Petri nets fundamental models, verification, and applications

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...

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Bibliographic Details
Main Author: Diaz, Michel
Format: eBook
Language:English
Published: Newark WILEY 2010
John Wiley & Sons, Incorporated
Wiley-Blackwell
Edition:1
Series:Control systems, robotics and manufacturing series
Subjects:
Applied
Distributed processing
Electronic data processing
MATHEMATICS
Parallel processing (Electronic computers)
Petri nets
System design
ISBN:9780470394304, 9781848210790, 1848210795, 0470394307
Online Access:Get full text
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Table of Contents:
  • 6.4. Temporal composition and temporal synchronization -- 6.4.1. The semantics of "waiting" -- 6.4.2. Pragmatics and time assumptions -- 6.5. Time stream PNs -- 6.5.1. Definition of the model -- 6.5.2. The different firing semantics -- 6.5.3. Relating times behavior -- 6.5.4. TSPN with structured streams -- 6.6. Application to multimedia systems -- 6.6.1. Jitter in streams -- 6.6.2. Intra- and inter-stream drifts -- 6.6.3. Modeling stream composition -- 6.6.4. Principle of modeling multimedia systems -- 6.6.5. Modeling multimedia scenarios -- 6.6.6. TSPN for designing hypermedia architectures -- 6.7. Conclusion -- 6.8. Bibliography -- Chapter 7. High Level Petri Nets -- 7.1. Introduction -- 7.2. Informal introduction to high level nets -- 7.2.1. A client-server model -- 7.2.2. Client distinction -- 7.2.3. Server distinction -- 7.2.4. Equivalent unfolded net -- 7.2.5. Colored model for the alternate bit protocol -- 7.3. Colored net definition -- 7.3.1. Notation -- 7.3.2. The formalismof colored nets -- 7.3.3. Unfolding of a colored net -- 7.4. Well-formed net definition -- 7.4.1. Color domains -- 7.4.2. Color functions -- 7.4.3. Guards -- 7.4.4. The formalismofwell-formed nets -- 7.4.5. Regular nets and ordered nets -- 7.5. Other high level formalisms -- 7.5.1. Interpreted nets -- 7.5.2. Algebraic nets -- 7.6. Conclusion -- 7.7. Bibliography -- Chapter 8. Analysis of High Level Petri Nets -- 8.1. Introduction -- 8.2. The symbolic reachability graph -- 8.2.1. Symbolic markings -- 8.2.2. Symbolic marking representation -- 8.2.3. Symbolic firing rule -- 8.2.4. Example of a symbolic reachability graph -- 8.2.5. Properties of the SRG -- 8.3. Colored invariants -- 8.3.1. Definition of invariants of high level Petri nets -- 8.3.2. Computing flows of a high level net: principles and difficulties -- 8.3.3. Computing a non-parametrized generative flow family
  • 14.2. Principles of the dynamic symmetry method
  • 11.2. Synchronized Markov chains -- 11.2.1. Tensor products -- 11.2.2. Tensor sum and continuous time Markov chains -- 11.3. Tensor algebra and SPN -- 11.3.1. Synchronous decomposition of generalized stochastic Petri nets -- 11.3.2. Asynchronous decomposition of generalized stochastic Petri nets -- 11.3.3. Tensor analysis of phase-type Petri nets -- 11.4. Tensor decomposition of stochastic well-formed Petri nets -- 11.4.1. Problems -- 11.4.2. The specification problem -- 11.4.3.The resolution problem -- 11.4.4. A tensor decomposition method for SWN -- 11.4.5. Application in the asynchronous case -- 11.5. Conclusion -- 11.6. Bibliography -- Part 2. Verification and Application of Petri Nets -- Chapter 12. Verification of Specific Properties -- 12.1. Introduction -- 12.2. Kripke structures and transitions systems -- 12.3. Temporal logic -- 12.3.1. Syntax and semantics -- 12.3.2. Methods evaluation -- 12.3.3. Temporal logic and Petri nets -- 12.4. Behavioral approach -- 12.4.1. Bisimulation relations -- 12.4.2. Weak equivalences -- 12.4.3. Modal characterizations of behavioral equivalences -- 12.5. Decidability of bisimulation and of evaluation of formulas -- 12.5.1. Undecidability results -- 12.5.2. Decidability results -- 12.6. Bibliography -- Chapter 13. Petri Net Unfoldings - Properties -- 13.1. Introduction -- 13.2. Elementary concepts -- 13.2.1. Preliminary information -- 13.2.2. Net homomorphisms -- 13.2.3. Occurrence nets -- 13.3. Branching processes and unfoldings -- 13.3.1. Branching processes -- 13.3.2. Unfoldings -- 13.4. Finite prefixes -- 13.4.1. Definition -- 13.4.2. Adequate orders and complete finite prefixes -- 13.4.3. Verification of safety properties -- 13.4.4. Detection of infinite behaviors -- 13.5. Conclusion -- 13.6. Bibliography -- Chapter 14. Symmetry and Temporal Logic -- 14.1. Introduction
  • 8.3.4. Parametrized generative family of flows for regular nets -- 8.3.5. Computation of positive flows -- 8.4. Structural reductions -- 8.4.1. Principles of extension to high level nets -- 8.4.2. Pre-agglomeration and post-agglomeration of transitions -- 8.4.3. Deletion of an implicit place -- 8.4.4. Application examples -- 8.5. Conclusion -- 8.6. Bibliography -- Chapter 9. Stochastic Petri Nets -- 9.1. Introduction -- 9.2. A stochastic semantics for discrete event systems -- 9.2.1. The stochastic model -- 9.2.2. Analysis with renewing theory -- 9.2.3. Discrete time Markov chains -- 9.2.4. Continuous time Markov chains -- 9.2.5. Semi-Markovian processes -- 9.2.6. Regenerative Markovian processes -- 9.3. Stochastic Petri nets -- 9.3.1. Stochastic Petri nets with general distributions -- 9.3.2. Stochastic Petri nets with exponential distributions -- 9.3.3. Generalized stochastic Petri nets -- 9.3.4. Deterministic stochastic Petri nets -- 9.3.5. Phase-type stochastic Petri nets -- 9.4. Some standard analysis methods -- 9.4.1. Research of a product form -- 9.4.2. Bound computations -- 9.4.3. Approximation methods -- 9.4.4. Unbounded Petri nets -- 9.5. Conclusion -- 9.6. Bibliography -- Chapter 10. Stochastic Well-formed Petri Nets -- 10.1. Introduction -- 10.2. Markovian aggregation -- 10.3. Presentation of stochastic well-formed Petri nets -- 10.3.1. The stochastic process of a well-formed Petri net -- 10.3.2. Definition of stochastic well-formed Petri nets -- 10.3.3. Modeling a multiprocessor system -- 10.4. From the symbolic graph to Markovian aggregation -- 10.4.1. Verification of the aggregation condition -- 10.4.2. Computation of the parameters of the aggregated chain -- 10.4.3. Performance indices of the multiprocessor system -- 10.5. Conclusion -- 10.6. Bibliography -- Chapter 11. Tensor Methods and Stochastic Petri Nets -- 11.1. Introduction
  • Intro -- Petri Nets: Fundamental Models, Verification and Applications -- Table of Contents -- Preface -- Introduction -- Part 1. Fundamental Models -- Chapter 1. Basic Semantics -- 1.1. Automata or state machines -- 1.1.1. Automata and state machine models -- 1.1.2. Tasks and processes -- 1.1.3. Some models -- 1.2. State machines and Petri nets (PN) -- 1.2.1. Composing state machines -- 1.2.2. Composition and synchronization -- 1.3. Concepts and definitions -- 1.3.1. Local states and enabling -- 1.3.2. Definition of the semantics of parallelism -- 1.3.3. Firing transitions -- 1.4. Accessibility graph or marking graph -- 1.5. Some basic models -- 1.5.1. Co-begin (parallel start) and co-end (synchronized termination) -- 1.5.2. Synchronization by a signal -- 1.5.3. Mutual exclusion -- 1.5.4. The reader and writer mechanisms -- 1.5.5. Bounded buffers -- 1.6. Conclusion -- 1.7. Bibliography -- Chapter 2. Application of Petri Nets to Communication Protocols -- 2.1. Basic models -- 2.2. A simple establishment of a connection -- 2.2.1. Different global semantics -- 2.2.2. Conclusion -- 2.3. The alternating bit protocol (ABP): model and verification -- 2.3.1. Loss of messages -- 2.3.2. Modeling losses -- 2.4. Communicating state machines and PNs -- 2.5. Conclusion -- 2.6. Bibliography -- Chapter 3. Analysis Methods for Petri -- 3.1. Introduction -- 3.2. Behavioral analysis of Petri nets -- 3.2.1. Semantics of a net -- 3.2.2. Usual properties -- 3.3. Analysis of nets by linear invariants -- 3.3.1. Definitions and first applications -- 3.3.2. Flow computations -- 3.3.3. Semiflow computation -- 3.3.4. Application of invariants to the analysis of a net -- 3.4. Net reductions -- 3.4.1. Pre-agglomeration of transitions -- 3.4.2. Post-agglomeration of transitions -- 3.4.3. Deletion of redundant places -- 3.5.The graph of a Petri net -- 3.5.1. General results
  • 3.5.2. State machines -- 3.5.3. Event graph -- 3.5.4. Free choice net -- 3.6. Bibliography -- Chapter 4. Decidability and Complexity of Petri Net Problems -- 4.1. Introduction -- 4.2. Decidability and complexity notions -- 4.3. Theoretical results about the reachability graph -- 4.4. Analysis of unbounded Petri nets -- 4.4.1. Construction of the covering graph -- 4.4.2. Shortest sequences -- 4.4.3. Backward analysis -- 4.5. The reachability problem -- 4.5.1. A necessary condition for reachability -- 4.5.2. A sufficient condition for reachability -- 4.6. Extensions of Petri nets -- 4.6.1. Netswith inhibitor arcs -- 4.6.2. Self-modifying nets -- 4.6.3. Recursive nets -- 4.7. Languages of Petri nets -- 4.8. Bibliography -- Chapter 5. Time Petri Nets -- 5.1. Introduction -- 5.2. Time Petri nets -- 5.2.1. Time nets -- 5.2.2. States and firing rule -- 5.2.3. Set of states, schedules -- 5.2.4. Firing domains -- 5.3. Behavior characterization - state state classes' method -- 5.3.1. State classes -- 5.3.2. Transitions between state classes -- 5.3.3. State class equality -- 5.3.4. Class graph -- 5.3.5. Marking graph and class graph -- 5.4. Analysis - operating the state class graph -- 5.4.1. Analyzing behavior of time-dependent systems -- 5.4.2. Marking reachability -- 5.4.3. Boundedness -- 5.4.4. Specific properties for set of markings or firing sequences -- 5.4.5. Time-dependent analyses, existence of schedules -- 5.5. Application example -- 5.6. Extensions and variations -- 5.6.1. Interpreting multi-enabled transitions -- 5.6.2. Other time extensions -- 5.7. Implementation using the Tina tool -- 5.7.1. Tina tool -- 5.7.2. Application example -- 5.8. Conclusion -- 5.9. Bibliography -- Chapter 6. Temporal Composition and Time Stream Petri Nets -- 6.1. Time, synchronization and autonomous behaviors -- 6.2. Limitation of time PNs -- 6.3. Temporal composition