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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.ModelingwithPetrinets 4
1.3.Petrinetstructure 6
1.4.DynamicbehaviorofPetrinets 7
1.5.Petrinetanalysis 11
1.5.1.Petrinetproperties 11
1.5.2.Temporallogic 14
1.5.3 Analysis methods 18
1.6.StochasticPetrinets 19
1.6.1.Stochasticprocess 21
1.6.2.Markovprocess 21
1.6.3 Stochastic Petri nets having exponential law 22
1.6.4 Quantitative properties 26
1.7.GeneralizedstochasticPetrinets 27
1.7.1.EmbeddedMarkovChain 29
1.8.Conclusion 32
Chapter 2 Reconfiguration Aspects in Petri Nets 33
2.1 Introduction 33
2.2.GraphTransformationSystems 34
2.3 Double-pushout approach for Petri nets 35
2.4 Net rewriting systems 38
2.5.Self-modifyingnets 41
2.6.ReconfigurablePetrinets 43
2.7 Improved net rewriting systems 47
2.8.Otherextensions 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.Illustrativeexample 61
3.5.Stochasticrewardnets 67
3.6.Configuration-dependentstochasticrewardnets 68
3.7.TransformationofCD-SRNsintobasicSRNs 69
3.8.Proofs 72
3.9.Illustrativeexample 73
3.10.Conclusion 79
Chapter 4 Generalized Stochastic Petri Nets with Dynamic Structure 81
4.1 Introduction 81
4.2.DynamicGSPNs 83
4.2.1 Formal definition 83
4.3.D-GSPNtransformationtowardsGSPNs 85
4.4 Qualitative/quantitative analysis of D-GSPNs 89
4.5.Proofs 90
4.6.Illustrativeexample 92
4.7.GeneralizedstochasticPetrinetswithinhibitorandresetarcs 98
4.8 Improved D-GSPNs under infinite-server semantics 99
4.9.UnfoldingID-GSPNsintoGSPNs 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.ReconfigurablegeneralizedstochasticPetrinets 125
5.2.1 Definition of RecGSPNs 125
5.2.2.Propertiespreservingnets 130
5.3.PreservationofpropertiesinRecGSPNs 131
5.3.1 Preservation of LBR, home state and deadlock-free 131
5.3.2.Preservationoflineartemporalproperties 136
5.4 Quantitative analysis 141
5.5.UsingRecGSPNsinpractice 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.Factor1:modelsize 157
6.3.2.Factor2:Markovchainspatialcomplexity 159
6.3.3.Factor3:Markovchaintimecomplexity 161
6.4.Conclusion 163
Conclusion 165
References 169
Index 177
