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Petri net
About: Petri net is a research topic. Over the lifetime, 25039 publications have been published within this topic receiving 406994 citations.
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TL;DR: This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints, which is shown to parallel the classical linear system theory in several ways.
Abstract: This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints. The linearity has to be understood with respect to nonstandard algebraic structures, e.g. the 'max-plus algebra'. A calculus is developed based on such structures, which is followed by tools for computing the time behaviour to such systems. This algebraic vision lays the foundation of a bona fide 'discrete event system theory', which is shown to parallel the classical linear system theory in several ways.
1,424 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: This self-contained paper develops the theory necessary to statically schedule SDF programs on single or multiple processors, and a class of static (compile time) scheduling algorithms is proven valid, and specific algorithms are given for scheduling SDF systems onto single ormultiple processors.
Abstract: Large grain data flow (LGDF) programming is natural and convenient for describing digital signal processing (DSP) systems, but its runtime overhead is costly in real time or cost-sensitive applications. In some situations, designers are not willing to squander computing resources for the sake of programmer convenience. This is particularly true when the target machine is a programmable DSP chip. However, the runtime overhead inherent in most LGDF implementations is not required for most signal processing systems because such systems are mostly synchronous (in the DSP sense). Synchronous data flow (SDF) differs from traditional data flow in that the amount of data produced and consumed by a data flow node is specified a priori for each input and output. This is equivalent to specifying the relative sample rates in signal processing system. This means that the scheduling of SDF nodes need not be done at runtime, but can be done at compile time (statically), so the runtime overhead evaporates. The sample rates can all be different, which is not true of most current data-driven digital signal processing programming methodologies. Synchronous data flow is closely related to computation graphs, a special case of Petri nets. This self-contained paper develops the theory necessary to statically schedule SDF programs on single or multiple processors. A class of static (compile time) scheduling algorithms is proven valid, and specific algorithms are given for scheduling SDF systems onto single or multiple processors.
1,380 citations
Journal Article•
TL;DR: Workflow Management as mentioned in this paper is an overview of workflow terminology and organization, as well as detailed coverage of workflow modeling with Petri nets, which facilitates communication between designers and users, and includes case studies, review exercises, and a glossary.
1,336 citations
1,252 citations