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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01 Jul 2017
TL;DR: A resource-oriented modular Petri net modelling methodology is introduced and applied to a tanning Industry and the overall system model is used to simulate alternative scenarios and to study the effect of changes in system's performance.
Abstract: A resource-oriented modular Petri net modelling methodology is introduced and applied to a tanning Industry. Two general modules are recognized and their models are implemented to represent machine performing multiple types of processes and seasonal drying. Then a well-defined connecting procedure is introduced in order to create the model of the overall system with respect to the resources used. The overall system model is used to simulate alternative scenarios and to study the effect of changes in system's performance.
Cites background from "Petri nets: Properties, analysis an..."
...TPN= {P, T, I, O, m0, D} with D representing time delay, a function from the set of non-negative real numbers } [10]- [12]....
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01 Jan 2021
TL;DR: The mathematical representation of the ordinary Petri net is provided by Peterson as discussed by the authors, and the mathematical model of Petri nets can be found in Petri Net Theory and Modeling of Systems.
Abstract: The mathematical representation of the ordinary Petri net is provided by (Peterson,.Petri Net Theory and Modeling of Systems, Prentice-Hall, Englewood Cliffs, New Jersey, 1981).
17 Aug 2012
TL;DR: A construcao de modelos tem fundamental importância for o estudo e simulacao de processos as mentioned in this paper, e as Redes de Petri sao uma ferramenta de modelagem that possibilitam uma visualizacao grafica do processo, a analise da qualidade do modelo and fornecem meios for identificar gargalos, bloqueios and apresentar otimizacoes.
Abstract: A construcao de modelos tem fundamental importância para o estudo e simulacao de processos. As Redes de Petri sao uma ferramenta de modelagem que possibilitam uma visualizacao grafica do processo, a analise da qualidade do modelo e fornecem meios para identificar gargalos, bloqueios e apresentar otimizacoes. Este trabalho apresenta um modelo em Redes de Petri utilizado para simular algumas funcoes de um Sistema de Monitoramento de Condicao de Maquina. Os resultados obtidos possibilitarao a economia de tempo e recursos na implementacao do sistema em um dispositivo embarcado microcontrolado.
Cites background from "Petri nets: Properties, analysis an..."
...…propriedades comportamentais e estruturais (CARDOSO; VALETTE, 1997; MACIEL; LINS; CUNHA, 1996; PETERSON, 1982) foram avaliadas sobre o modelo em RPCH. Especificamente, três propriedades fundamentais para o sistema são avaliadas no modelo: vivacidade, repetitividade e limitação (MURATA, 1989)....
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01 Jul 2019
TL;DR: Methods for implementing state-transition formal models, such as finite state and pushdown automata, as well as extended Petri nets (A-nets) by means of IEC 61499 function blocks are proposed.
Abstract: Efficient application of model-based software design methodologies in industrial automation requires methods and tools for automatic code generation. Formal models can be especially useful to avoid ambiguity, to verify and evaluate performance, which ultimately will improve the quality and reliability of the project and lead to lower design costs. This paper proposes methods for implementing state-transition formal models, such as finite state and pushdown automata, as well as extended Petri nets (A-nets) by means of IEC 61499 function blocks. These implementation approaches can be used in the design of industrial cyber-physical systems for monitoring, diagnostics, conformance checking, detection and selection of specified sequences of events and parameterized objects from an input stream. One of the proposed applications is illustrated using an example of an assembly process with LEGO blocks.
Cites background from "Petri nets: Properties, analysis an..."
...There are many kinds of STM such as finite automata (FA) [3,5], pushdown automata (PDA) [3], Petri nets (PN) [6], abstract state machines (ASM) [7], etc....
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TL;DR: In this article, the constraints and objective functions in the target optimization problems are represented as fundamental characteristics of Petri net models and then converted into binary quadratic nets, equivalent to Ising models.
Abstract: Quantum annealing is an emerging new platform for combinatorial optimization, requiring an Ising model formulation for optimization problems. The formulation can be an essential obstacle to the permeation of this innovation into broad areas of everyday life. Our research is aimed at the proposal of a Petri net modeling approach for an Ising model formulation. Although the proposed method requires users to model their optimization problems with Petri nets, this process can be carried out in a relatively straightforward manner if we know the target problem and the simple Petri net modeling rules. With our method, the constraints and objective functions in the target optimization problems are represented as fundamental characteristics of Petri net models, extracted systematically from Petri net models, and then converted into binary quadratic nets, equivalent to Ising models. The proposed method can drastically reduce the difficulty of the Ising model formulation.
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
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
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
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
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