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Full Description
This book explores the world of reconfigurable stochastic Petri nets (RSPNs), a powerful method for modeling and verifying complex, dynamic and reconfigurable systems. As modern discrete-event systems become increasingly flexible, requiring structural adaptability at runtime, classical Petri nets are proving insufficient. This book presents innovative extensions to Petri nets, offering enhanced modeling capabilities for reconfigurable systems, while ensuring efficient verification.
Through a structured approach, this book introduces reconfigurable generalized stochastic Petri nets (RecGSPNs), an advanced framework that integrates reconfigurability while preserving crucial system properties such as liveness, boundedness and deadlock-freedom. This book systematically explores modeling techniques, including stochastic reward nets and dynamic topology transformations, demonstrating their effectiveness through quantitative and qualitative analyses. By addressing challenges in state-space explosion and computational complexity, this book provides essential methodologies for researchers and practitioners working on reconfigurable systems, and serves as a valuable resource for those working in network security, manufacturing systems and distributed computing, where dynamic reconfigurations are essential.
Contents
Preface ix
General Introduction xi
Part 1. State of the Art 1
Chapter 1. From Petri Nets to Stochastic Petri Nets 3
1.1. Introduction 3
1.2. Modeling with Petri nets 4
1.3. Petri net structure 6
1.4. Dynamic behavior of Petri nets 7
1.5. Petri net analysis 11
1.5.1. Petri net properties 11
1.5.2. Temporal logic 14
1.5.3. Analysis methods 18
1.6. Stochastic Petri nets 19
1.6.1. Stochastic process 21
1.6.2. Markov process 21
1.6.3. Stochastic Petri nets having exponential law 22
1.6.4. Quantitative properties 26
1.7. Generalized stochastic Petri nets 27
1.7.1. Embedded Markov Chain 29
1.8. Conclusion 32
Chapter 2. Reconfiguration Aspects in Petri Nets 33
2.1. Introduction 33
2.2. Graph Transformation Systems 34
2.3. Double-pushout approach for Petri nets 35
2.4. Net rewriting systems 38
2.5. Self-modifying nets 41
2.6. Reconfigurable Petri nets 43
2.7. Improved net rewriting systems 47
2.8. Other extensions 48
2.9. Trade-off between expressiveness and calculability in PN-based reconfigurable formalisms 49
2.10.Conclusion 51
Part 2. Orientation 1 53
Chapter 3. Rewritable Topology in Generalized Stochastic Petri Nets 55
3.1. Introduction 55
3.2. GSPNs with rewritable topology 56
3.2.1. Formal definition 58
3.3. Proofs 60
3.4. Illustrative example 61
3.5. Stochastic reward nets 67
3.6. Configuration-dependent stochastic reward nets 68
3.7. Transformation of CD-SRNs into basic SRNs 69
3.8. Proofs 72
3.9. Illustrative example 73
3.10.Conclusion 79
Chapter 4. Generalized Stochastic Petri Nets with Dynamic Structure 81
4.1. Introduction 81
4.2. Dynamic GSPNs 83
4.2.1. Formal definition 83
4.3. D-GSPN transformation towards GSPNs 85
4.4. Qualitative/quantitative analysis of D-GSPNs 89
4.5. Proofs 90
4.6. Illustrative example 92
4.7. Generalized stochastic Petri nets with inhibitor and reset arcs 98
4.8. Improved D-GSPNs under infinite-server semantics 99
4.9. Unfolding ID-GSPNs into GSPNs 105
4.10. Running examples 110
4.11. Conclusion 119
Part 3. Orientation 2 121
Chapter 5. Reconfigurable Generalized Stochastic Petri Nets 123
5.1. Introduction 123
5.2. Reconfigurable generalized stochastic Petri nets 125
5.2.1. Definition of RecGSPNs 125
5.2.2. Properties preserving nets 130
5.3. Preservation of properties in RecGSPNs 131
5.3.1. Preservation of LBR, home state and deadlock-free 131
5.3.2. Preservation of linear temporal properties 136
5.4. Quantitative analysis 141
5.5. Using RecGSPNs in practice 144
5.6. Conclusion 149
Part 4. Evaluation, Discussion and Conclusion 151
Chapter 6. Evaluation and Discussion 153
6.1. Introduction 153
6.2. Qualitative aspects 153
6.3. Quantitative aspects 156
6.3.1. Factor 1: model size 157
6.3.2. Factor 2: Markov chain spatial complexity 159
6.3.3. Factor 3: Markov chain time complexity 161
6.4. Conclusion 163
Conclusion 165
References 169
Index 177
