Structural characterization of decomposition in rate-insensitive stochastic Petri nets

This paper focuses on stochastic Petri nets that have an equilibrium distribution that is a product form over the number of tokens at the places. We formulate a decomposition result for the class of nets that have a product form solution irrespective of the values of the transition rates. These nets where algebraically characterized by Haddad et al.~as $S\Pi^2$ nets. By providing an intuitive interpretation of this algebraical characterization, and associating state machines to sets of $T$-invariants, we obtain a one-to-one correspondence between the marking of the original places and the places of the added state machines. This enables us to show that the subclass of stochastic Petri nets under study can be decomposed into subnets that are identified by sets of its $T$-invariants

Vérification de réseaux de Petri avec états sous une sémantique d'ordres partiels

National audienceIn order to study MSC specifications with counters, timers and other features, we introduce the model of Petri nets with states together with a non-branching non-sequential process semantics.We obtain a framework that is more expressive and more concise than MSGs.We consider then three classical verification problems for the set of markings reached by prefixes of processes: boundedness, covering and reachability. We show that each of these problems boils down to the equivalent problem for Petri nets. We consider also the notion of semi-structural property in order to study parametrized systems. In this way, only part of the places are provided with an initial marking. Unfolding such a system leads to a simpler problem in the form of a linear programme.Afin de munir le formalisme des MSG de compteurs, de timers et d'autres aspects, nous introduisons le modèle des réseaux de Petri avec états et une sémantique de processus non-branchants. Ce modèle est non seulement plus expressif que les MSG, mais il permet également des spécifications plus concises. Nous nous intéressons à trois problèmes de vérification classiques sur l'ensemble des marquages accessibles par les préfixes des processus : le caractère borné, la couverture et l'accessibilité. Nous montrons comment réduire ces problèmes au cas particulier des réseaux de Petri de telle sorte que tous les résultats de complexité et de décidabilité s'étendent des réseaux de Petri aux réseaux avec états sous la sémantique des processus. Nous introduisons aussi la notion de borne semi-structurelle afin de considérer des systèmes paramétrés. Cela consiste à fixer le marquage initial d'un sous-ensemble approprié de places, puis à vérifier que le système est borné quel que soit les valeurs des paramètres. Nous montrons comment un dépliage conduit à un problème plus simple à vérifier à l'aide de la Programmation Linéaire

Computer aided Petri net design for decision-making organizations

Caption title. "August 1988."Includes bibliographical references.Support provided by the Basic Research Group of the Technical Panel on C3 of the Joint Directors of Laboratories through the Office of Naval Research under contract N00014-85-K-0782I.M. Kyratzoglou, Alexander H. Levis

Energy aware knowledge extraction from Petri nets supporting decision-making in service-oriented automation

This paper introduces an approach to decision support systems in service-oriented automation control systems, which considers the knowledge extracted from the Petri nets models used to describe and execute the process behavior. Such solution optimizes the decision-making taking into account multi-criteria, namely productive parameters and also energy parameters. In fact, being manufacturing processes typically energy-intensive, this allows contributing for a clean and saving environment (i.e. a better and efficient use of energy). The preliminary experimental results, using a real laboratorial case study, demonstrate the applicability of the knowledge extracted from the Petri nets models to support real-time decision-making systems in service-oriented automation systems, considering some energy efficiency criteria

Efficient encoding schemes for symbolic analysis of Petri nets

Petri nets are a graph-based formalism appropriate to model concurrent systems such as asynchronous circuits or network protocols. Symbolic techniques based on Binary Decision Diagrams (BDDs) have emerged as one of the strategies to overcome the state explosion problem in the analysis of systems modeled by Petri nets. The existing techniques for state encoding use a variable-per-place strategy that leads to encoding schemes with very low density. This drawback has been partially mitigated by using Zero-Suppressed BDDs, that provide a typical reduction of BDD sizes by a factor of two. This work presents novel encoding schemes for Petri nets. By using algebraic techniques to analyze the topology of the net, sets of placesPeer ReviewedPostprint (published version

On the generation of organizational architectures using Petri nets

Bibliography: p. 22-23.Partial support by the U.S. Office of Naval Research under Contract No. N00014-84-K-0519 Partial support by the Joint Directors of Laboratories under Contract No. ONR/N00014-85-K-0782by Pascal A. Remy, Alexander H. Levis

A petri net approach to the modelling and analysis of flexible manufacturing systems

In this paper we present an approach for modelling and analyzing flexible manufacturing systems (FMSs) using Petri nets. In this approach, we first build a Petri net model (PNM) of the given FMS in a bottom-up fashion and then analyze important qualitative aspects of FMS behaviour such as existence/absence of deadlocks and buffer overflows. The basis for our approach is a theorem we state and prove for computing the invariants of the union of a finite number of Petri nets when the invariants of the individual nets are known. We illustrate our approach using two typical manufacturing systems: an automated transfer line and a simple FMS

Structural methods to improve the symbolic analysis of Petri nets

Symbolic techniques based on BDDs (Binary Decision Diagrams) have emerged as an efficient strategy for the analysis of Petri nets. The existing techniques for the symbolic encoding of each marking use a fixed set of variables per place, leading to encoding schemes with very low density. This drawback has been previously mitigated by using Zero-Suppressed BDDs, that provide a typical reduction of BDD sizes by a factor of two. Structural Petri net theory provides P-invariants that help to derive more efficient encoding schemes for the BDD representations of markings. P-invariants also provide a mechanism to identify conservative upper bounds for the reachable markings. The unreachable markings determined by the upper bound can be used to alleviate both the calculation of the exact reachability set and the scrutiny of properties. Such approach allows to drastically decrease the number of variables for marking encoding and reduce memory and CPU requirements significantly.Peer ReviewedPostprint (author's final draft

Decidability Issues for Petri Nets

This is a survey of some decidability results for Petri nets, covering the last three decades. The presentation is structured around decidability of specific properties, various behavioural equivalences and finally the model checking problem for temporal logics