
5.1 The iSPN Modeling Environment ......................... 103
5.1.1 High-Level Modeling Approaches ................... 104
5.1.2 Basic Idea and Related Approaches ................. 105
5.1.3 Formal Definition of iSPNs ........................ 106
5.1.4 An Example iSPN Model .......................... 109
5.2 Equivalence to QBD Markov chains ....................... 111
5.2.1 Preliminaries .................................... 111
5.2.2 The Simple Case:
Two Successive Submarking-Equivalent j-Sets ........ 113
5.2.3 The General Case: All iSPNs Lead to QBD Processes. 116
5.2.4 Coverage of all QBDs by iSPNs .................... 121
Table of Contents XI
5.3 Implementation Issues .................................. 125
5.3.1 Tightly Choosing jrnin ............................ 125
5.3.2 State Space Generation ........................... 130
5.3.3 Accounting for Immediate Transitions ............... 135
5.3.4 Modeling Batch Arrivals and Departures ............ 138
5.4 Extensions for Buffer Resets and Quasi-Stationary Models ... 139
5.5 Summary and Concluding Remarks ....................... 140
6. Application Examples: Node Analysis .................... 143
6.1 Connection Management for Video Traffic ................. 143
6.1.1 System Description ............................... 144
6.1.2 Model Development .............................. 145
6.1.3 Parameterization ................................. 146
6.1.4 Numerical Results ................................ 146
6.1.5 Conclusion ...................................... 153
6.2 WWW Traffic and TCP lIP Congestion Control ............ 153
6.2.1 System Description ............................... 154
6.2.2 Model Development .............................. 156
6.2.3 Parameterization ................................. 161
6.2.4 Numerical Results ................................ 164
6.2.5 Conclusion ...................................... 170
6.3 Accounting for Self-Similar Traffic ........................ 171
6.3.1 Self-Similar Stochastic Processes ................... 172
6.3.2 Self-Similar Traffic Models ......................... 174
6.3.3 Parameterization ................................. 178
6.3.4 Numerical Results ................................ 179
6.3.5 Conclusion ...................................... 181
6.4 Summary and Concluding Remarks ....................... 183
Part III. Network Analysis
7. Queueing Network Analysis Techniques ................... 187
7.1 Main Problems and Existing Work ........................ 188
7.1.1 Main Issues ...................................... 188
7.1.2 Parametric Decomposition Approaches .............. 190
7.1.3 Conclusion ...................................... 193
7.2 The Queueing Network Analyzer ......................... 194
7.2.1 Basic QNA ...................................... 195
7.2.2 Finite Buffers .................................... 200
7.2.3 From QNA Nodes to QBD Nodes .................. 204
7.2.4 Using QBDs to Improve QNA ...................... 206
7.2.5 Conclusion ...................................... 212
7.3 Embedding iSPNs ...................................... 212
7.3.1 Job Arrivals ..................................... 214
XII Table of Contents
7.3.2 Departure Process Derivation ...................... 216
7.3.3 Conclusion ...................................... 225
7.4 Splitting and Merging Traffic Streams ..................... 225
7.4.1 Splitting ........................................ 225
7.4.2 Merging ......................................... 227
7.4.3 Dealing With the Distributional Explosion ........... 228
7.4.4 Conclusion ...................................... 231
7.5 Summary and Concluding Remarks ....................... 233
8. Conclusions and Outlook .. ............................... 235
A. Linear Algebra and Probability Theory Primer ........... 239
A.l Polynomial Eigenvalue Problems ......................... 239
A.l.l Definition ............ . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
A.l.2 Linearization .................................... 239
A.l.3 Other Solution Approaches ........................ 243
A.2 Phase-Type Distributions ................................ 243
A.3 Markovian Arrival Processes ............................. 244
B. Tool Description .. ........................................ 247
B .1 User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
B.l.l Model Specification ............................... 247
B.l.2 Execution Control ................................ 252
B.l.3 Output Format .................................. 252
B.2 Implementation ........................................ 254
C. Model Specifications ...................................... 255
C.l An IN Model Based on MIGII Node Models ............... 255
C.2 A Checkpointing Transaction Processing System ........... 256
C.2.l Parameterization ................................. 257
C.2.2 Variable Definitions ............................... 257
C.2.3 Petri Net Specification ............................ 258
C.2.4 Definition of Reward-Based Measures ............... 259
C.3 Connection Management for Video Traffic ................. 260
C.3.l Variable Definitions ............................... 260
C.3.2 Petri Net Specification ............................ 260
C.3.3 Definition of Reward-Based Measures ............... 262
C.4 WWW Traffic and TCP lIP Congestion Control ............ 262
C.4.l Variable Definitions ............................... 262
C.4.2 Petri Net Specification ............................ 263
C.4.3 Definition of Reward-Based Measures ............... 266
C.5 Pseudo-Self-Similar Arrival Processes ..................... 266
C.5.l Variable Definitions ............................... 267
C.5.2 Petri Net Specification ............................ 267
C.5.3 Definition of Reward-Based Measures ............... 268