Petri Nets for Modeling of Large Discrete Systems (Asset Analytics)

Description

This book offers a new Modular Petri Net as a solution to the vast Petri net models. It presents some approaches centering around modules (known as “Petri modules”). The goal of this book is to introduce a methodology in which Petri nets are moved to a new level. In this new level, large Petri net models are made of Petri modules, which are independent and run on different computers. This book also contains the literature study on modular Petri nets and definitions for the newer Petri modules. Also, algorithms for extracting Petri modules, and algorithms for connecting Petri modules, and applications are given in this book. Besides, the ideas and algorithms given in this book are implemented in the software General-purpose Petri Net Simulator (GPenSIM). Hence, with the use of this book the readers/users would be able to know that real-life discrete event systems could be modeled, analyzed, and performance-optimized with GPenSIM. 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