Theory of modeling and simulation : discrete event and iterative system computational foundations

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. 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

Theory of Modeling and Simulation: Discrete Event & Iterative System Computational Foundations, Third Edition, continues the legacy of this authoritative and complete theoretical work. It is ideal for graduate and PhD students and working engineers interested in posing and solving problems using the tools of logico-mathematical modeling and computer simulation. Continuing its emphasis on the integration of discrete event and continuous modeling approaches, the work focuses light on DEVS and its potential to support the co-existence and interoperation of multiple formalisms in model components.

New sections in this updated edition include discussions on important new extensions to theory, including chapter-length coverage of iterative system specification and DEVS and their fundamental importance, closure under coupling for iteratively specified systems, existence, uniqueness, non-deterministic conditions, and temporal progressiveness (legitimacy).

• Presents a 40% revised and expanded new edition of this classic book with many important post-2000 extensions to core theory
• Provides a streamlined introduction to Discrete Event System Specification (DEVS) formalism for modeling and simulation
• Packages all the "need-to-know" information on DEVS formalism in one place
• Expanded to include an online ancillary package, including numerous examples of theory and implementation in DEVS-based software, student solutions and instructors manual