Theory of Modeling and Simulation 3rd Edition by Bernard Zeigler, Alexandre Muzy, Ernesto Kofman 0128133708 9780128133705

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ISBN 10: 0128133708

ISBN 13: 9780128133705

Author: Bernard Zeigler, Alexandre Muzy, Ernesto Kofman

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

Theory of Modeling and Simulation 3rd Table of contents:

Part 1 Basics: Modeling Formalisms and Simulation Algorithms

1 Introduction to Systems Modeling Concepts

1.1 Systems Specification Formalisms

1.1.1 Relation to Object Orientation

1.1.2 Evolution of Systems Formalisms

1.1.3 Continuous and Discrete Formalisms

1.1.4 Quantized Systems

1.1.5 Extensions of DEVS

1.2 Levels of System Knowledge

1.3 Introduction to the Hierarchy of Systems Specifications

1.4 The Specification Levels Informally Presented

1.4.1 Observation Frame

1.4.2 I/O Behavior and I/O Function

1.4.3 State Transition System Specification

1.4.4 Coupled Component System Specification

1.5 System Specification Morphisms: Basic Concepts

1.6 Evolution of DEVS

1.7 Summary

1.8 Sources

Definitions, Acronyms, Abbreviations

References

2 Framework for Modeling and Simulation

2.1 The Entities of the Framework

2.1.1 Source System

2.1.2 Experimental Frame

Objectives and Experimental Frames

2.1.3 Model

2.1.4 Simulator

2.2 Primary Relations Among Entities

2.2.1 Modeling Relation: Validity

2.2.2 Simulation Relation: Simulator Correctness

2.3 Other Important Relationships

Modeling as Valid Simplification

Experimental Frame – Model Relationships

2.4 Time

2.5 Historical Trace of V&V Streams

2.5.1 Informal V&V Concepts and Processes

2.5.2 Theory-Based and Model-Driven Developments

2.5.3 Generic Methodology Processes and Best Practice Guides

2.6 Summary

2.7 Sources

References

3 Modeling Formalisms and Their Simulators

Introduction

3.1 Discrete Time Models and Their Simulators

3.1.1 Discrete Time Simulation

3.1.2 Cellular Automata

3.1.3 Cellular Automaton Simulation Algorithms

3.1.4 Discrete Event Approach to Cellular Automaton Simulation

3.1.5 Switching Automata/Sequential Machines

3.1.6 Linear Discrete Time Networks and Their State Behavior

3.2 Differential Equation Models and Their Simulators

3.2.1 Linear ODE Models

Non-Linear Models

3.2.2 Continuous System Simulation

3.2.3 Euler’s Methods

3.2.4 Accuracy of the Approximations

3.2.5 Convergence of the Numerical Scheme

3.2.6 Numerical Stability

3.2.7 One-Step Methods

Explicit Runge-Kutta Methods

Implicit One-Step Methods

3.2.8 Multi-Step Methods

Multi-Step Explicit Methods

Implicit Multi-Step Methods

3.2.9 Step Size Control

One-Step Methods

3.2.9.1 Multi-Step Methods

3.2.10 Stiff, Marginally Stable and Discontinuous Systems

Stiff Systems

Marginally Stable Systems

Discontinuous Systems

3.3 Discrete Event Models and Their Simulators

3.3.1 Introduction

3.3.2 Discrete Event Cellular Automata

3.3.3 Discrete Event World Views

Event Scheduling World View

3.4 Summary

3.5 Sources

References

4 Introduction to Discrete Event System Specification (DEVS)

4.1 Introduction

4.2 Classic DEVS System Specification

4.2.1 DEVS Examples

Passive

Storage

Generator

Binary Counter

Processor

Ramp

4.2.2 Classic DEVS With Ports

Switch

4.2.3 Classic DEVS Coupled Models

Simple Pipeline

Switch Network

4.3 Parallel DEVS System Specification

Processor With Buffer

4.3.1 Parallel DEVS Coupled Models

Simple Pipeline (Parallel DEVS)

4.4 Hierarchical Models

4.5 Object-Oriented Implementations of DEVS: an Introduction

4.5.1 Structural Inheritance

4.6 DEVS and Hierarchy of System Specifications: Turing Machine Example

4.6.1 Turing Machine as a Modular Composition

4.6.2 Tape System

4.6.3 TM Control

TM Example

4.6.4 Simulation of the TM Coupled Model

4.6.5 Example of Simulation Run

4.6.6 Turing Machine Example of Hierarchy of System Specifications

I/O Frame at Level 0

I/O Relation Observation at Level 1

I/O Function Observation at Level 2

DEVS I/O System Specification at Level 4

4.6.7 Empirical Investigation of Halting

4.7 Are DEVS State Sets Essentially Discrete?

4.8 Summary

4.9 Sources

References

5 Hierarchy of System Specifications

5.1 Time Base

5.2 Segments and Trajectories

5.2.1 Piecewise Continuous Segments

5.2.2 Piecewise Constant Segments

5.2.3 Event Segments

Correspondence Between Piecewise Constant and Event Segments

5.2.4 Sequences

5.3 I/O Observation Frame

5.4 I/O Relation Observation

5.5 I/O Function Observation

5.6 I/O System

5.6.1 Going From System Structure to Behavior

5.6.2 Time Invariant Systems

Example: Linear Systems

5.6.3 Special Cases: Input-Free and Memoryless Systems

Input-Free Systems

Memoryless Systems

5.7 Multi-Component System Specification

5.8 Network of System Specifications (Coupled Systems)

5.8.1 Coupled System Specification

5.8.2 Coupled System Specification at the Structured System Level

5.9 Summary

6 Basic Formalisms: DEVS, DESS, DTSS

6.1 Basic System Specification Formalisms

6.2 Discrete Event System Specification (DEVS)

6.2.1 Classic DEVS

6.2.2 Structure Specified by DEVS

6.2.3 Legitimacy: When is the Structure Specified by a DEVS Really a System?

6.3 Parallel DEVS

6.3.1 System Specified by Parallel DEVS

6.4 Discrete Time System Specification (DTSS)

6.5 Differential Equation System Specification (DESS)

6.6 Example of DESS

When is the System Specified by a DESS Well-Defined?

6.7 Summary

References

7 Basic Formalisms: Coupled Multi-Component Systems

7.1 Discrete Event Specified Network Formalism

7.1.1 Classic DEVS Coupled Models

Closure Under Coupling of Classic DEVS

7.1.2 Parallel DEVS Coupled Models

7.1.3 Closure Under Coupling of Parallel DEVS

Output Function

Internal Transition Function

External Transition Function

7.1.4 The Confluent Transition Function

7.2 Multi-Component Discrete Event System Formalism

7.2.1 Cellular Automata Multi-Component DEVS of GOL Event Model

Cellular Automata Multi-Component DEVS of GOL Event Model

7.2.2 Event Scheduling Models

Implementing Event Scheduling Simulation Systems in Imperative Programming Languages

7.2.3 Combined Event Scheduling, Activity Scanning Simulation Strategy

7.2.4 Process Interaction Models

7.2.5 Translating Non-Modular Multi-Component DEVS Models Into Modular Form

7.2.6 State Updating in Distributed Simulation

7.3 Discrete Time Specified Network Formalism

Delay-Free (Algebraic) Cycles

Definition of Discrete Time Coupled Models

Closure Under Coupling of DTSS

7.4 Multi-Component Discrete Time System Formalism

Spatial DTSS: Cellular Automata

7.5 Differential Equation Specified Network Formalism

Closure Under Coupling of DESS

7.6 Multi-Component Differential Equations Specified System Formalism

7.6.1 Spatial DESS: Partial Differential Equation Models

7.7 Multi-Component Parallel Discrete Event System Formalism

7.8 Summary

7.9 Sources

Appendix 7.A

References

8 Simulators for Basic Formalisms

8.1 Simulators for DEVS

8.1.1 Simulator for Basic DEVS

8.1.2 Simulators for Modular DEVS Networks

8.1.3 The Root-Coordinator

8.2 DEVS Bus

8.2.1 Simulator for Event Scheduling Multi-Component DEVS

8.2.2 Simulator for Activity Scanning and Process Interaction Multi-Component DEVS

8.3 Simulators for DTSS

8.3.1 Simulator for Atomic DTSS

8.3.2 Simulator for Instantaneous Functions

8.3.3 Simulator for Non-Modular Multi-Component DTSS

8.3.4 Simulators for Coupled DTSS

8.3.5 The Root-Coordinator

8.4 Simulators for DESS

8.4.1 Causal Simulator for DESS

8.4.2 Non-Causal Simulator for DESS

8.5 Summary

8.6 Sources

References

9 Multi-Formalism Modeling and Simulation

9.1 Brief Introduction to Specialized Formalisms

9.1.1 DESS Subformalisms: Systems Dynamics and Bond Graphs

9.1.2 DEVS Subformalisms: Petri Nets and Statecharts

9.2 Multi-Formalism Modeling

9.3 DEV&DESS: Combined Discrete Event and Differential Equation Specified Systems

9.3.1 A Simple Example: DEV&DESS Model of a Barrel Filler

9.3.2 System Specified by a DEV&DESS

9.4 Multi-Modeling With DEV&DESS

9.4.1 Example: Pot System With Command Inputs and Threshold Value Outputs

9.5 Coupled DEV&DESS: Network of Multi-Formalism Models

9.5.1 Basic Formalisms Are Subsumed by DEV&DESS

DESS Are Special DEV&DESS

DTSS Can Be Represented by Equivalent DEV&DESS

DEVS Can Be Represented by Equivalent DEV&DESS

9.5.2 Coupled DEV&DESS Formalism

9.6 Simulator for DEVS&DESS

9.6.1 The dev&dess-Simulator and -Coordinator

9.6.2 Integrating Different Modeling Formalisms

devs-Interface

dtss-Interface

dess-Interface

9.7 Update on DEV&DESS and Cyber-Physical Systems

9.8 Sources

Appendix 9.A The System Specified by a DEV&DESS

Appendix 9.B The System Specified by a Multi-Formalism System – Closure Under Coupling of Networks

References

Part 2 Iterative System Specification

10 Introduction to Iterative System Specification

10.1 Overview of Iterative System Specification

10.2 Abstraction, Formalization, and Implementation

10.3 Deriving Iterative System Specification

10.4 Input Generators

10.5 Progressivity and Well-Definition of Systems

10.6 Active/Passive Compositions

10.7 How Can Feedback Coupled Components Define a System?

10.8 Example: Emergence of Human Conversational Language Interaction

10.9 Simulation of Iterative System Specification by DEVS

10.10 Closure Under Coupling: Concept, Proofs, and Importance

10.10.1 Example: Multi-Level DEVS

10.10.2 Example: Routed DEVS

10.10.3 Example: Min-Max DEVS

10.11 Activity Formalization and Measurement

10.12 Summary

Appendix 10.A Activity Definitions

10.A.1 Activity of Continuous Segments

10.A.2 Event-Based Activity

Activity in a Discrete Event Set

Event-Based Activity in a Cartesian Space

10.A.3 Activity in Discrete Event System Specification (DEVS)

Model

Activity-Based Abstract Simulator

Abstract Simulator for Weighted Activity

References

11 Basic Iterative System Specification (IterSpec)

11.1 Basic Iterative System Specification: IterSpec Definition

11.2 Composition Process

11.3 Specific Maximal Length Segmentations

11.3.1 Definition of Specific Maximal Length Segmentations

11.3.2 Combination of Specific Maximal Length Segmentations

11.3.3 Iterative System Specification

11.4 Composition of Segments

11.5 Dilatable Generator Classes

11.6 Summary

Appendix 11.A

11.A.1 Generator Segments

References

12 Iterative Specification Subformalisms

12.1 Class Mapping of Iterative System Specifications

12.2 Basic Iterative Specification (IterSpec)

12.3 Scheduled Iterative System Specification

12.3.1 DEVS Is a Scheduled Iterative System Specification

12.4 Sample-Based Iterative System Specification

12.4.1 Formal Definition of Sample-Based Iterative System Specification

12.4.2 Preservation of Scheduled Time Under Update

12.4.3 Example of Sample-Based Iterative System Specification

12.4.4 System Specified by a Sample-Based Iterative Specification

12.5 Hybrid Iterative System Specification

12.5.1 Example of Hybrid Barrel Filling Iterative Specification

12.6 Coupled Iterative Specifications

12.7 Active-Passive Systems

12.8 DEVS Simulation of Iterative Specifications

12.9 Summary

Appendix 12.A Proof That DEVS Is a Scheduled Iterative System Specification

Appendix 12.B Coupled Iterative Specification at the I/O System Level

Appendix 12.C Composition Property for Sample-Based Systems

Appendix 12.D Closure Under Coupling of Sample-Based Iterative Specification

Appendix 12.E Abstract Simulator for Sample-Based Iterative Specification

Appendix 12.F Example of Closure Under Coupling: Memoryless Systems

Appendix 12.G Proof That a DEVS Atomic Model Can Simulate an Iterative Specification

References

13 Finite and Timed Iterative Specifications and Simulations

13.1 Time Management

13.2 Basic Finite Iterative Specification (FinIterSpec)

13.3 Finite PDEVS

13.4 Basic Timed Iterative Specification (TimedIterSpec)

13.5 Basic Finite Timed Iterative Specification (FiniTimedIterSpec)

13.6 Event Based Control and Finite Timed PDEVS

13.7 Summary

References

Part 3 System Morphisms: Abstraction, Representation, Approximation

14 Parallel and Distributed Discrete Event Simulation

James Nutaro Was the Primary Author of This Chapter

14.1 The Value of Information

14.2 The Value of Parallel Model Execution

14.3 Speedup, Scaling, and Parallel Execution

14.3.1 Parallel Experiments

14.3.2 Parallel Discrete Event Simulation

14.3.3 Understanding Speedup via State-Based Critical Path Analysis

14.4 Parallel DEVS Simulator

14.4.1 Critical Paths in PDEVS

14.5 Optimistic and Conservative Simulation

14.5.1 Conservative DEVS Simulator

14.5.2 Optimistic DEVS Simulator

14.5.3 Critical Paths in Optimistic and Conservative Simulators

14.5.4 Survey of Optimistic and Conservative Simulation Algorithms

14.5.5 A Statistical Approach to Speedup

14.6 Summary

References

15 Hierarchy of System Morphisms

15.1 The I/O Frame Morphism

15.2 The I/O Relation Observation Morphism

Example: Sampled Data Representation of Continuous I/O Signals

15.3 The I/O Function Morphism

Example: Scaling a System to Different Rates

15.3.1 IOFO System Morphism Implies IORO System Morphism

15.4 The I/O System Morphism

Example: Linear System Homomorphism

15.4.1 I/O System Morphism Implies IOFO and IORO Morphism

15.4.2 The Lattice of Partitions and the Reduced Version of a System

15.5 System Morphism for Iteratively Specified Systems

15.5.1 Iterative Specification Morphism Implies I/O System Morphism

15.5.2 Specialization of Morphisms for Iteratively Specified Systems

DTSS Specification Morphisms

Discrete Event Case

15.6 The Structured System Morphism

Example: Structure Morphism for Linear Systems

15.7 Multi-Component System Morphism

15.8 The Network of Systems Morphism

15.9 Homomorphism and Cascade Decompositions

15.10 Characterization of Realizable I/O Relations and Functions

15.10.1 Canonical Realization

15.11 Summary

15.12 Sources

References

16 Abstraction: Constructing Model Families

16.1 Scope/Resolution/Interaction Product

16.1.1 Complexity

16.1.2 Size/Resolution Trade-off: Simplification Methods

16.1.3 How Objectives and Experimental Frame Determine Abstraction Possibilities

16.2 Integrated Families of Models

16.2.1 Integrated Model Family Example: Space Travel

16.2.2 Space Travel Base Model

Why DEV&DESS?

Why Dynamic Structure?

Why Distributed Simulation?

16.3 Aggregation: Homogeneity/Coupling Indifference Principles

16.3.1 Coupling Conditions Imposed by Anonymity

16.3.2 Constructing Lumped Models Based on Identity-Erasing Aggregation

State Census Redistribution Under Equal Input

Output Census

Randomized Coupling

16.4 All-to-One Coupling

16.4.1 Example of Aggregation Model Construction: Space Travel

16.4.2 Constructing Lumped Models Based on Identity-Erasing Aggregation

State Census Mapping

Output Census

Input Census: All-to-All and Randomized Coupling

16.4.3 Example of Aggregation Model Construction: Space Travel

16.4.4 Constructing Aggregations Through State and Block Refinement

16.4.5 Universality/Applicability of Identity-Erasing Aggregations

16.5 Abstractions for Event-Based Control

16.5.1 Boundary-Based DEVS

16.5.2 DEVS Abstraction: Space Travel Example

16.6 Parameter Morphisms

16.6.1 Linear Systems Parameter Morphisms

16.6.2 Example Lumpable: Linear DTSS and Parameter Morphisms

16.6.3 Constraints on Parameter and State Spaces: Disaggregation

16.6.4 Using Parameter Morphisms in an Integrated Model Family

16.7 Summary

16.8 Sources

References

17 Verification, Validation, Approximate Morphisms: Living With Error

17.1 Verification

17.2 Validation at the Behavioral Level

17.2.1 Quantitative Comparison

17.2.2 Qualitative Comparison

17.3 Performance/Validity (e.g. Speed/Accuracy) Trade-off

Example of Speed/Accuracy Trade-off: Watershed Modeling

17.4 Approximate Morphisms and Error Behavior

17.4.1 Approximate Morphisms and the Specification Hierarchy

17.4.2 Approximate Homomorphisms and Error Propagation

Error Propagation and Accumulation: Bounded and Unbounded Growth

17.4.3 Example: Approximate Linear System Homomorphisms

17.5 Approximate Morphisms at the Coupled System Level

17.5.1 Error-Driven Aggregation Refinement

Identifying Critical Sources of Error

Effect of Error Accumulation

17.6 Validation at Structural Levels

17.6.1 Calibration, Parameter Identification, Sensitivity

17.6.2 Local/Global, Cross-Model Validation

17.7 Handling Time Granularity Together With Abstraction

17.8 Multi-Fidelity Modeling and Simulation Methodology

17.9 Summary

References

18 DEVS and DEVS-Like Systems: Universality and Uniqueness

Global vs. Local (Component-Wise) Representation

18.1 Relation Between Classical and Parallel DEVS: Are There One DEVS or Two?

18.2 Universality and Uniqueness of DEVS

18.2.1 Systems With DEVS Interfaces

18.2.2 Behavior of DEVS-Like Systems

18.2.3 Universality of DEVS

18.2.4 Example: DEVS Realization of DEVS-Like System

18.2.5 Uniqueness of DEVS

18.3 DEVS Representation of DTSS

18.3.1 Input-Free Moore

18.3.2 Multi-Ported FNSS

18.3.3 Moore DTSS With Input

18.3.4 Mealy DTSS

18.3.5 DEVS Strong Simulation of DTSS Coupled Models

Example: DEVS Strong Simulation of DTSS Network

18.4 Efficient DEVS Simulation of DTSS Networks

Summary

18.5 Sources

Appendix 18.A Isomorphically Representing DEVS-Like Systems by DEVS

References

19 Quantization-Based Simulation of Continuous Time Systems

19.1 Quantization Principles

19.1.1 A Motivating Example

19.1.2 Quantization and DEVS Representation

19.1.3 Generalization of Quantized Systems

19.2 Quantized State Systems

19.2.1 Hysteretic Quantization

19.2.2 First Order Quantized State Systems Method

19.2.3 DEVS Representation of QSS1

19.2.4 QSS1 Simulation Examples

19.2.5 QSS Legitimacy, Stability, Convergence, and Error Bounds

19.3 QSS Extensions

19.3.1 Higher Order QSS Methods

19.3.2 Linearly Implicit QSS

19.4 QSS Simulation of Hybrid Systems

19.5 Logarithmic Quantization

19.6 Software Implementations of QSS Methods

19.6.1 PowerDEVS

19.6.2 Stand Alone QSS Solver

19.7 Applications of QSS Methods

19.7.1 A DC-DC Buck Converter Circuit

19.7.2 A Population of Air Conditioners

19.7.3 Advection-Diffusion-Reaction Equation

19.8 Comparison of QSS With Discrete Time Methods: Activity-Based Approach

Sources and Further Reading

Exercise for Future Research

References

20 DEVS Representation of Iteratively Specified Systems

20.1 DEVS Bus Revisited

20.1.1 Approaches to DEVS Representation of Continuous Systems

20.2 DEVS Simulation of DESS With Arbitrarily Small Error

20.2.1 Discretized Simulation of a DESS With Arbitrarily Small Error

20.2.2 Discretized Simulation of Coupled DESSs With Arbitrarily Small Error

20.2.3 Simulation of a DESS by QSS With Arbitrarily Small Error

20.2.4 QSS Simulation of Coupled DESS With Arbitrarily Small Error

20.2.5 Convergence of Coupling of QSS and DTSS

20.3 DEVS Component-Wise Simulation of Iteratively Specified Coupled Systems

20.4 Simulation Study of Message Reduction Under Quantization

20.4.1 Some Indicative Simulation Results

20.4.2 Comparing Quantized DEVS With DTSS in Distributed Simulation of DESS

20.4.3 Insight From 2nd Order Linear Oscillator

20.4.4 Conjectures for Further Research

Caveat: Effect of Integration Method

20.5 Summary

20.6 Sources

References

Part 4 Enhanced DEVS Formalisms

21 DEVS Markov Modeling and Simulation

21.1 Markov Modeling

21.2 Background

21.3 Mapping DEVS Markov Models

21.3.1 General Framework for Stochastic DEVS

21.3.2 Stochastic DEVS With Finite Sets

21.3.3 SES for DEVS Markov Models

21.3.4 Uncoupling Decision Probabilities from Transition Times

21.3.4.1 DEVS Markov Model Classes

21.4 Hidden Markov Models

21.5 Preview: Closure Under Coupling of DEVS Markov Models

21.5.1 System Specification Hierarchy for Hidden Markov Models

21.6 Formalization of DEVS Markov Models

21.6.1 Probability Core DEVS

21.6.2 Markov Chain

21.6.2.1 Example of DEVS Markov Core

21.6.3 Transient Behavior

21.6.4 Extension With Input/Output Sets and Functions

21.6.5 Input/Output Behavior of DEVS Markov Models

21.6.6 Coupled Models – DEVS Networks of Markov Components

21.6.7 Proof of DEVS Markov Class Closure Under Coupling

21.7 Continuous and Discrete Time Subclasses of Markov Models

21.8 Relations Between DEVS CTM and DTM

21.8.1 Example: DEVS Markov Coupled Model

Mobile Worker

21.8.2 DEVS Hidden Markov Models

21.8.3 Example: Dynamic Structure via Variable Transition Probability

Appendix 21.A Exponential Distribution and Markov Model Basics

21.A.1 Exponential Distribution Properties

21.A.2 Zero-Memory Property

21.A.3 Poisson Process

21.A.4 Markov Modeling

Appendix 21.B Traditional Approach to CTM Implementation

References

22 DEVS Markov Model Lumping

22.1 Overall Approach

22.2 Homomorphism of Timed Non-Deterministic Models

22.3 Homomorphism of DEVS Markov Models

22.3.1 Random Phase Regime for Coupled DEVS Markov Models

22.4 Example: Combat Attrition Modeling

22.4.1 Base Model Component: Realizing a Poisson Process With DEVS Markov Model

22.4.2 Base Coupled Model

Lumped Model Component

22.4.3 Lumped Coupled Model

22.4.4 Homomorphism From Base to Lumped Models

22.5 Approximate Morphisms

22.5.1 Introducing Non-Uniformity Into the Base Model

22.5.2 Lumpability Zone Evaluation for Departure in Uniformity of Structure

Lumpability Dependence on Force Ratio

Lumpability Dependence on Force Sizes

Departure From Uniformity in Coupling

Lumpability Dependence on Distribution of Fire

22.6 Application to General Markov Matrix Lumpability

22.7 Lumping of DEVS Markov Models to Study Speedup in Multiprocessor Computation

22.7.1 Base Model of Multiprocessor

22.7.2 Relation Between Speedup and Probability of Active State

22.7.3 Lumped Model of Multiprocessor

22.7.4 Taking Component Identity Into Account

22.8 Summary

Appendix 22.A Prioritized Communication in Multiprocessor Clusters

References

23 Spiking Neuron Modeling – Iterative Specification

23.1 A Biological Neuron as a Dynamic System

23.2 Discrete Event Modeling of a Leaky Integrate and Fire Neuron

23.3 Multi-Level Iterative Specification

23.4 Iterative Specification Modeling of Spiky Neurons

23.5 Summary

Appendix 23.A Iterative System Specification of a Spiking Neuron

Appendix 23.B Iterative Specification Modeling of Bursty Neurons

References

24 Open Research Problems: Systems Dynamics, Complex Systems

Rodrigo Castro Was the Primary Author of This Chapter

24.1 Systems Dynamics, DEVS, and Challenges for M&S of Complex Systems

24.1.1 Introduction

24.2 System Dynamics

SD Basics

24.2.1 SD Strengths and Limitations

24.3 Mapping SD Into DEVS

24.3.1 XMILE

24.3.2 DEVSML

24.3.3 Core Mapping Idea

24.3.4 Example: Prey-Predator Model

24.3.5 Experimental Results

24.4 Challenges for Sound Interdisciplinary M&S of Large Complex Systems: the Case of Socio-Ecologic

24.4.1 Brief History of Global Modeling

24.4.2 Current M&S Challenges in Global Models

24.5 Theory-Based Research Needed

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