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Journal ArticleDOI

Petri nets: Properties, analysis and applications

01 Apr 1989-Vol. 77, Iss: 4, pp 541-580
TL;DR: The author proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis, and one section is devoted to marked graphs, the concurrent system model most amenable to analysis.
Abstract: Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets. >

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03 Aug 2005
TL;DR: In this paper, the authors present a system for hazard analysis based on the idea of fault trees, and present a set of guidelines to avoid common mistakes in such a system, as well as some advantages and disadvantages of using fault trees.
Abstract: PREFACE. ACKNOWLEDGMENTS. 1. System Safety. 1.1 Introduction. 1.2 System Safety Background. 1.3 System Safety Characterization. 1.4 System Safety Process. 1.5 System Concept. 1.6 Summary. 2. Hazards, Mishap, and Risk. 2.1 Introduction. 2.2 Hazard-Related Definitions. 2.3 Hazard Theory. 2.4 Hazard Actuation. 2.5 Hazard Causal Factors. 2.6 Hazard-Mishap Probability. 2.7 Recognizing Hazards. 2.8 Hazard Description. 2.9 Summary. 3. Hazard Analysis Types and Techniques. 3.1 Types and Techniques. 3.2 Description of Hazard Analysis Types. 3.3 Timing of Hazard Analysis Types. 3.4 Interrelationship of Hazard Analysis Types. 3.5 Hazard Analysis Techniques. 3.6 Inductive and Deductive Techniques. 3.7 Qualitative and Quantitative Techniques. 3.8 Summary. 4. Preliminary Hazard List. 4.1 Introduction. 4.2 Background. 4.3 History. 4.4 Theory. 4.5 Methodology. 4.6 Worksheet. 4.7 Hazard Checklists. 4.8 Guidelines. 4.9 Example: Ace Missile System. 4.10 Advantages and Disadvantages. 4.11 Common Mistakes to Avoid. 4.12 Summary. 5. Preliminary Hazard Analysis. 5.1 Introduction. 5.2 Background. 5.3 History. 5.4 Theory. 5.5 Methodology. 5.6 Worksheet. 5.7 Guidelines. 5.8 Example: Ace Missile System. 5.9 Advantages and Disadvantages. 5.10 Common Mistakes to Avoid. 5.11 Summary. 6. Subsystem Hazard Analysis. 6.1 Introduction. 6.2 Background. 6.3 History. 6.4 Theory. 6.5 Methodology. 6.6 Worksheet. 6.7 Guidelines. 6.8 Example: Ace Missile System. 6.9 Advantages and Disadvantages. 6.10 Common Mistakes to Avoid. 6.11 Summary. 7. System Hazard Analysis. 7.1 Introduction. 7.2 Background. 7.3 History. 7.4 Theory. 7.5 Methodology. 7.6 Worksheet. 7.7 Guidelines. 7.8 Example. 7.9 Advantages and Disadvantages. 7.10 Common Mistakes to Avoid. 7.11 Summary. 8. Operating and Support Hazard Analysis. 8.1 Introduction. 8.2 Background. 8.3 History. 8.4 Definitions. 8.5 Theory. 8.6 Methodology. 8.7 Worksheet. 8.8 Hazard Checklists. 8.9 Support Tools. 8.10 Guidelines. 8.11 Examples. 8.12 Advantages and Disadvantages. 8.13 Common Mistakes to Avoid. 8.14 Summary. 9. Health Hazard Assessment. 9.1 Introduction. 9.2 Background. 9.3 History. 9.4 Theory. 9.5 Methodology. 9.6 Worksheet. 9.7 Checklist. 9.8 Example. 9.9 Advantages and Disadvantages. 9.10 Common Mistakes to Avoid. 9.11 Summary. 10. Safety Requirements/Criteria Analysis. 10.1 Introduction. 10.2 Background. 10.3 History. 10.4 Theory. 10.5 Methodology. 10.6 Worksheets. 10.7 Example. 10.8 Advantages and Disadvantages. 10.9 Common Mistakes to Avoid. 10.10 Summary. 11. Fault Tree Analysis. 11.1 Introduction. 11.2 Background. 11.3 History. 11.4 Theory. 11.5 Methodology. 11.6 Functional Block Diagrams. 11.7 Cut Sets. 11.8 MOCUS Algorithm. 11.9 Bottom-Up Algorithm. 11.10 Mathematics. 11.11 Probability. 11.12 Importance Measures. 11.13 Example 1. 11.14 Example 2. 11.15 Example 3. 11.16 Phase- and Time-Dependent FTA. 11.17 Dynamic FTA. 11.18 Advantages and Disadvantages. 11.19 Common Mistakes to Avoid. 11.20 Summary. 12. Event Tree Analysis. 12.1 Introduction. 12.2 Background. 12.3 History. 12.4 Definitions. 12.5 Theory. 12.6 Methodology. 12.7 Worksheet. 12.8 Example 1. 12.9 Example 2. 12.10 Example 3. 12.11 Example 4. 12.12 Advantages and Disadvantages. 12.13 Common Mistakes to Avoid. 12.14 Summary. 13. Failure Mode and Effects Analysis. 13.1 Introduction. 13.2 Background. 13.3 History. 13.4 Definitions. 13.5 Theory. 13.6 Methodology. 13.7 Worksheet. 13.8 Example 1: Hardware Product FMEA. 13.9 Example 2: Functional FMEA. 13.10 Level of Detail. 13.11 Advantages and Disadvantages. 13.12 Common Mistakes to Avoid. 13.13 Summary. 14. Fault Hazard Analysis. 14.1 Introduction. 14.2 Background. 14.3 History. 14.4 Theory. 14.5 Methodology. 14.6 Worksheet. 14.7 Example. 14.8 Advantages and Disadvantages. 14.9 Common Mistakes to Avoid. 14.10 Summary. 15. Functional Hazard Analysis. 15.1 Introduction. 15.2 Background. 15.3 History. 15.4 Theory. 15.5 Methodology. 15.6 Worksheets. 15.7 Example 1: Aircraft Flight Functions. 15.8 Example 2: Aircraft Landing Gear Software. 15.9 Example 3: Ace Missile System. 15.10 Advantages and Disadvantages. 15.11 Common Mistakes to Avoid. 15.12 Summary. 16. Sneak Circuit Analysis. 16.1 Introduction. 16.2 Background. 16.3 History. 16.4 Definitions. 16.5 Theory. 16.6 Methodology. 16.7 Example 1: Sneak Path. 16.8 Example 2: Sneak Label. 16.9 Example 3: Sneak Indicator. 16.10 Example Sneak Clues. 16.11 Software Sneak Circuit Analysis. 16.12 Advantages and Disadvantages. 16.13 Common Mistakes to Avoid. 16.14 Summary. 17. Petri Net Analysis (PNA). 17.1 Introduction. 17.2 Background. 17.3 History. 17.4 Definitions. 17.5 Theory. 17.6 Methodology. 17.7 Examples. 17.8 Advantages and Disadvantages. 17.9 Common Mistakes to Avoid. 17.10 Summary. 18. Markov Analysis. 18.1 Introduction. 18.2 Background. 18.3 History. 18.4 Definitions. 18.5 Theory. 18.6 Methodology. 18.7 Examples. 18.8 Markov Analysis and FTA Comparisons. 18.9 Advantages and Disadvantages. 18.10 Common Mistakes to Avoid. 18.11 Summary. 19. Barrier Analysis. 19.1 Introduction. 19.2 Background. 19.3 History. 19.4 Definitions. 19.5 Theory. 19.6 Methodology. 19.6.1 Example Checklist of Energy Sources. 19.6.2 Considerations. 19.7 Worksheet. 19.8 Example. 19.9 Advantages and Disadvantages. 19.10 Common Mistakes to Avoid. 19.11 Summary. 20. Bent Pin Analysis. 20.1 Introduction. 20.2 Background. 20.3 History. 20.4 Theory. 20.5 Methodology. 20.6 Worksheet. 20.7 Example. 20.8 Advantages and Disadvantages. 20.9 Common Mistakes to Avoid. 20.10 Summary. 21. Hazard and Operability Analysis. 21.1 Introduction. 21.2 Background. 21.3 History. 21.4 Theory. 21.5 Methodology. 21.5.1 Design Representations. 21.5.2 System Parameters. 21.5.3 Guide Words. 21.5.4 Deviation from Design Intent. 21.6 Worksheet. 21.7 Example 1. 21.8 Example 2. 21.9 Advantages and Disadvantages. 21.10 Common Mistakes to Avoid. 21.11 Summary. 22. Cause-Consequence Analysis. 22.1 Introduction. 22.2 Background. 22.3 History. 22.4 Definitions. 22.5 Theory. 22.6 Methodology. 22.7 Symbols. 22.8 Worksheet. 22.9 Example 1: Three-Component Parallel System. 22.10 Example 2: Gas Pipeline System. 22.10.1 Reducing Repeated Events. 22.11 Advantages and Disadvantages. 22.12 Common Mistakes to Avoid. 22.13 Summary. 23. Common Cause Failure Analysis. 23.1 Introduction. 23.2 Background. 23.3 History. 23.4 Definitions. 23.5 Theory. 23.6 Methodology. 23.7 Defense Mechanisms. 23.8 Example. 23.9 Models. 23.10 Advantages and Disadvantages. 23.11 Common Mistakes to Avoid. 23.12 Summary. 24. Management Oversight Risk Tree Analysis. 24.1 Introduction. 24.2 Background. 24.3 History. 24.4 Theory. 24.5 Methodology. 24.6 Worksheet. 24.7 Advantages and Disadvantages. 24.8 Common Mistakes to Avoid. 24.9 Summary. 25. Software Safety Assessment. 25.1 Introduction. 25.2 Background. 25.3 History. 25.4 Theory. 25.5 Methodology. 25.6 Worksheet. 25.7 Software Risk Level. 25.8 Example. 25.9 Advantages and Disadvantages. 25.10 Common Mistakes to Avoid. 25.11 Summary. 26. Summary. 26.1 Principle 1: Hazards, Mishaps, and Risk are Not Chance Events. 26.2 Principle 2: Hazards are Created During Design. 26.3 Principle 3: Hazards are Comprised of Three Components. 26.4 Principle 4: Hazard and Mishap Risk Management Is the Core Safety Process. 26.5 Principle 5: Hazard Analysis Is a Key Element of Hazard and Mishap Risk Management. 26.6 Principle 6: Hazard Management Involves Seven Key Hazard Analysis Types. 26.7 Principle 7: Hazard Analysis Primarily Encompasses Seven Hazard Analysis Techniques. 26.8 Finis. Appendix A: List of Acronyms. Appendix B: Glossary. Appendix C: Hazard Checklists. Index.

683 citations

Journal ArticleDOI
01 Jan 2004
TL;DR: It is proved that by adding a control place for each elementary siphon to make sure that it is marked, deadlock can be successfully prevented and is suitable for large-scale Petri nets.
Abstract: A variety of important Petri net-based methods to prevent deadlocks arising in flexible manufacturing systems (FMS) are to add some control places and related arcs to strict minimal siphons (SMS) such that no siphon can be emptied. Since the number of minimal siphons grows in general exponentially with respect to a Petri net size, their disadvantages lie in that they often add too many additional places to the net, thereby making the resulting net model much more complex than the original one. This paper explores ways to minimize the new additions of places while achieving the same control purpose. It proposes for the first time the concept of elementary siphons that are a special class of siphons. The set of elementary siphons in a Petri net is generally a proper subset of the set of all SMS. Its smaller cardinality becomes evident in large Petri net models. This paper proves that by adding a control place for each elementary siphon to make sure that it is marked, deadlock can be successfully prevented. Compared with the existing methods, the new method requires a much smaller number of control places and, therefore, is suitable for large-scale Petri nets. An FMS example is used to illustrate the proposed concepts and policy, and show the significant advantage over the previous methods.

631 citations


Cites background from "Petri nets: Properties, analysis an..."

  • ...Petri nets [1], [2] have a simple mathematical representation useful for the analysis and design of discrete event systems including FMS....

    [...]

Journal ArticleDOI
01 Jan 1995
TL;DR: This work examines the benefits and problems inherent in asynchronous computations, and in some of the more notable design methodologies, which include Huffman asynchronous circuits, burst-mode circuits, micropipelines, template-based and trace theory-based delay-insensitive circuits, signal transition graphs, change diagrams, and complication-based quasi-delay-insensitivity circuits.
Abstract: Asynchronous design has been an active area of research since at least the mid 1950's, but has yet to achieve widespread use. We examine the benefits and problems inherent in asynchronous computations, and in some of the more notable design methodologies. These include Huffman asynchronous circuits, burst-mode circuits, micropipelines, template-based and trace theory-based delay-insensitive circuits, signal transition graphs, change diagrams, and complication-based quasi-delay-insensitive circuits. >

622 citations


Cites methods from "Petri nets: Properties, analysis an..."

  • ...This methodology is founded upon use of an I-Net, a model based on Petri Nets [ 23 ]....

    [...]

Journal ArticleDOI
TL;DR: The fundamental concepts of Petri nets are introduced to researchers and practitioners, both from academia and industry, who are involved in the work in the areas of modelling and analysis of industrial types of systems, as well as those who may potentially be involved in these areas.
Abstract: Petri nets, as a graphical and mathematical tool, provide a uniform environment for modelling, formal analysis, and design of discrete event systems. The main objective of this paper is to introduce the fundamental concepts of Petri nets to researchers and practitioners, both from academia and industry, who are involved in the work in the areas of modelling and analysis of industrial types of systems, as well as those who may potentially be involved in these areas. The paper begins with an overview of applications of Petri nets, mostly industrial ones. Then, it proceeds with a description of Petri nets, properties, and analysis methods. The discussion of properties is put in the context of industrial applications. The analysis methods are illustrated using an example of a simple robotic assembly system. The performance analysis, using Petri nets, is discussed for deterministic and stochastic Petri nets. The presented techniques are illustrated by examples representing simple production systems. In addition, the paper introduces high-level Petri nets, fuzzy Petri nets, and temporal Petri nets. This is done in the context of application prospects. The paper also briefly discusses some of the reasons restricting the use of Petri nets, mostly, to academic institutions. >

615 citations

BookDOI
01 Jan 2001

570 citations

References
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01 Jan 1962
TL;DR: The theory of automata is shown not capable of representing the actual physical flow of information in the solution of a recursive problem and a theory of communication is proposed that yields a means of representation that with equal rigor and simplicity accomplishes more than the theory of synchronous automata.
Abstract: Diese Arbeit befasst sich mit den begrifflichen Grundlagen einer Theorie der Kommunikation. Die Aufgabe dieser Theorie soll es sein, moglichst viele Erscheinungen bei der Informationsubertragung und Informationswandlung in einheitlicher und exakter Weise zu beschreiben. The theory of automata is shown not capable of representing the actual physical flow of information in the solution of a recursive problem. The argument proceeds as follows: 1. We assume the following postulates: a) there exists an upper bound on the speed of signals; b) there exists an upper bound on the density with which information can be stored. 2. Automata of fixed, finite size can recognize, at best, only iteratively defined classes of input sequences. (See Kleene (11) and Copi, Elgot, and Wright (8).) 3. Recursively defined classes of input sequences that cannot be defined iteratively can be recognized only by automata of unbounded size. 4. In order for an automaton to solve a (soluble) recursive problem, the possibility must be granted that it can be extended unboundedly in whatever way might be required. 5. Automata (as actual hardware) formulated in accordance with automata theory will, after a finite number of extensions, conflict with at least one of the postulates named above. Suitable conceptual structures for an exact theory of communication are then discussed, and a theory of communication proposed. All of the really useful results of automata theory may be expressed by means of these new concepts. Moreover, the results retain their usefulness and the new nrocedure has definite advantages over the older ones. The proposed representation differs from each of the presently known theories concerning information on at least one of the following essential points: 1. The existence of a metric is assumed for either space nor time nor for other physical magnitudes. 2. Time is introduced as a strictly local relation between states. 3. The objects of the theory are discrete, and they are combined and produced only by means of strictly finite techniques. The following conclusions drawn from the results of this work may be cited as of some practical interest: 1. The tolerance requirements for the response characteristics of computer components can be substantially weakened if the computer is suitably structured. 2. It is possible to design computers structurally in such a way that they are asynchronous, all parts operating in parallel, and can be extended arbitrarily without interrupting their computation. 3. For complicated organizational processes of any given sort the theory yields a means of representation that with equal rigor and simplicity accomplishes more than the theory of synchronous automata.

2,523 citations

Journal ArticleDOI
TL;DR: It is shown that GSPN are equivalent to continuous-time stochastic processes, and solution methods for the derivation of the steady state probability distribution are presented.
Abstract: Generalized stochastic Petri nets (GSPNs) are presented and are applied to the performance evaluation of multiprocessor systems. GSPNs are derived from standard Petri nets by partitioning the set of transitions into two subsets comprising timed and immediate transitions. An exponentially distributed random firing time is associated with each timed transition, whereas immediate transitions fire in zero time. It is shown that GSPN are equivalent to continuous-time stochastic processes, and solution methods for the derivation of the steady state probability distribution are presented. Examples of application of gspn models to the performance evaluation of multiprocessor systems show the usefulness and the effectiveness of this modeling tool. 15 references.

1,394 citations

Journal ArticleDOI
TL;DR: An isomorphism between the behavior of Petri nets with exponentially distributed transition rates and Markov processes is presented and this work solves for the steady state average message delay and throughput on a communication link when the alternating bit protocol is used for error recovery.
Abstract: An isomorphism between the behavior of Petri nets with exponentially distributed transition rates and Markov processes is presented. In particular, k-bounded Petri nets are isomorphic to finite Markov processes and can be solved by standard techniques if k is not too large. As a practical example, we solve for the steady state average message delay and throughput on a communication link when the alternating bit protocol is used for error recovery.

1,090 citations

Journal ArticleDOI
TL;DR: This paper introduces a model called the parallel program schema for the representation and study of programs containing parallel sequencing, related to Ianov's program schema, but extends it, both by modelling memory structure in more detail and by admitting parallel computation.

1,040 citations

Journal ArticleDOI
TL;DR: The time-Petri net (TPN) appears to be a suitable model for the study of practical recoverable processes and several practical communication protocols are formally designed and analyzed using this new model.
Abstract: A study is presented which permits the formal analysis and synthesis of recoverable computer communication protocols. This study is based on a formal representation of processes by a model of computation, the Petri nets (PN's). The PN model is generalized to include a representation of the possible failures, and then, the concept of "recoverability" is formally defined. A set of necessary and sufficient conditions which a process must satisfy in order to be recoverable is derived. In the PN model, the processes that satisfy these conditions are shown to have some practical limitations. A new model, the time-Petri net (TPN), is introduced to remove these limitations. This new model allows the introduction of constraints in the execution times of its part. As shown in this paper, the TPN appears to be a suitable model for the study of practical recoverable processes. Several practical communication protocols are formally designed and analyzed using this new model, and some interesting properties of these protocols are formally derived.

917 citations