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

A Model-Based Evaluation with Matrix-Geometric Methods

By: Alexander Ost

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Hardcover | 1 July 2009

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308 Pages

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This book is about efficient communication. The role of communication, as a means for the transmission of information among people, is one of the key factors driving the development of our civilization. There are numerous examples where new achievements in the communi- cations area had a crucial impact on our society. The human language can be considered as one of the first steps for the efficient delivery of informa- tion between people. Similarly, the influence of other milestones like written communication, bookprinting, telegraphy and the telephone and television system was essential. Facilities for quickly accessing existing information and for the fast delivery of information have become one of the most important economical factors nowadays. Clearly, fulfilling the ever-increasing demand for fast, cheap and reliable communications represents itself an important industry, leading to substan- tial technical achievements in this area. After only being used by an "infor- mation elite" in the beginning, developments like the telephone system and the Internet quickly spread and are now widely accepted, as witnessed by the ubiquitous presence of mobile phones and Internet applications like the World Wide Web.

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Introduction and Motivation
Introduction	p. 3
Modern Telecommunication Networks	p. 9
Common Channel Signaling	p. 10
CCSN Objectives	p. 11
Signaling System Number 7	p. 11
Intelligent Networks	p. 12
Service Provision	p. 13
The in Conceptual Model	p. 15
Discussion	p. 15
The TINA Approach	p. 17
TINA and the in Concept	p. 18
he TINA Computing Architecture	p. 19
Discussion	p. 21
Guiding the Network Design Process	p. 22
Impact of Network Architectures on Performance Analysis	p. 23
Requirements	p. 24
Summary and Concluding Remarks	p. 26
The View from Industry: First Modeling Approaches	p. 27
Modeling and Evaluation Requirements: The Practitioner's View	p. 28
A First Modeling Approach	p. 30
Model Description	p. 30
Model Evaluation	p. 32
Application Example	p. 35
System Description	p. 35
Analysis	p. 38
Relationto Other Approaches	p. 44
Single System Evaluation Approaches	p. 44
Approaches Dealing with the Mapping Problem	p. 46
Discussion	p. 47
Summaryand Concluding Remarks	p. 47
Node Analysis
Quasi-Birth-and-Death Processes	p. 51
Definition	p. 52
State Space and Transition Structure	p. 52
Generator Matrix and Steady-State Characterization	p. 53
Matrix-Geometric Solution Methods	p. 56
Preliminaries	p. 56
The Successive Substitution (SS) Method	p. 58
The Logarithmic Reduction (LR) Approach	p. 59
Naoumov's Improved LR Algorithm	p. 61
Transform Methods	p. 63
The Cyclic Reduction Method	p. 63
The Invariant Subspace Approach	p. 64
The Spectral Expansion Method	p. 66
Non-Skip-Free QBDs	p. 72
Reduction to Standard QBD Processes	p. 72
Approaches for Direct Solution	p. 75
Numerical Comparison of Solution Methods	p. 76
Candidate Solution Algorithms	p. 77
The Model under Investigation	p. 78
Numerical Results	p. 79
Conclusion	p. 93
QBD Extensions	p. 94
Approximate Analysis	p. 94
Buffer Resets	p. 96
Quasi-Stationary Solution	p. 98
Multi-Dimensional QBD Processes	p. 99
Summary and Concluding Remarks	p. 100
High-Level System Specification with iSPNs	p. 103
The iSPN Modeling Environment	p. 103
High-Level Modeling Approaches	p. 104
Basic Idea and Related Approaches	p. 105
Formal Definition of iSPNs	p. 106
An Examplei SPN Model	p. 109
Equivalence to QBD Markov chains	p. 111
Preliminaries	p. 111
The Simple Case: Two Successive Submarking-Equivalent j-Sets	p. 113
The General Case: All iSPNs Lead to QBD Processes	p. 116
Coverage of all QBDs by iSPNs	p. 121
Implementation Issues	p. 125
Tightly Choosing j_min	p. 125
State Space Generation	p. 130
Accounting for Immediate Transitions	p. 135
Modeling Batch Arrivals and Departures	p. 138
Extensions for Buffer Resets and Quasi-Stationary Models	p. 139
Summaryand Concluding Remarks	p. 140
Application Examples: Node Analysis	p. 143
Connection Management for Video Traffic	p. 143
System Description	p. 144
Model Development	p. 145
Parameterization	p. 146
Numerical Results	p. 146
Conclusion	p. 153
WWW Traffic and TCP/IP Congestion Control	p. 153
System Description	p. 154
Model Development	p. 156
Parameterization	p. 161
Numerical Results	p. 164
Conclusion	p. 170
Accounting for Self-Similar Traffic	p. 171
Self-Similar Stochastic Processes	p. 172
Self-Similar Traffic Models	p. 174
Parameterization	p. 178
Numerical Results	p. 179
Conclusion	p. 181
Summaryand Concluding Remarks	p. 183
Network Analysis
Queueing Network Analysis Techniques	p. 187
Main Problemsand Existing Work	p. 188
Main Issues	p. 188
Parametric Decomposition Approaches	p. 190
Conclusion	p. 193
The Queueing Network Analyzer	p. 194
Basic QNA	p. 195
Finite Buffers	p. 200
From QNA Nodes to QBD Nodes	p. 204
Using QBDS to Improve QNA	p. 206
Conclusion	p. 212
Embeddingi SPNs	p. 212
Job Arrivals	p. 214
Departure Process Derivation	p. 216
Conclusion	p. 225
Splitting and Merging Traffic Streams	p. 225
Splitting	p. 225
Merging	p. 227
Dealing With the Distributional Explosion	p. 228
Conclusion	p. 231
Summaryand Concluding Remarks	p. 233
Conclusions and Outlook	p. 235
Linear Algebra and Probability Theory Primer	p. 239
Polynomial Eigenvalue Problems	p. 239
Definition	p. 239
Linearization	p. 239
Other Solution Approaches	p. 243
Phase-Type Distributions	p. 243
Markovian Arrival Processes	p. 244
Tool Description	p. 247
User Interface	p. 247
Model Specification	p. 247
Execution Control	p. 252
Output Format	p. 252
Implementation	p. 254
Model Specifications	p. 255
An in Model Basedon M G
A Checkpointing Transaction Processing System	p. 256
Parameterization	p. 257
Variable Definitions	p. 257
Petri Net Specification	p. 258
Definition of Reward-Based Measures	p. 259
Connection Management for Video Traffic	p. 260
Variable Definitions	p. 260
Petri Net Specification	p. 260
Definition of Reward-Based Measures	p. 262
WWW Traffic and TCP/IP Congestion Control	p. 262
Variable Definitions	p. 262
Petri Net Specification	p. 263
Definition of Reward-Based Measures	p. 266
Pseudo-Self-Similar Arrival Processes	p. 266
Variable Definitions	p. 267
Petri Net Specification	p. 267
Definition of Reward-Based Measures	p. 268
Notation and Abbreviations	p. 269
Bibliography	p. 273
Index	p. 285
Table of Contents provided by Publisher. All Rights Reserved.

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

A Model-Based Evaluation with Matrix-Geometric Methods

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