Theory of Modeling and Simulation

674 Pages·2019·16.42 MB·English

by  Bernard P. Zeigler

Theory of
Modeling and Simulation
Discrete Event and Iterative System
Computational Foundations

Theory of
Modeling and Simulation
Discrete Event and Iterative System
Computational Foundations
Third Edition
Bernard P. Zeigler
University of Arizona
Tucson, USA
Alexandre Muzy
CNRS, I3S Laboratory
Universté Côte d’Azur
Nice Sophia Antipolis, France
Ernesto Kofman
FCEIA – Universidad Nacional de Rosario
CIFASIS – CONICET
Rosario, Argentina
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ThisisthethirdandrevisededitionofTheoryofModelingandSimulation,BernardP.Zeigler,publishedbyWileyInterscience,1976
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Contents
Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
Preface to the Third Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx1
Preface to the Second Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii
PART 1 BASICS: MODELING FORMALISMS AND SIMULATION
ALGORITHMS
CHAPTER 1 Introduction to Systems Modeling Concepts ........................ . 3
1.1 Systems Specification Formalisms ... .. .... ...... .. ........... ... .. . 4
1. 1.1 Relation to Object Orientation .............................. . 5
1.1.2 Evolution of Systems Formalisms ..... ............... .. .. ... . 6
1.1.3 Continuous and Discrete Formalisms ........................ . 7
1.1.4 Quantized Systems .......... .. ........... .. ............. . 8
1.1.5 Extensions of DEVS .. ......... .... ...................... . 9
1.2 Levels of System Knowledge ..................................... . 10
1.3 Introduction to the Hierarchy of Systems Specifications .. ........ ... .... . 12
1.4 The Specification Levels Informally Presented .... ..... . .. ....... ..... . 14
1.4.1 Observation Frame ...... . ........... .. .. ........... .. ... . 14
1.4.2 1/0 Behavior and 1/0 Function ... ............... ........... . 15
1.4.3 State Transition System Specification .... ..... ............... . 16
1. 4.4 Coupled Component System Specification ... .... .. ...... ... .. . 16
1.5 System Specification Morphisms: Basic Concepts ..................... . 17
1.6 Evolution of DEVS ............................................ . 20
1.7 Summary .................................................... . 23
1.8 Sources ... .... ........... .. ................................. . 23
Definitions, Acronyms, Abbreviations ........ .. ......... ........... . 24
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
CHAPTER 2 Framework for Modeling and Simulation .......................... . 27
2.1 The Entities of the Framework .................................... . 28
2.1.1 Source System . .... ... . . .. .. .. ...... . .. .. .. ....... .. .. . . 28
2.1.2 Experimental Frame .... ... . ..... ...... ... . ......... ... . . . 29
Objectives and Experimental Frames ......................... . 29
2.1.3 Model .............................. .................. . 31
2.1 .4 Simulator .... .......... ............. .................. . 32
2.2 Primary Relations Among Entities .. .... ... .... .. .. ................ . 32
2.2. I Modeling Relation: Validity .... ....... ............... ..... . 32
2.2.2 Simulation Relation: Simulator Correctness .......... ......... . 33
2.3 Other Important Relationships ... . . ... .... ...... .. ....... .... .. ... . 34
V
vi Contents
Modeling as Valid Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Experimental Frame - Model Relationships . . . . . . . . . . . . . . . . . . . . 35
2.4 Time 36
2.5 Historical Trace of V & V Streams ................................. . 36
2.5. l Informal V & V Concepts and Processes ....................... . 37
2.5.2 Theory-Based and Model-Driven Developments ................ . 38
2.5.3 Generic Methodology Processes and Best Practice Guides ......... . 38
2.6 Summary ............................. ........... ............ . 39
2.7 Sources ..................................................... . 39
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40
CHAPTER 3 Modeling Formalisms and Their Simulators .. ...................... . 43
Introduction .................................................. . 44
3.1 Discrete Time Models and Their Simulators .......................... . 44
3.1.1 Discrete Time Simulation ................................. . 46
3.1.2 Cellular Automata ....................................... . 46
3.1.3 Cellular Automaton Simulation Algorithms .................... . 48
3.1.4 Discrete Event Approach to CeUular Automaton Simulation ....... . 50
3.1.5 Switching Automata/Sequential Machines .. ........... .... .... . 51
3.1.6 Linear Discrete Time Networks and Their State Behavior ......... . 53
3.2 Differential Equation Models and Their Simulators .................... . 55
3.2.1 Linear ODE Models ..................................... . 57
3.2.2 Continuous System Simulation ............................. . 63
3.2.3 Euler's Methods ........................................ . 64
3.2.4 Accuracy of the Approximations .......... . .............. . .. . 65
3.2.5 Convergence of the Numerical Scheme ....................... . 68
3.2.6 Numerical Stability ...................................... . 70
3.2.7 One-Step Methods ...................................... . 72
3.2.8 Multi-Step Methods ..................................... . 74
3.2.9 Step Size Control ....................................... . 75
3.2.10 Stiff, Marginally Stable and Discontinuous Systems ............. . 78
3.3 Discrete Event Models and Their Simulators ......................... . 84
3.3.1 Introduction .................... ...... ................. . 84
3.3.2 Discrete Event Cellular Automata ........................... . 84
3.3.3 Discrete Event World Views ............................... . 87
Event Scheduling World View ....... ..... . ............ . .... . 87
3.4 Summary ..... ............................................... . 89
3.5 Sources ......... .. ...... ..... ........ ...... ................. . 90
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
CHAPTER 4 Introduction to Discrete Event System Specification {DEVS) . . . . . . . . . . . . . 93
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.2 Classic DEVS System Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.2.1 DEVS Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Passive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Contents vii
Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Binary Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Processor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l Ol
Ramp ................................................. 101
4.2.2 Classic DEVS With Ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2.3 Classic DEVS Coupled Models...... ................... . . . . . 104
Simple Pipeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Switch Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.3 Parallel DEVS System Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Processor With Buffer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3.l Parallel DEVS Coupled Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Simple Pipeline (Parallel DEVS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.4 Hierarchical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.5 Object-Oriented Implementations of DEVS: an Introduction . . . . . . . . . . . . . . 111
4.5.1 Structural Inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.6 DEVS and Hierarchy of System Specifications: Turing Machine Example . . . . 114
4.6.1 Turing Machine as a Modular Composition . . . . . . . . . . . . . . . . . . . . . 114
4.6.2 Tape System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.6.3 TM Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
TM Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.6.4 Simulation of the TM Coupled Model . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.6.5 Example of Simulation Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.6.6 Turing Machine Example of Hierarchy of System Specifications . . . . . 120
1/0 Frame at Level 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
1/0 Relation Observation at Level 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 121
1/0 Function Observation at Level 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 122
DEVS 1/0 System Specification at Level 4 . . . . . . . . . . . . . . . . . . . . . 122
4.6.7 Empirical Investigation of Halting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.7 Are DEVS State Sets Essentially Discrete? . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.9 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
CHAPTER 5 Hierarchy of System Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.1 Time Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.2 Segments and Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.2. l Piecewise Continuous Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5.2.2 Piecewise Constant Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5.2.3 Event Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Correspondence Between Piecewise Constant and Event Segments . . . 132
5.2.4 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.3 1/0 Observation Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.4 1/0 Relation Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
viii Contents
5.5 1/0 Function Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.6 1/0 System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.6.1 Going From System Structure to Behavior . . . . . . . . . . . . . . . . . . . . . 139
5.6.2 Time Invariant Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Example: Linear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.6.3 Special Cases: Input-Free and Memoryless Systems . . . . . . . . . . . . . . 143
Input-Free Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Memoryless Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.7 Multi-Component System Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.8 Network of System Specifications (Coupled Systems) . . . . . . . . . . . . . . . . . . . 146
5.8.1 Coupled System Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.8.2 Coupled System Specification at the Structured System Level . . . . . . . 148
5.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
CHAPTER 6 Basic Formalisms: DEVS, DESS, DTSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.1 Basic System Specification Formalisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.2 Discrete Event System Specification (DEVS) . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.2.1 Classic DEVS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.2.2 Structure Specified by DEVS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.2.3 Legitimacy: When is the Structure Specified by a DEVS Really a
System? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.3 Parallel DEVS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.3.1 System Specified by Parallel DEVS . . . . . . . . . . . . . . . . . . . . . . . . . . 160
6.4 Discrete Time System Specification (DTSS) . . . . . . . . . . . . . . . . . . . . . . . . . . 160
6.5 Differential Equation System Specification (DESS) . . . . . . . . . . . . . . . . . . . . . 162
6.6 Example of DESS ....... ...... ...................... .. ......... 163
When is the System Specified by a DESS Well-Defined? . . . . . . . . . . . 164
6.7 Summary..................................................... 164
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
CHAPTER 7 Basic Formalisms: Coupled Multi-Component Systems . . . . . . . . . . . . . . . . . 167
7.1 Discrete Event Specified Network Formalism. . . . . . . . . . . . . . . . . . . . . . . . . . 168
7 .1.1 Classic DEVS Coupled Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Closure Under Coupling of Classic DEVS . . . . . . . . . . . . . . . . . . . . . . 170
7 .1.2 Parallel DEVS Coupled Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
7 .1.3 Closure Under Coupling of Parallel DEVS . . . . . . . . . . . . . . . . . . . . . 171
Output Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Internal Transition Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
External Transition Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7.1.4 The Confluent Transition Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
7.2 Multi-Component Discrete Event System Formalism . . . . . . . . . . . . . . . . . . . . 174
7 .2.1 Cellular Automata Multi-Component DEVS of GOL Event Model . . . 176
Cellular Automata Multi-Component DEVS of GOL Event Model . . . 177
7.2.2 Event Scheduling Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Implementing Event Scheduling Simulation Systems in Imperative
Programming Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Contents ix
7.2.3 Combined Event Scheduling, Activity Scanning Simulation Strategy.. 179
7.2.4 Process Interaction Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.2.5 Translating Non-Modular Multi-Component DEVS Models Into
Modular Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
7.2.6 State Updating in Distributed Simulation. . . . . . . . . . . . . . . . . . . . . . . 182
7.3 Discrete Time Specified Network Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Delay-Free (Algebraic) Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Definition of Discrete Time Coupled Models . . . . . . . . . . . . . . . . . . . . 184
Closure Under Coupling of DTSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
7.4 Multi-Component Discrete Time System Formalism . . . . . . . . . . . . . . . . . . . . 185
Spatial DTSS: Cellular Automata . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
7.5 Differential Equation Specified Network Formalism... . . . . . . . . . . . . . . . . . . 187
Closure Under Coupling of DESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
7.6 Multi-Component Differential Equations Specified System Formalism . . . . . . . 188
7.6.1 Spatial DESS: Partial Differential Equation Models. . . . . . . . . . . . . . . 189
7.7 Multi-Component Parallel Discrete Event System Formalism.............. 191
7.8 Summary.................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
7 .9 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Appendix 7 .A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
CHAPTER 8 Simulators for Basic Formalisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
8.1 Simulators for DEVS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
8.1.1 Simulator for Basic DEVS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
8.1.2 Simulators for Modular DEVS Networks . . . . . . . . . . . . . . . . . . . . . . 200
8.1.3 The Root-Coordinator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
8.2 DEVS Bus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
8.2.1 Simulator for Event Scheduling Multi-Component DEVS . . . . . . . . . . 206
8.2.2 Simulator for Activity Scanning and Process Interaction
Multi-Component DEVS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
8.3 Simulators for DTSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
8.3. I Simulator for Atomic DTSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
8.3.2 Simulator for Instantaneous Functions . . . . . . . . . . . . . . . . . . . . . . . . . 212
8.3.3 Simulator for Non-Modular Multi-Component DTSS . . . . . . . . . . . . . 213
8.3.4 Simulators for Coupled DTSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
8.3.5 The Root-Coordinator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
8.4 Simulators for DESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
8.4.1 Causal Simulator for DESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
8.4.2 Non-Causal Simulator for DESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
8.6 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
CHAPTER 9 Multi-Formalism Modeling and Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 223
9.1 Brief Introduction to Specialized Formalisms . . . . . . . . . . . . . . . . . . . . . . . . . . 224