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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30 Sep 1999TL;DR: This edition includes recent research results pertaining to the diagnosis of discrete event systems, decentralized supervisory control, and interval-based timed automata and hybrid automata models.
Abstract: Introduction to Discrete Event Systems is a comprehensive introduction to the field of discrete event systems, offering a breadth of coverage that makes the material accessible to readers of varied backgrounds. The book emphasizes a unified modeling framework that transcends specific application areas, linking the following topics in a coherent manner: language and automata theory, supervisory control, Petri net theory, Markov chains and queuing theory, discrete-event simulation, and concurrent estimation techniques. This edition includes recent research results pertaining to the diagnosis of discrete event systems, decentralized supervisory control, and interval-based timed automata and hybrid automata models.
4,330 citations
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
Cites background from "Petri nets: Properties, analysis an..."
...For a review of the history of Petri nets and an extensive bibliography the reader is referred to [ Mur89 ]....
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TL;DR: A new algorithm is presented to extract a process model from a so-called "workflow log" containing information about the workflow process as it is actually being executed and represent it in terms of a Petri net.
Abstract: Contemporary workflow management systems are driven by explicit process models, i.e., a completely specified workflow design is required in order to enact a given workflow process. Creating a workflow design is a complicated time-consuming process and, typically, there are discrepancies between the actual workflow processes and the processes as perceived by the management. Therefore, we have developed techniques for discovering workflow models. The starting point for such techniques is a so-called "workflow log" containing information about the workflow process as it is actually being executed. We present a new algorithm to extract a process model from such a log and represent it in terms of a Petri net. However, we also demonstrate that it is not possible to discover arbitrary workflow processes. We explore a class of workflow processes that can be discovered. We show that the /spl alpha/-algorithm can successfully mine any workflow represented by a so-called SWF-net.
1,953 citations
Cites methods from "Petri nets: Properties, analysis an..."
...First, we introduce standard Petri-net notations, then we define the class of WF-nets....
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TL;DR: A comprehensive survey of efforts in the past couple of decades to address the problems of representation, recognition, and learning of human activities from video and related applications is presented.
Abstract: The past decade has witnessed a rapid proliferation of video cameras in all walks of life and has resulted in a tremendous explosion of video content. Several applications such as content-based video annotation and retrieval, highlight extraction and video summarization require recognition of the activities occurring in the video. The analysis of human activities in videos is an area with increasingly important consequences from security and surveillance to entertainment and personal archiving. Several challenges at various levels of processing-robustness against errors in low-level processing, view and rate-invariant representations at midlevel processing and semantic representation of human activities at higher level processing-make this problem hard to solve. In this review paper, we present a comprehensive survey of efforts in the past couple of decades to address the problems of representation, recognition, and learning of human activities from video and related applications. We discuss the problem at two major levels of complexity: 1) "actions" and 2) "activities." "Actions" are characterized by simple motion patterns typically executed by a single human. "Activities" are more complex and involve coordinated actions among a small number of humans. We will discuss several approaches and classify them according to their ability to handle varying degrees of complexity as interpreted above. We begin with a discussion of approaches to model the simplest of action classes known as atomic or primitive actions that do not require sophisticated dynamical modeling. Then, methods to model actions with more complex dynamics are discussed. The discussion then leads naturally to methods for higher level representation of complex activities.
1,426 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
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