Coloured Petri Nets: Basic Concepts, Analysis Methods and Practical Use. Vol. 2, Analysis Methods
01 Jan 1995-
TL;DR: This is the third volume of a definitive work on coloured Petri nets and contains a detailed presentation of 19 applications of CP-nets across a broad range of application areas, including a security system, ATM networks, audio/video systems, transaction processing, ISDN services, VLSI chips, document storage, distributed programming, electronic funds transfer, and many more.
Abstract: This is the third volume of a definitive work on coloured Petri nets. It contains a detailed presentation of 19 applications of CP-nets across a broad range of application areas, including a security system, ATM networks, audio/video systems, transaction processing, ISDN services, VLSI chips, document storage, distributed programming, electronic funds transfer, a naval vessel, chemical processing, nuclear waste management, and many more. Most of the projects were carried out in an industrial setting, and in each case the original authors have cooperated with the author and approved the new presentation. The author has taken care to unify the terminology and the CPN diagrams and to ensure that the background knowledge required has been provided in the first two volumes of the work.
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TL;DR: This paper introduces workflow management as an application domain for Petri nets, presents state-of-the-art results with respect to the verification of workflows, and highlights some Petri-net-based workflow tools.
Abstract: Workflow management promises a new solution to an age-old problem: controlling, monitoring, optimizing and supporting business processes. What is new about workflow management is the explicit representation of the business process logic which allows for computerized support. This paper discusses the use of Petri nets in the context of workflow management. Petri nets are an established tool for modeling and analyzing processes. On the one hand, Petri nets can be used as a design language for the specification of complex workflows. On the other hand, Petri net theory provides for powerful analysis techniques which can be used to verify the correctness of workflow procedures. This paper introduces workflow management as an application domain for Petri nets, presents state-of-the-art results with respect to the verification of workflows, and highlights some Petri-net-based workflow tools.
2,862 citations
01 Jan 2011
TL;DR: In this paper, a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions is presented.
Abstract: This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol’s method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent. Mathematical modeling of complex systems often requires sensitivity analysis to determine how an output variable of interest is influenced by individual or subsets of input variables. A traditional local sensitivity analysis entails gradients or derivatives, often invoked in design optimization, describing changes in the model response due to the local variation of input. Depending on the model output, obtaining gradients or derivatives, if they exist, can be simple or difficult. In contrast, a global sensitivity analysis (GSA), increasingly becoming mainstream, characterizes how the global variation of input, due to its uncertainty, impacts the overall uncertain behavior of the model. In other words, GSA constitutes the study of how the output uncertainty from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [1].
1,296 citations
TL;DR: Coloured Petri Nets (CPNs) is a language for the modelling and validation of systems in which concurrency, communication, and synchronisation play a major role and CPN Tools is an industrial-strength computer tool for constructing and analysed CPN models.
Abstract: Coloured Petri Nets (CPNs) is a language for the modelling and validation of systems in which concurrency, communication, and synchronisation play a major role. Coloured Petri Nets is a discrete-event modelling language combining Petri nets with the functional programming language Standard ML. Petri nets provide the foundation of the graphical notation and the basic primitives for modelling concurrency, communication, and synchronisation. Standard ML provides the primitives for the definition of data types, describing data manipulation, and for creating compact and parameterisable models. A CPN model of a system is an executable model representing the states of the system and the events (transitions) that can cause the system to change state. The CPN language makes it possible to organise a model as a set of modules, and it includes a time concept for representing the time taken to execute events in the modelled system. CPN Tools is an industrial-strength computer tool for constructing and analysing CPN models. Using CPN Tools, it is possible to investigate the behaviour of the modelled system using simulation, to verify properties by means of state space methods and model checking, and to conduct simulation-based performance analysis. User interaction with CPN Tools is based on direct manipulation of the graphical representation of the CPN model using interaction techniques, such as tool palettes and marking menus. A license for CPN Tools can be obtained free of charge, also for commercial use.
1,165 citations
01 Jan 2002
TL;DR: This paper motivates the need for a new workflow language, specifies the semantics of the language, and shows that soundness can be verified in a compositional way.
Abstract: Based on a rigorous analysis of existing workflow management systems and workflow languages, a new workflow language is proposed: yet another workflow language (YAWL). To identify the differences between the various languages, we have collected a fairly complete set of workflow patterns. Based on these patterns we have evaluated several workflow products and detected considerable differences in their ability to capture control flows for non-trivial workflow processes. Languages based on Petri nets perform better when it comes to state-based workflow patterns. However, some patterns (e.g. involving multiple instances, complex synchronisations or non-local withdrawals) are not easy to map onto (high-level) Petri nets. This inspired us to develop a new language by taking Petri nets as a starting point and adding mechanisms to allow for a more direct and intuitive support of the workflow patterns identified. This paper motivates the need for such a language, specifies the semantics of the language, and shows that soundness can be verified in a compositional way. Although YAWL is intended as a complete workflow language, the focus of this paper is limited to the control-flow perspective.
977 citations
01 Jan 2006
TL;DR: This paper presents the first systematic review of the original twenty control-flow patterns and provides a formal description of each of them in the form of a Coloured Petri-Net (CPN) model and identifies twenty three new patterns relevant to the control- flow perspective.
Abstract: The Workflow Patterns Initiative was established with the aim of delineating the fundamental requirements that arise during business process modelling on a recurring basis and describe them in an imperative way. The first deliverable of this research project was a set of twenty patterns describing the control-flow perspective of workflow systems. Since their release, these patterns have been widely used by practitioners, vendors and academics alike in the selection, design and development of workflow systems [vdAtHKB03]. This paper presents the first systematic review of the original twenty control-flow patterns and provides a formal description of each of them in the form of a Coloured Petri-Net (CPN) model. It also identifies twenty three new patterns relevant to the control-flow perspective. Detailed context conditions and evaluation criteria are presented for each pattern and their implementation is assessed in fourteen commercial offerings including workflow and case handling systems, business process modelling formalisms and business process execution languages.
669 citations