Petri Nets for Modeling of Large Discrete Systems (2021) [Davidrajuh] [9789811652028]

Foreword
Preface
	The Structure of This Book
	Companion Website
	Acknowledgement
Contents
About the Author
Nomenclature
List of Figures
List of Tables
List of Algorithms
Part I Petri Nets and GPenSIM
1 Introduction to Petri Nets
	1.1 Petri Nets
	1.2 Formal Definitions
		1.2.1 P/T Petri Nets
		1.2.2 State Space (aka Reachability Graph)
		1.2.3 State Equation and the Incidence Matrix
		1.2.4 Structural Property: P-Invariant
		1.2.5 Structural Property: T-Invariant
		1.2.6 Timed Petri Nets
		1.2.7 Strongly Connected Event Graphs (SCEGs)
	References
2 Introduction to GPenSIM
	2.1 Time in GPenSIM
	2.2 Automicity and Virtual Tokens
	2.3 Layered Architecture
	2.4 Modeling with GPenSIM: The Basics
		2.4.1 Separating the Static and Dynamic Details
		2.4.2 Processor Files
		2.4.3 Global Info
		2.4.4 Integrating with MATLAB Environment
	2.5 Creating a Simple Petri Net Model with GPenSIM
		2.5.1 Creating a Simple Petri Net Model: An Example
	2.6 GPenSIM and Its Applications
	References
3 Models of Real-Life Systems
	3.1 Model-1: Flexible Manufacturing System
		3.1.1 The Petri Net Model
		3.1.2 Analysis of the Petri Net Model: P-Invariants
		3.1.3 Analysis of the Petri Net Model: T-Invariants
		3.1.4 Analysis of the Petri Net Model: State Space
	3.2 Model-2: Circular AGVs
		3.2.1 The Petri Net Model of Circular AVG Transport System
		3.2.2 Analysis of the Petri Net Model: State Space
		3.2.3 Analysis of the Petri Net Model: P-Invariants
		3.2.4 Analysis of the Petri Net Model: T-Invariants
	3.3 Model-3: Cyclic Processes
		3.3.1 Petri Net Model of the Cyclic Processes
		3.3.2 Analysis of the Petri Net Model: State Space
		3.3.3 Analysis of the Petri Net Model: P-Invariants
		3.3.4 Analysis of the Petri Net Model: T-Invariants
	3.4 The Problem with Petri Net Models
	3.5 Research Goals of This Book
	References
4 GPenSIM for Monolithic Petri Nets
	4.1 Revisiting the Files in GPenSIM
	4.2 Transitions and Their Visibility
	4.3 Visibility in Monolithic Petri Net
		4.3.1 Global Visibility
		4.3.2 Private Visibility
	4.4 GPenSIM Application-I: Model Checking
		4.4.1 The Soda Vending Machine
		4.4.2 The Petri Net Model
		4.4.3 GPenSIM Implementation
		4.4.4 Model Checking the Petri Net
	4.5 GPenSIM Application-II: Performance Evaluation
		4.5.1 Performance Evaluation of an FMS
		4.5.2 GPenSIM Files for Simulation
		4.5.3 The Simulation Results
		4.5.4 GPenSIM for Performance Evaluation
	4.6 Colored Petri Nets with GPenSIM
	References
Part II Design of Modular Petri Nets
5 Literature Review on Modular Petri Nets
	5.1 First-Generation Works: Ease of Modeling
	5.2 Second-Generation Works: Analysis
	5.3 Third-Generation Works: Applications and Tools
	5.4 Fourth-Generation Works: Independent Modules for Modeling Smart Manufacturing
	5.5 Research Gap: Conclusions of Literature Study
	References
6 Toward Developing a New Modular Petri Net
	6.1 Toward Independent Development of Modules
	6.2 Design of Modular Petri Nets
		6.2.1 Composition of Modular Petri Nets
		6.2.2 Transitions in Modular Petri Nets
		6.2.3 Visibility of Transitions in a Modular Petri Net
	References
7 Design of a New Modular Petri Nets
	7.1 Petri Module
	7.2 Inter-Modular Connectors
	7.3 Formal Definitions for the New Entities
		7.3.1 Formal Definition of Petri Module
		7.3.2 Formal Definition of Inter-Modular Connector
		7.3.3 Formal Definition of Modular Petri Net
	7.4 Application Example: A Modular Petri Net
		7.4.1 The Problem: Computing a Quadratic Function
		7.4.2 Petri Module of a Communicating Agent
		7.4.3 Modular Petri Net Model
	7.5 Chapter Summary
		7.5.1 Technical Notes on TCP/IP Based Communication
	References
8 GPenSIM Support for Petri Modules
	8.1 Modular Model Building
		8.1.1 Declaring Modules with the IO Ports
	8.2 Modular Processor Files
	8.3 Modular Visibility of Transitions
		8.3.1 Modular Visibility: An Example
		8.3.2 Modular Visibility: Summary
	8.4 Developing Modules with GPenSIM
		8.4.1 The Adder Module
		8.4.2 The Multiplier Module
		8.4.3 The Client Module
		8.4.4 Putting All Together
		8.4.5 Technical Note on Independent Module Development
	References
Part III Legacy Petri Nets
9 Module Extraction
	9.1 Rules of Interfacing
	9.2 Algorithm: Module Extraction
		9.2.1 Fixing Violations in Pass-1
		9.2.2 Fixing Violations in Pass-2
	9.3 Application of Module Extraction Algorithm
		9.3.1 Input Modules
		9.3.2 Machining Modules
		9.3.3 Finishing and Output Module
		9.3.4 Inter-Modular Connector
		9.3.5 The Complete Modular Petri Net
	9.4 Analyzing the Fixes
		9.4.1 General Analysis of the Fixes
		9.4.2 P-Invariants
		9.4.3 T-Invariants
	References
10 Activity-Oriented Petri Nets (AOPN)
	10.1 The Background of AOPN
		10.1.1 Formal Definition of AOPN
	10.2 Two Phases of the AOPN Approach
	10.3 Application Example on AOPN
		10.3.1 Phase-1: Creating the Static Petri Net Graph
		10.3.2 Phase-2: Adding the Run-Time Dynamics
		10.3.3 GPenSIM Functions for AOPN Realization
		10.3.4 Simulation of the AOPN Model
		10.3.5 Discussion: Advantage of AOPN Approach
	10.4 When Not to Use AOPN
	References
Part IV Collaborating Modules
11 Discrete Systems as Petri Modules
	11.1 Module Abstraction
		11.1.1 Collaborativeness and Timing
		11.1.2 Collaborative Module
	11.2 Loosely Connected Modules
		11.2.1 Serial Block
		11.2.2 Parallel Block
		11.2.3 Cyclic (Iterating) Block
		11.2.4 Alternating (Mutual-Exclusion) Block
		11.2.5 Independent Block
		11.2.6 Assembly Block
		11.2.7 Disassembly Block
		11.2.8 Source Block and Sink Block
	11.3 Analysis: Connectivity of Modules
	11.4 Adjacency Matrix and Laplacian Matrix
	11.5 Spanning Tree and Connectedness
		11.5.1 Spanning Tree and Connected Components
	11.6 The Four Matrices
		11.6.1 Reachability Matrix
		11.6.2 Rader\'s Matrix
		11.6.3 Connection Matrix
		11.6.4 Component Matrix
	11.7 Algorithms for Modular Connectivity
	References
12 Algorithms for Modular Connectivity
	12.1 Algorithm: Existence of Spanning Tree
	12.2 Algorithm: Source of a Spanning Tree
	12.3 Algorithm: Functional Spanning Tree
	12.4 Algorithm: Existence of Connected Components
	12.5 Algorithm: Steiner Spanning Tree
		12.5.1 Steiner Spanning Tree: The Basics
		12.5.2 Steiner Spanning Tree: The Algorithm
	12.6 Applications of the Algorithms
		12.6.1 Scenario for Creation of Networks
	12.7 Leader-Followers Networking (LFN)
		12.7.1 Algorithm for Creation of LFN
		12.7.2 Example for Creation of LFN
	12.8 Steiner-Mode Networking (SMN)
		12.8.1 Algorithm for Creation of SMN
		12.8.2 Example for Creation of SMN
	12.9 Negotiating-Peers Networking (NPN)
		12.9.1 Algorithm for Creating NPN
		12.9.2 Example for Creation of NPN
	12.10 Chapter Summary
	References
13 Model Checking for Collaborativeness
	13.1 The Problem
	13.2 Towards a New Approach
	13.3 Step-1: Identifying the Group of Modules
	13.4 Step-2: Inviting a Module
	13.5 Step-3: Generating the State Space
		13.5.1 Terminal State and Terminal Transition
		13.5.2 Possibility for Deadlocks
		13.5.3 Possibility for Livelocks
		13.5.4 Free from Livelocks and Deadlocks
	13.6 Step-4: Analyzing the State Space
		13.6.1 Making a Decision on Collaborativeness
	13.7 Step-5: Establishing the Connectivity
	13.8 The New Approach
	13.9 Application Example
	13.10 Chapter Summary
	References
14 Generic Petri Module
	14.1 Structure of Petri Module for Collaboration
	14.2 Colored Petri Module
	14.3 Generic Petri Module
	Reference
Appendix A GPenSIM Webpage
Index