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. >

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Petri nets and industrial applications: A tutorial

Coloured Petri nets (CP-nets or CPNs) provide a framework for the design, specification, validation, and verification of systems. CP-nets have a wide range of application areas and many CPN projects have been carried out in industry, e.g., in the areas of communication protocols, operating systems, hardware designs, embedded systems, software system designs, and business process re-engineering. Design/CPN is a graphical computer tool supporting the practical use of CP-nets. The tool supports the construction, simulation, and functional and performance analysis of CPN models. The tool is used by more than four hundred organisations in forty different countries – including one hundred commercial companies. It is available free of charge, also for commercial use. This paper provides a comprehensive road map to the practical use of CP-nets and the Design/CPN tool. We give an informal introduction to the basic concepts and ideas underlying CP-nets. The key components and facilities of the Design/CPN tool are presented and their use illustrated. The paper is self-contained and does not assume any prior knowledge of Petri nets and CP-nets nor any experience with the Design/CPN tool.

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The practitioner's guide to coloured Petri nets

A computer program specification system is disclosed for interactively creating program specifications responsive to user input. The system includes facilities to respond to changes, supplied interactively, to a program specification without recompiling the program specification, and immediately to display a simulation of those changes. The system also supports the merging of actors, which are software objects comprising data structures and program procedures, and the merging of actor behavior. A user of the system creates a program specification by specifying actors for use in a plurality of scenarios, and operational steps of the plurality of scenarios. The system executes operational steps of a scenario to evaluate the consistency of the specification and actor data. Execution of an operational step comprises simulating the operational step upon the occurrence of predetermined conditions and storing the results of the simulation. Execution of a sequence of operational steps can be reversed or undone in order to insert a change in the specification prior to resimulating the undone sequence or other related sequences. Simulation of an operational step comprises one or more of: executing communications among actors, asserting relationships among actors, executing a logical or arithmetical computation for actors or requesting input of a decision choice.

Interactive computer program specification and simulation system

This paper presents the basic theoretical aspects of Coloured Petri Nets (CP-nets or CPN). CP-nets have been developed, from being a promising theoretical model, to being a full-fledged language for the design, specification, simulation, validation and implementation of large software systems (and other systems in which human beings and/or computers communicate by means of some more or less formal rules). The paper contains the formal definition of CP-nets and their basic concepts (e.g., the different dynamic properties such as liveness and fairness). The paper also contains a short introduction to the analysis methods, in particular occurrence graphs and place invariants.

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An Introduction to the Theoretical Aspects of Coloured Petri Nets

Petri nets are a powerful language for describing processes in digital hardware, and particularly asynchronous or self-timed circuits. Self-timed circuits are designed to operate without the use of a global clock signal. Applications for such circuits are likely to increase during the next decade, due to problems with on-chip event coordination as VLSI technology approaches a density of one hundred million transistors per chip. Designing such circuits without help of formal tools does not seem to be possible. We present an overview of the methods for specification, verification and synthesis of asynchronous circuits with the aid of Petri nets. We present a number of design examples which are used to illustrate the authors' belief that Petri nets could become widely accepted by digital system designers as a design method.

Robert M. Shapiro

Papers

Validation of a VLSI chip using hierarchical colored Petri nets