Stochastic Discrete Event Systems

Modeling, Evaluation, Applications

By: Armin Zimmermann

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Hardcover | 2 October 2007

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408 Pages

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24.13 x 15.88 x 2.54

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Armin Zimmermann delivers a coherent and comprehensive overview on modeling with and quantitative evaluation of SDES. An abstract model class for SDES is presented as a pivotal unifying result. Several important model classes, including queuing networks, Petri nets and automata, are detailed together with their formal translation into this abstract model class. Standard and recently developed algorithms for the performance evaluation, optimization and control of SDES are presented in the context of the abstract model class. The necessary software tool support is also covered. The book is completed with nontrivial examples from areas like manufacturing control, performance of communication systems, and supply-chain management, highlighting the application of the techniques presented.

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Introduction	p. 1
Stochastic Discrete Event Systems	p. 2
Applications and Goals of Modeling	p. 4
Overview of Topics	p. 5
Notation and Selected Background	p. 9
Modeling
A Unified Description for Stochastic Discrete Event Systems	p. 17
Informal Description	p. 18
Static Model Definition	p. 19
Dynamic Behavior of Stochastic Discrete Event Systems	p. 23
Rules for a Behavioral Definition	p. 24
The Stochastic Process Defined by an SDES	p. 26
Measuring the Performance of SDES	p. 36
Reward Variable Specification	p. 37
Derivation of Reward Variables	p. 40
Stochastic Timed Automata	p. 45
Informal Introduction	p. 46
Model Class Definition	p. 48
Automata as SDES	p. 49
UML Statecharts	p. 51
Transformation of Statecharts into Stochastic Petri Nets	p. 57
States	p. 58
Transitions	p. 59
A Transformation Algorithm	p. 62
Queuing Models	p. 65
Informal Introduction	p. 66
Model Class Definition	p. 71
Representing Queuing Networks as SDES	p. 73
Simple Petri Nets	p. 79
Introduction to Stochastic Petri Nets	p. 80
The Dynamic Behavior of a SPN	p. 88
A Formal Definition	p. 91
An SDES description of SPNs	p. 93
Colored Petri Nets	p. 99
Informal Introduction	p. 100
Token Types or Colors	p. 100
Places	p. 101
Arcs and Arc Inscriptions	p. 102
Transitions	p. 104
Model Hierarchy	p. 106
Syntax of Expressions	p. 107
Performance Measures of Colored Petri Nets	p. 108
On the Dynamic Behavior of Stochastic Colored Petri Nets	p. 109
Model Class Definition	p. 112
A SDES Description of Colored Petri Nets	p. 115
Variable-Free Colored Petri Nets	p. 118
An Example	p. 119
Model Class Definition	p. 121
Representing vfSCPNs as SDES	p. 122
Evaluation
Standard Quantitative Evaluation Methods for SDES	p. 127
Prerequisites	p. 130
Next-Event Time Advance Simulation	p. 133
Common Functions	p. 135
Estimation of Steady-State Measures	p. 138
Estimation of Transient Measures	p. 141
Numerical Analysis	p. 143
Reachability Graph Generation	p. 144
Continuous-Time Markov Chain Analysis	p. 147
Steady-State Analysis of Non-Markovian Models	p. 151
An Iterative Approximation Method	p. 157
Model Partitioning	p. 159
MIMO Graph-Based Aggregation	p. 159
The Initial MIMO Graph	p. 160
Aggregation of the MIMO Graph	p. 162
Translation into an Aggregated Petri Net	p. 164
Aggregation of vfSCPN Models	p. 165
Low-Level Systems and the Basic Skeleton	p. 166
Iterative Throughput Approximation	p. 166
Efficient Simulation of SDES Models	p. 169
Distributed Simulation of SDES Models	p. 170
Fine-Grained Model Partitioning	p. 173
A Logical Time Scheme for SDES Models with Immediate Actions and Priorities	p. 178
Discussion of Compound Simulation Time	p. 192
A Distributed Simulation Algorithm for SDES	p. 200
Simulation of Models with Rare Events	p. 213
The Restart Method	p. 214
Restart Simulation of SDES Models	p. 218
System Optimization	p. 223
Indirect Optimization	p. 224
Simulated Annealing	p. 226
Avoidance of Recomputations with a Cache	p. 228
A Two-Phase Optimization Strategy	p. 229
Preliminary Notes on Petri Nets	p. 231
Computation of Performance Bounds	p. 233
Approximate Derivation of Profit Values	p. 240
Model-Based Direct Control	p. 245
A Control Interpretation for Petri Nets	p. 246
An Example	p. 247
Model-Based Control of SDES	p. 249
Behavior of a Control-Interpreted SDES	p. 251
Software Tool Support	p. 253
TimeNET	p. 253
Supported Net Classes and Analysis Methods	p. 254
Software Architecture of TimeNET 4.0	p. 257
A Model-Class Generic Graphical User Interface	p. 261
Software Packages for Stochastic Discrete Event Systems	p. 262
Applications
Optimization of a Manufacturing System	p. 269
Types of Manufacturing Systems	p. 270
Typical Design and Optimization Issues	p. 271
Profit Function Elements	p. 273
A Manufacturing System Example	p. 276
A Generalized Stochastic Petri Net Model of the Example	p. 277
Profit Function Approximation Quality	p. 279
Results of the Two-Phase Optimization	p. 283
Communication System Performability Evaluation	p. 287
The Future European Train Control System ETCS	p. 288
Train Operation with Moving Blocks vs. Fixed Blocks	p. 290
Fixed Blocks	p. 291
Moving Blocks	p. 292
An ETCS Train Operation and Communication Model	p. 293
A Communication System Failure Model	p. 294
Alternative UML Statechart Model and its Transformation	p. 297
Derivation of a Condensed Failure Model	p. 300
A Moving Block Operation Model	p. 301
ETCS Performance Under Failures	p. 302
Supply Chain Performance Evaluation and Design	p. 307
A Supply Chain Logistics Example	p. 308
Colored Petri Net Model of the Supply Chain Example	p. 309
Customer Model	p. 310
Dealership Model	p. 312
Plant Model	p. 312
Vehicle Logistics Model	p. 313
Order-To-Delivery Time Evaluation and Improvement	p. 314
Popular Configuration Storage at the Dealership	p. 315
Order Scheduling at the Plant	p. 318
Truck Transport of Customer-Ordered Vehicles	p. 319
Model-Based Design and Control of a Production Cell	p. 325
A Production Cell Application Example	p. 325
Production Cell Modeling with vfSCPN	p. 327
Main Hierarchical Model	p. 327
Refined Model of the Rotary Picker Arm	p. 329
Integration of Work Plan Information	p. 330
Performance Evaluation	p. 332
Partition and Aggregation	p. 333
Performance Evaluation Results	p. 335
Model-Based Online Control	p. 337
Summary and Outlook	p. 341
Symbols and Abbreviations	p. 345
List of Figures	p. 353
List of Algorithms	p. 357
List of Tables	p. 359
References	p. 361
Index	p. 383
Table of Contents provided by Ingram. All Rights Reserved.

Stochastic Discrete Event Systems

Modeling, Evaluation, Applications

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