Enhancing Stochastic Petri Nets with Reconfigurability

Samir Tigane is Associate Professor at the University of Biskra and researcher at the Laboratoire de l'Informatique Intelligente (LINFI), Algeria. His research includes software engineering, formal methods and artificial intelligence.Laid Kahloul is Professor at the University of Biskra and researcher at the Laboratoire de l'Informatique Intelligente (LINFI), Algeria. His research includes software engineering, formal methods, security and artificial intelligence.Abdelhamid Mellouk is Full-time University Professor, Director of the IT4H High School Engineering Department and Head of the TincNET Research Team, UPEC, France. He is also the founder of Network Control Research and Curricula activities at UPEC, President of the Policies and Programs commission at the National Council for Scientific Research and Technologies, a HCERES Expert, a CNU member and Co-President of the DS-AI Systematic Deep Tech Hub.

• Preface ixGeneral Introduction xiPart 1 State of the Art 1Chapter 1 From Petri Nets to Stochastic Petri Nets 31.1 Introduction 31.2.ModelingwithPetrinets 41.3.Petrinetstructure 61.4.DynamicbehaviorofPetrinets 71.5.Petrinetanalysis 111.5.1.Petrinetproperties 111.5.2.Temporallogic 141.5.3 Analysis methods 181.6.StochasticPetrinets 191.6.1.Stochasticprocess 211.6.2.Markovprocess 211.6.3 Stochastic Petri nets having exponential law 221.6.4 Quantitative properties 261.7.GeneralizedstochasticPetrinets 271.7.1.EmbeddedMarkovChain 291.8.Conclusion 32Chapter 2 Reconfiguration Aspects in Petri Nets 332.1 Introduction 332.2.GraphTransformationSystems 342.3 Double-pushout approach for Petri nets 352.4 Net rewriting systems 382.5.Self-modifyingnets 412.6.ReconfigurablePetrinets 432.7 Improved net rewriting systems 472.8.Otherextensions 482.9 Trade-off between expressiveness and calculability in PN-based reconfigurable formalisms 492.10.Conclusion 51Part 2 Orientation 1 53Chapter 3 Rewritable Topology in Generalized Stochastic Petri Nets 553.1 Introduction 553.2 GSPNs with rewritable topology 563.2.1 Formal definition 583.3.Proofs 603.4.Illustrativeexample 613.5.Stochasticrewardnets 673.6.Configuration-dependentstochasticrewardnets 683.7.TransformationofCD-SRNsintobasicSRNs 693.8.Proofs 723.9.Illustrativeexample 733.10.Conclusion 79Chapter 4 Generalized Stochastic Petri Nets with Dynamic Structure 814.1 Introduction 814.2.DynamicGSPNs 834.2.1 Formal definition 834.3.D-GSPNtransformationtowardsGSPNs 854.4 Qualitative/quantitative analysis of D-GSPNs 894.5.Proofs 904.6.Illustrativeexample 924.7.GeneralizedstochasticPetrinetswithinhibitorandresetarcs 984.8 Improved D-GSPNs under infinite-server semantics 994.9.UnfoldingID-GSPNsintoGSPNs 1054.10 Running examples 1104.11.Conclusion 119Part 3 Orientation 2 121Chapter 5 Reconfigurable Generalized Stochastic Petri Nets 1235.1 Introduction 1235.2.ReconfigurablegeneralizedstochasticPetrinets 1255.2.1 Definition of RecGSPNs 1255.2.2.Propertiespreservingnets 1305.3.PreservationofpropertiesinRecGSPNs 1315.3.1 Preservation of LBR, home state and deadlock-free 1315.3.2.Preservationoflineartemporalproperties 1365.4 Quantitative analysis 1415.5.UsingRecGSPNsinpractice 1445.6.Conclusion 149Part 4 Evaluation, Discussion and Conclusion 151Chapter 6 Evaluation and Discussion 1536.1 Introduction 1536.2 Qualitative aspects 1536.3 Quantitative aspects 1566.3.1.Factor1:modelsize 1576.3.2.Factor2:Markovchainspatialcomplexity 1596.3.3.Factor3:Markovchaintimecomplexity 1616.4.Conclusion 163Conclusion 165References 169Index 177