Petri Nets

A Petri net is a mathematical representation of a network. This book first introduces the basic models including time and stochastic extensions, in particular place-transition and high level Petri nets. Their modeling and design capabilities are illustrated by a set of representations of interest in operating and communication systems. The volume then addresses the related verification problems and proposes corresponding solutions by introducing the main notions needed to fully understand the behavior and properties behind Petri nets. Particular attention is devoted to how systems can be fully represented and analyzed in terms of their behavioral, time, and stochastic aspects by using the same formal approach and semantic basis. Finally, illustrative examples are presented in the important fields of interoperability in telecommunication services, programming languages, multimedia architectures, manufacturing systems, and communication protocols. Preface xv

Introduction xvii

PART 1. FUNDAMENTAL MODELS 1

Chapter 1. Basic Semantics 3
Michel DIAZ

Chapter 2. Application of Petri Nets to Communication Protocols 27
Michel DIAZ

Chapter 3. Analysis Methods for Petri 41
Serge HADDAD and François VERNADAT

Chapter 4. Decidability and Complexity of Petri Net Problems 87
Serge HADDAD

Chapter 5. Time Petri Nets 123
Bernard BERTHOMIEU, Marc BOYER and Michel DIAZ

Chapter 6. Temporal Composition and Time Stream Petri Nets 163
Michel DIAZ and Patrick SÉNAC

Chapter 7. High Level Petri Nets 185
Claude GIRAULT and Jean-François PRADAT-PEYRE

Chapter 8. Analysis of High Level Petri Nets 221
Claude GIRAULT and Jean-François PRADAT-PEYRE

Chapter 9. Stochastic Petri Nets 269
Serge HADDAD and Patrice MOREAUX

Chapter 10. Stochastic Well-formed Petri Nets 303
Serge HADDAD and Patrice MOREAUX

Chapter 11. Tensor Methods and Stochastic Petri Nets 321
Serge HADDAD and Patrice MOREAUX

PART 2. VERIFICATION AND APPLICATION OF PETRI NETS 347

Chapter 12. Verification of Specific Properties 349
Serge HADDAD and François VERNADAT

Chapter 13. Petri Net Unfoldings – Properties 415
Jean-Michel COUVREUR and Denis POITRENAUD

Chapter 14. Symmetry and Temporal Logic 435
Serge HADDAD and Jean-Michel ILIÉ

Chapter 15. Hierarchical Time Stream Petri Nets 461
Patrick SÉNAC and Michel DIAZ

Chapter 16. Petri Nets and Linear Logic 481
Brigitte PRADIN, Robert VALETTE and Nicolas RIVIÈRE

Chapter 17. Modeling of Multimedia Architectures: the Case of Videoconferencing with Guaranteed Quality of Service 501
Philippe OWEZARSKI and Marc BOYER

Chapter 18 Performance Evaluation in Manufacturing Systems 527
Isabel DEMONGODIN, Nathalie SAUER and Laurent TRUFFET

Conclusion 577

List of Authors 579

Index 581 "We think that this volume should greatly help any designer to build the new forthcoming generation of distributed systems." (Mathematical Reviews, 2011)

Michel Diaz is director of research at the National Center of Scientific Research (CNRS), Paris, France and leads the critical computer systems research department at LAAS-CNRS, Toulouse.