A consensus on the fundamental status of theory of modeling and simulation is emerging – some recognize
the need for a theoretical foundation for M&S as a science. Such a foundation is necessary
to foster the development of M&S-specific methods and the use of such methods to solve real world
problems faced by practitioners. “[Theory of Modeling and Simulation (1976)] gives a theory for simulation
that is based on general system theory and this theory is considered the only major theory
for simulation. This book showed that simulation has a solid foundation and is not just some ad hoc
way of solving problems.” (Sargent, 2017). “Theory of Modeling and Simulation is a major reference
for modeling formalisms, particularly the Discrete Event Systems Specification (DEVS). ... We mention
the System Entity Structures and Model Base (SES/MB) framework as breakthrough in this field
[Model-base management]. It enables efficiency, reusability and interoperability.” (Durak et al., 2017).
For others there is the acknowledgment that certain of the theory’s basic distinctions such as the
separation, and inter-relation, of models and simulators, are at least alternatives to be considered in
addressing core M&S research challenges. Such challenges, and the opportunities to address them, are
identified in areas including conceptual modeling, computational methods and algorithms for simulation,
fidelity issues and uncertainty in M&S, and model reuse, composition, and adaptation (Fujimoto
et al., 2017).
With the assertion that “an established body of knowledge is one of the pillars of an established
discipline” (Durak et al., 2017), this third edition is dedicated to the inference that theory of M&S is an
essential component, and organizing structure, for such a body of knowledge. A prime emphasis of this
edition is on the central role of iterative specification of systems. The importance of iterative system
specification is that it provides a solid foundation for the computational approach to complex systems
manifested in modeling and simulation. While earlier editions introduced iterative specification as the
common form of specification for unifying continuous and discrete systems, this edition employs it
more fundamentally throughout the book. In addition to the new emphasis, throughout the book there
are updates to earlier material outlining significant enhancements from a broad research community. To
accommodate space for such additions some sections of the last edition have been omitted, not because
of obsolescence – indeed, new editions may re-instate these parts.
This Third Edition coordinates with a second book. “Model Engineering for Simulation” (MES) to
provide both a theoretical and application-oriented account of modeling and simulation. This makes
sense as a coordinated “package”, since most of the background theory material will be contained in
this book and the application to model engineering will be contained in MES. This partitioning into
theory and practice avoids unnecessary redundancy. The books will be published synchronously (or as
closely timed as practical). The editor/leaders of the two books have coordinated closely to assure that
a coherent whole emerges that is attractive to a large segment of the simulation community.
Author(s): Bernard P. Zeigler, Alexandre Muzy, Ernesto Kofman
Publisher: Academic Press
Year: 2019
Language: English
Pages: 674
City: 2019
Contents......Page 6
Contributions......Page 20
References......Page 21
Preface to the Second Edition......Page 23
Part 1. Basics: Modeling Formalisms and Simulatin Algorithms......Page 25
1 Introduction to Systems Modeling Concepts......Page 26
1.1 Systems Specification Formalisms......Page 27
1.1.1 Relation to Object Orientation......Page 28
1.1.2 Evolution of Systems Formalisms......Page 29
1.1.3 Continuous and Discrete Formalisms......Page 30
1.1.4 Quantized Systems......Page 31
1.1.5 Extensions of DEVS......Page 32
1.2 Levels of System Knowledge......Page 33
1.3 Introduction to the Hierarchy of Systems Specifications......Page 35
1.4.1 Observation Frame......Page 37
1.4.2 I/O Behavior and I/O Function......Page 38
1.4.4 Coupled Component System Specification......Page 39
1.5 System Specification Morphisms: Basic Concepts......Page 40
1.6 Evolution of DEVS......Page 43
1.8 Sources......Page 46
References......Page 47
2 Framework for Modeling and Simulation......Page 49
2.1.1 Source System......Page 50
Objectives and Experimental Frames......Page 51
2.1.3 Model......Page 53
2.2.1 Modeling Relation: Validity......Page 54
2.2.2 Simulation Relation: Simulator Correctness......Page 55
Modeling as Valid Simplification......Page 56
Experimental Frame - Model Relationships......Page 57
2.5 Historical Trace of V&V Streams......Page 58
2.5.1 Informal V&V Concepts and Processes......Page 59
2.5.3 Generic Methodology Processes and Best Practice Guides......Page 60
2.7 Sources......Page 61
References......Page 62
3 Modeling Formalisms and Their Simulators......Page 64
3.1 Discrete Time Models and Their Simulators......Page 65
3.1.2 Cellular Automata......Page 67
3.1.3 Cellular Automaton Simulation Algorithms......Page 69
3.1.4 Discrete Event Approach to Cellular Automaton Simulation......Page 71
3.1.5 Switching Automata/Sequential Machines......Page 72
3.1.6 Linear Discrete Time Networks and Their State Behavior......Page 74
3.2 Differential Equation Models and Their Simulators......Page 76
3.2.1 Linear ODE Models......Page 78
3.2.2 Continuous System Simulation......Page 84
3.2.3 Euler's Methods......Page 85
3.2.4 Accuracy of the Approximations......Page 86
3.2.5 Convergence of the Numerical Scheme......Page 89
3.2.6 Numerical Stability......Page 91
Explicit Runge-Kutta Methods......Page 93
Implicit One-Step Methods......Page 94
Multi-Step Explicit Methods......Page 95
One-Step Methods......Page 96
Stiff Systems......Page 99
Marginally Stable Systems......Page 101
Discontinuous Systems......Page 103
3.3.2 Discrete Event Cellular Automata......Page 105
Event Scheduling World View......Page 108
3.4 Summary......Page 110
3.5 Sources......Page 111
References......Page 112
4 Introduction to Discrete Event System Specification (DEVS)......Page 113
4.2 Classic DEVS System Specification......Page 114
Passive......Page 116
Storage......Page 118
Generator......Page 119
Binary Counter......Page 120
Ramp......Page 121
4.2.2 Classic DEVS With Ports......Page 122
Switch......Page 123
4.2.3 Classic DEVS Coupled Models......Page 124
Simple Pipeline......Page 125
4.3 Parallel DEVS System Specification......Page 127
Processor With Buffer......Page 128
4.3.1 Parallel DEVS Coupled Models......Page 129
Simple Pipeline (Parallel DEVS)......Page 130
4.5 Object-Oriented Implementations of DEVS: an Introduction......Page 131
4.5.1 Structural Inheritance......Page 132
4.6.1 Turing Machine as a Modular Composition......Page 134
4.6.2 Tape System......Page 135
TM Example......Page 136
4.6.4 Simulation of the TM Coupled Model......Page 138
4.6.5 Example of Simulation Run......Page 139
I/O Frame at Level 0......Page 140
I/O Relation Observation at Level 1......Page 141
DEVS I/O System Specification at Level 4......Page 142
4.6.7 Empirical Investigation of Halting......Page 143
4.7 Are DEVS State Sets Essentially Discrete?......Page 144
References......Page 145
5.1 Time Base......Page 147
5.2 Segments and Trajectories......Page 148
5.2.3 Event Segments......Page 151
5.2.4 Sequences......Page 152
5.3 I/O Observation Frame......Page 153
5.4 I/O Relation Observation......Page 154
5.5 I/O Function Observation......Page 155
5.6 I/O System......Page 157
5.6.1 Going From System Structure to Behavior......Page 159
5.6.2 Time Invariant Systems......Page 160
Example: Linear Systems......Page 162
Input-Free Systems......Page 163
Memoryless Systems......Page 164
5.7 Multi-Component System Specification......Page 165
5.8 Network of System Specifications (Coupled Systems)......Page 166
5.8.1 Coupled System Specification......Page 167
5.8.2 Coupled System Specification at the Structured System Level......Page 168
5.9 Summary......Page 170
6.1 Basic System Specification Formalisms......Page 173
6.2.2 Structure Specified by DEVS......Page 175
6.2.3 Legitimacy: When is the Structure Specified by a DEVS Really a System?......Page 177
6.3 Parallel DEVS......Page 179
6.4 Discrete Time System Specification (DTSS)......Page 180
6.5 Differential Equation System Specification (DESS)......Page 182
6.6 Example of DESS......Page 183
6.7 Summary......Page 184
References......Page 185
7 Basic Formalisms: Coupled Multi-Component Systems......Page 186
7.1.1 Classic DEVS Coupled Models......Page 187
Closure Under Coupling of Classic DEVS......Page 189
7.1.3 Closure Under Coupling of Parallel DEVS......Page 190
External Transition Function......Page 191
7.1.4 The Confluent Transition Function......Page 192
7.2 Multi-Component Discrete Event System Formalism......Page 193
7.2.1 Cellular Automata Multi-Component DEVS of GOL Event Model......Page 195
Cellular Automata Multi-Component DEVS of GOL Event Model......Page 196
Implementing Event Scheduling Simulation Systems in Imperative Programming Languages......Page 197
7.2.3 Combined Event Scheduling, Activity Scanning Simulation Strategy......Page 198
7.2.4 Process Interaction Models......Page 199
7.2.5 Translating Non-Modular Multi-Component DEVS Models Into Modular Form......Page 200
7.2.6 State Updating in Distributed Simulation......Page 201
Delay-Free (Algebraic) Cycles......Page 202
Closure Under Coupling of DTSS......Page 203
7.4 Multi-Component Discrete Time System Formalism......Page 204
Spatial DTSS: Cellular Automata......Page 205
7.5 Differential Equation Specified Network Formalism......Page 206
7.6 Multi-Component Differential Equations Specified System Formalism......Page 207
7.6.1 Spatial DESS: Partial Differential Equation Models......Page 208
7.8 Summary......Page 210
Appendix 7.A......Page 211
References......Page 212
8 Simulators for Basic Formalisms......Page 214
8.1 Simulators for DEVS......Page 216
8.1.1 Simulator for Basic DEVS......Page 217
8.1.2 Simulators for Modular DEVS Networks......Page 219
8.1.3 The Root-Coordinator......Page 223
8.2 DEVS Bus......Page 224
8.2.1 Simulator for Event Scheduling Multi-Component DEVS......Page 225
8.2.2 Simulator for Activity Scanning and Process Interaction Multi-Component DEVS......Page 227
8.3.1 Simulator for Atomic DTSS......Page 229
8.3.2 Simulator for Instantaneous Functions......Page 231
8.3.3 Simulator for Non-Modular Multi-Component DTSS......Page 232
8.3.4 Simulators for Coupled DTSS......Page 233
8.4 Simulators for DESS......Page 235
8.4.1 Causal Simulator for DESS......Page 236
8.4.2 Non-Causal Simulator for DESS......Page 237
8.5 Summary......Page 239
References......Page 240
9 Multi-Formalism Modeling and Simulation......Page 241
9.1.2 DEVS Subformalisms: Petri Nets and Statecharts......Page 242
9.2 Multi-Formalism Modeling......Page 243
9.3 DEV&DESS: Combined Discrete Event and Differential Equation Specified Systems......Page 245
9.3.1 A Simple Example: DEV&DESS Model of a Barrel Filler......Page 247
9.3.2 System Specified by a DEV&DESS......Page 249
9.4 Multi-Modeling With DEV&DESS......Page 251
9.4.1 Example: Pot System With Command Inputs and Threshold Value Outputs......Page 253
DESS Are Special DEV&DESS......Page 254
DTSS Can Be Represented by Equivalent DEV&DESS......Page 255
9.5.2 Coupled DEV&DESS Formalism......Page 256
9.6 Simulator for DEVS&DESS......Page 259
9.6.1 The dev&dess-Simulator and -Coordinator......Page 260
9.6.2 Integrating Different Modeling Formalisms......Page 262
devs-Interface......Page 263
dess-Interface......Page 264
9.8 Sources......Page 265
Appendix 9.A The System Specified by a DEV&DESS......Page 266
Appendix 9.B The System Specified by a Multi-Formalism System - Closure Under Coupling of Networks of DEV&DESS......Page 267
References......Page 269
Part 2. Iterative System Specification......Page 270
10.1 Overview of Iterative System Specification......Page 271
10.2 Abstraction, Formalization, and Implementation......Page 272
10.3 Deriving Iterative System Specification......Page 274
10.4 Input Generators......Page 275
10.5 Progressivity and Well-Definition of Systems......Page 277
10.6 Active/Passive Compositions......Page 279
10.7 How Can Feedback Coupled Components Define a System?......Page 280
10.9 Simulation of Iterative System Specification by DEVS......Page 282
10.10 Closure Under Coupling: Concept, Proofs, and Importance......Page 284
10.10.1 Example: Multi-Level DEVS......Page 285
10.10.2 Example: Routed DEVS......Page 286
10.11 Activity Formalization and Measurement......Page 287
10.A.1 Activity of Continuous Segments......Page 288
Activity in a Discrete Event Set......Page 290
Event-Based Activity in a Cartesian Space......Page 291
Model......Page 292
Activity-Based Abstract Simulator......Page 293
Abstract Simulator for Weighted Activity......Page 294
References......Page 295
11 Basic Iterative System Specification (IterSpec)......Page 297
11.1 Basic Iterative System Specification: IterSpec Definition......Page 298
11.2 Composition Process......Page 299
11.3 Specific Maximal Length Segmentations......Page 300
11.3.1 Definition of Specific Maximal Length Segmentations......Page 301
11.3.2 Combination of Specific Maximal Length Segmentations......Page 304
11.3.3 Iterative System Specification......Page 307
11.4 Composition of Segments......Page 308
11.5 Dilatable Generator Classes......Page 309
11.A.1 Generator Segments......Page 312
References......Page 313
12 Iterative Specification Subformalisms......Page 314
12.1 Class Mapping of Iterative System Specifications......Page 316
12.2 Basic Iterative Specification (IterSpec)......Page 317
12.3 Scheduled Iterative System Specification......Page 318
12.3.1 DEVS Is a Scheduled Iterative System Specification......Page 319
12.4 Sample-Based Iterative System Specification......Page 320
12.4.2 Preservation of Scheduled Time Under Update......Page 322
12.4.4 System Specified by a Sample-Based Iterative Specification......Page 323
12.5 Hybrid Iterative System Specification......Page 325
12.5.1 Example of Hybrid Barrel Filling Iterative Specification......Page 326
12.6 Coupled Iterative Specifications......Page 328
12.7 Active-Passive Systems......Page 329
12.9 Summary......Page 331
Appendix 12.A Proof That DEVS Is a Scheduled Iterative System Specification......Page 332
Appendix 12.B Coupled Iterative Specification at the I/O System Level......Page 333
Appendix 12.D Closure Under Coupling of Sample-Based Iterative Specification......Page 334
Appendix 12.E Abstract Simulator for Sample-Based Iterative Specification......Page 336
Appendix 12.F Example of Closure Under Coupling: Memoryless Systems......Page 337
Appendix 12.G Proof That a DEVS Atomic Model Can Simulate an Iterative Specification......Page 338
References......Page 339
13.1 Time Management......Page 340
13.2 Basic Finite Iterative Specification (FinIterSpec)......Page 341
13.3 Finite PDEVS......Page 343
13.4 Basic Timed Iterative Specification (TimedIterSpec)......Page 345
13.5 Basic Finite Timed Iterative Specification (FiniTimedIterSpec)......Page 346
13.6 Event Based Control and Finite Timed PDEVS......Page 347
13.7 Summary......Page 349
References......Page 350
Part 3. System Morphisms: Abstraction, Representation, Approximation......Page 351
James Nutaro Was the Primary Author of This Chapter......Page 352
14.1 The Value of Information......Page 353
14.2 The Value of Parallel Model Execution......Page 354
14.3 Speedup, Scaling, and Parallel Execution......Page 356
14.3.2 Parallel Discrete Event Simulation......Page 359
14.3.3 Understanding Speedup via State-Based Critical Path Analysis......Page 361
14.4 Parallel DEVS Simulator......Page 363
14.4.1 Critical Paths in PDEVS......Page 364
14.5 Optimistic and Conservative Simulation......Page 368
14.5.1 Conservative DEVS Simulator......Page 369
14.5.2 Optimistic DEVS Simulator......Page 371
14.5.3 Critical Paths in Optimistic and Conservative Simulators......Page 375
14.5.4 Survey of Optimistic and Conservative Simulation Algorithms......Page 380
14.5.5 A Statistical Approach to Speedup......Page 382
14.6 Summary......Page 383
References......Page 384
15 Hierarchy of System Morphisms......Page 386
15.2 The I/O Relation Observation Morphism......Page 388
Example: Sampled Data Representation of Continuous I/O Signals......Page 389
15.3 The I/O Function Morphism......Page 390
Example: Scaling a System to Different Rates......Page 391
15.4 The I/O System Morphism......Page 392
15.4.1 I/O System Morphism Implies IOFO and IORO Morphism......Page 394
15.4.2 The Lattice of Partitions and the Reduced Version of a System......Page 396
15.5 System Morphism for Iteratively Specified Systems......Page 399
15.5.1 Iterative Specification Morphism Implies I/O System Morphism......Page 400
Discrete Event Case......Page 401
15.6 The Structured System Morphism......Page 402
15.7 Multi-Component System Morphism......Page 403
15.8 The Network of Systems Morphism......Page 406
15.9 Homomorphism and Cascade Decompositions......Page 410
15.10 Characterization of Realizable I/O Relations and Functions......Page 412
15.11 Summary......Page 415
References......Page 416
16 Abstraction: Constructing Model Families......Page 417
16.1 Scope/Resolution/Interaction Product......Page 418
16.1.1 Complexity......Page 419
16.1.2 Size/Resolution Trade-off: Simplification Methods......Page 421
16.1.3 How Objectives and Experimental Frame Determine Abstraction Possibilities......Page 422
16.2.1 Integrated Model Family Example: Space Travel......Page 423
Why DEV&DESS?......Page 424
Why Distributed Simulation?......Page 425
16.3 Aggregation: Homogeneity/Coupling Indifference Principles......Page 427
16.3.1 Coupling Conditions Imposed by Anonymity......Page 430
Output Census......Page 432
Randomized Coupling......Page 434
16.4 All-to-One Coupling......Page 435
16.4.1 Example of Aggregation Model Construction: Space Travel......Page 437
State Census Mapping......Page 438
Output Census......Page 439
Input Census: All-to-All and Randomized Coupling......Page 440
16.4.3 Example of Aggregation Model Construction: Space Travel......Page 442
16.4.4 Constructing Aggregations Through State and Block Refinement......Page 443
16.5 Abstractions for Event-Based Control......Page 445
16.5.1 Boundary-Based DEVS......Page 446
16.5.2 DEVS Abstraction: Space Travel Example......Page 448
16.6 Parameter Morphisms......Page 450
16.6.2 Example Lumpable: Linear DTSS and Parameter Morphisms......Page 451
16.6.4 Using Parameter Morphisms in an Integrated Model Family......Page 453
16.7 Summary......Page 454
References......Page 455
17 Verification, Validation, Approximate Morphisms: Living With Error......Page 456
17.2 Validation at the Behavioral Level......Page 457
17.2.1 Quantitative Comparison......Page 459
17.2.2 Qualitative Comparison......Page 460
17.3 Performance/Validity (e.g. Speed/Accuracy) Trade-off......Page 461
Example of Speed/Accuracy Trade-off: Watershed Modeling......Page 463
17.4.1 Approximate Morphisms and the Specification Hierarchy......Page 464
17.4.2 Approximate Homomorphisms and Error Propagation......Page 466
Error Propagation and Accumulation: Bounded and Unbounded Growth......Page 468
17.4.3 Example: Approximate Linear System Homomorphisms......Page 469
17.5.1 Error-Driven Aggregation Refinement......Page 471
Identifying Critical Sources of Error......Page 472
Effect of Error Accumulation......Page 473
17.6.1 Calibration, Parameter Identification, Sensitivity......Page 474
17.7 Handling Time Granularity Together With Abstraction......Page 475
17.8 Multi-Fidelity Modeling and Simulation Methodology......Page 477
References......Page 478
18 DEVS and DEVS-Like Systems: Universality and Uniqueness......Page 480
18.1 Relation Between Classical and Parallel DEVS: Are There One DEVS or Two?......Page 481
18.2.1 Systems With DEVS Interfaces......Page 483
18.2.2 Behavior of DEVS-Like Systems......Page 484
18.2.3 Universality of DEVS......Page 485
18.2.5 Uniqueness of DEVS......Page 486
18.3 DEVS Representation of DTSS......Page 488
18.3.2 Multi-Ported FNSS......Page 489
18.3.4 Mealy DTSS......Page 490
18.3.5 DEVS Strong Simulation of DTSS Coupled Models......Page 491
18.4 Efficient DEVS Simulation of DTSS Networks......Page 492
Appendix 18.A Isomorphically Representing DEVS-Like Systems by DEVS......Page 494
References......Page 497
19 Quantization-Based Simulation of Continuous Time Systems......Page 498
19.1.1 A Motivating Example......Page 499
19.1.2 Quantization and DEVS Representation......Page 501
19.1.3 Generalization of Quantized Systems......Page 503
19.2.2 First Order Quantized State Systems Method......Page 506
19.2.3 DEVS Representation of QSS1......Page 507
19.2.4 QSS1 Simulation Examples......Page 509
19.2.5 QSS Legitimacy, Stability, Convergence, and Error Bounds......Page 511
19.3 QSS Extensions......Page 515
19.3.1 Higher Order QSS Methods......Page 516
19.3.2 Linearly Implicit QSS......Page 520
19.4 QSS Simulation of Hybrid Systems......Page 527
19.5 Logarithmic Quantization......Page 529
19.6 Software Implementations of QSS Methods......Page 531
19.6.1 PowerDEVS......Page 532
19.6.2 Stand Alone QSS Solver......Page 535
19.7 Applications of QSS Methods......Page 538
19.7.1 A DC-DC Buck Converter Circuit......Page 539
19.7.2 A Population of Air Conditioners......Page 541
19.7.3 Advection-Diffusion-Reaction Equation......Page 543
19.8 Comparison of QSS With Discrete Time Methods: Activity-Based Approach......Page 545
Sources and Further Reading......Page 548
References......Page 549
20 DEVS Representation of Iteratively Specified Systems......Page 551
20.1.1 Approaches to DEVS Representation of Continuous Systems......Page 552
20.2.2 Discretized Simulation of Coupled DESSs With Arbitrarily Small Error......Page 554
20.2.4 QSS Simulation of Coupled DESS With Arbitrarily Small Error......Page 557
20.2.5 Convergence of Coupling of QSS and DTSS......Page 558
20.3 DEVS Component-Wise Simulation of Iteratively Specified Coupled Systems......Page 559
20.4 Simulation Study of Message Reduction Under Quantization......Page 563
20.4.1 Some Indicative Simulation Results......Page 564
20.4.2 Comparing Quantized DEVS With DTSS in Distributed Simulation of DESS......Page 566
20.4.3 Insight From 2nd Order Linear Oscillator......Page 569
Caveat: Effect of Integration Method......Page 571
20.6 Sources......Page 572
References......Page 573
Part 4. Enhanced DEVS Formalisms......Page 574
21 DEVS Markov Modeling and Simulation......Page 575
21.1 Markov Modeling......Page 576
21.3.1 General Framework for Stochastic DEVS......Page 577
21.3.3 SES for DEVS Markov Models......Page 578
21.3.4 Uncoupling Decision Probabilities from Transition Times......Page 581
21.4 Hidden Markov Models......Page 583
21.5 Preview: Closure Under Coupling of DEVS Markov Models......Page 584
21.6.1 Probability Core DEVS......Page 585
21.6.2 Markov Chain......Page 587
21.6.2.1 Example of DEVS Markov Core......Page 588
21.6.3 Transient Behavior......Page 592
21.6.5 Input/Output Behavior of DEVS Markov Models......Page 593
21.6.6 Coupled Models - DEVS Networks of Markov Components......Page 595
21.6.7 Proof of DEVS Markov Class Closure Under Coupling......Page 596
21.7 Continuous and Discrete Time Subclasses of Markov Models......Page 597
21.8 Relations Between DEVS CTM and DTM......Page 598
Mobile Worker......Page 599
21.8.2 DEVS Hidden Markov Models......Page 600
21.8.3 Example: Dynamic Structure via Variable Transition Probability......Page 601
21.A.1 Exponential Distribution Properties......Page 603
21.A.2 Zero-Memory Property......Page 604
21.A.4 Markov Modeling......Page 605
Appendix 21.B Traditional Approach to CTM Implementation......Page 606
References......Page 607
22 DEVS Markov Model Lumping......Page 608
22.2 Homomorphism of Timed Non-Deterministic Models......Page 609
22.3 Homomorphism of DEVS Markov Models......Page 611
22.3.1 Random Phase Regime for Coupled DEVS Markov Models......Page 613
22.4 Example: Combat Attrition Modeling......Page 614
22.4.2 Base Coupled Model......Page 615
Lumped Model Component......Page 616
22.5.1 Introducing Non-Uniformity Into the Base Model......Page 617
Lumpability Dependence on Force Sizes......Page 620
Lumpability Dependence on Distribution of Fire......Page 621
22.6 Application to General Markov Matrix Lumpability......Page 623
22.7.1 Base Model of Multiprocessor......Page 625
22.7.2 Relation Between Speedup and Probability of Active State......Page 627
22.7.3 Lumped Model of Multiprocessor......Page 628
22.8 Summary......Page 630
Appendix 22.A Prioritized Communication in Multiprocessor Clusters......Page 631
References......Page 632
23.1 A Biological Neuron as a Dynamic System......Page 633
23.2 Discrete Event Modeling of a Leaky Integrate and Fire Neuron......Page 635
23.3 Multi-Level Iterative Specification......Page 636
23.4 Iterative Specification Modeling of Spiky Neurons......Page 639
23.5 Summary......Page 640
Appendix 23.A Iterative System Specification of a Spiking Neuron......Page 641
Appendix 23.B Iterative Specification Modeling of Bursty Neurons......Page 642
References......Page 645
Rodrigo Castro Was the Primary Author of This Chapter......Page 647
SD Basics......Page 648
24.2.1 SD Strengths and Limitations......Page 649
24.3 Mapping SD Into DEVS......Page 650
24.3.3 Core Mapping Idea......Page 651
24.3.4 Example: Prey-Predator Model......Page 654
24.3.5 Experimental Results......Page 657
24.4 Challenges for Sound Interdisciplinary M&S of Large Complex Systems: the Case of Socio-Ecological Global Sustainability......Page 658
24.4.1 Brief History of Global Modeling......Page 659
24.4.2 Current M&S Challenges in Global Models......Page 660
24.5 Theory-Based Research Needed......Page 661
References......Page 663
Index......Page 665
