Petri net as a modeling tool

A set of non-negative integral vectors is said to be right-closed if the presence of a vector in the set implies all term-wise larger vectors also belong to the set. A set of markings is control invariant with respect to a Petri Net (PN) structure if the firing of any uncontrollable transition at any marking in this set results in a new marking that is also in the set. Every right-closed set of markings has a unique supremal control invariant subset, which is the largest subset that is control invariant with respect to the PN structure. This subset is not necessarily right-closed. In this paper, we present an algorithm that computes the supremal right-closed control invariant subset of a right-closed of markings with respect to an arbitrary PN structure. This set plays a critical role in the synthesis of Liveness Enforcing Supervisory Policies (LESPs) for a class of PN structures, and consequently, the proposed algorithm plays a key role in the synthesis of LESPs for this class of PN structures.

The authors propose evolutionary Petri net consisting of units in order to obtain a structural model of team medical care automatically. The number of medical staffs is not sufficient in aged societies, so the work efficiency must be improved. The authors conceive that a Petri net can be used to express cooperative operation; therefore, the structure of a Petri net might assist in understanding the whole team medical care in hospitals and facilities. Evolutionary Petri net is a method to create the best structure of a Petri net that expresses a target workflow well and evolves the genes of individuals correspond to Petri nets. In the previous work, the authors represented each gene as a combination of nodes. However, the representation frequently generated worthless individuals that do not have a Petri net structure. In this work, the authors represent each gene as a combination of units that consist of two types of nodes. Additionally, the authors propose a new method to separately calculate the fitness value on the Petri net structure and that on the unit structures. The authors verified that the total fitness value of the best individual quickly reached the best value by applying genetic operators along with the balance of the two fitness values.

This article addresses expressiveness problems for Petri nets and their useful extension for modeling and control of a system that can be modeled with Petri nets. We construct some Petri net modules, namely, an enabling module, an inhibitor module and a Modulo-N counter, which are useful for system operations. We also present the simplifications for the enabling and inhibitor modules. Then, we propose two new types of arcs, namely, enabling and inhibitor arcs, with a weighted function set. The arcs with the weighted function set from places to transitions are the marked arcs. A function set is employed to denote the weight of an arc according to the system requirements. They are very useful to solve the resource reallocation problem in a resource allocation system, where resource sharing contributes to the occurrences of deadlocks. Finally, two examples are used to show the advantages of the presented new types of arcs.

In this paper we introduce an approach for defining semantics for AUML agent interaction protocol diagrams using Petri net code structures. This approach is based on the usage of net components which provide basic tasks and the structure for Petri nets. Agent interaction protocol diagrams are used to model agent conversations on an abstract level. By mapping elements of the diagrams to net components we are able to translate the diagrams into Petri nets, i.e to generate code structures from the drawings. We provide tool support for this approach by combining a tool for net components with a tool for drawing agent interaction protocol diagrams. This combined tool is available as a plug-in for Renew (Reference Net Workshop).Keywordsagentsagent interaction protocolsAUML Capa high-level Petri nets Mulan net componentsoperational semanticsreference nets Renew

This paper presents an approach to modeling aircraft airline maintenance circuit through a particular Petri Nets structures, called Treble transitions Petri Nets. In order to meet the requirements of the simulation of aircraft airline maintenance circuit, several enhancements were proposed. The first of them consider the characteristic of circuit, the places, transitions and arcs of classical Petri Nets are extended. In the Second enhancement, the rules of transitions were modified. Finally, the relating matrix and the state transfer equation are redefined. One case is included illustrating the applicability and efficiency of the proposed modeling method.

The understanding of the molecular mechanism of cell-to-cell communication is fundamental for system biology. Up to now, the main objectives of bioinformatics have been reconstruction, modeling and analysis of metabolic, regulatory and signaling processes, based on data generated from high-throughput technologies. Cell-to-cell communication or quorum sensing (QS), the use of small molecule signals to coordinate complex patterns of behavior in bacteria, has been the focus of many reports over the past decade. Based on the quorum sensing process of the organism Aliivibrio salmonicida, we aim at developing a functional Petri net, which will allow modeling and simulating cell-to-cell communication processes. Using a new editor-controlled information system called VANESA (http://vanesa.sf.net), we present how to combine different fields of studies such as life-science, database consulting, modeling, visualization and simulation for a semi-automatic reconstruction of the complex signaling quorum sensing network. We show how cell-to-cell communication processes and information-flow within a cell and across cell colonies can be modeled using VANESA and how those models can be simulated with Petri net network structures in a sophisticated way.

The development of the complex data structures systems requires models that are capable of describing the systems' requirements, design, verification, implementation and testing. This paper shows the development of such systems using Object Enhanced Time Petri Nets (OETPNs) framework. OETPN can model concurrency, reaction to internal and external events, synchronization and temporal behavior with fix and dynamic delays. OETPN keeps the bipartite graph structure of the classical Petri Nets, but the unique kind of tokens in PNs are changed to be any kind of objects to represent the data, or tasks (sub OETPN) that can either be active (i.e. threads of execution) or passive. OETPNs are capable to communicate with each other through input and output channels and to distribute concurrent tasks that are moved through a computer network with a dynamical structure (i.e. Task migration) without the need to stop the execution of the other OETPN. Guards and mappings are used to control the flow of execution in order to model the creation, insertion, modification and extraction of information of complex data structures. The mappings are also used to implement the information transformation and the placement of the resulted information at the output places of the transitions. The types of the places are specified to allow setting of objects or tasks. A new OETPN dynamic structure that is best suited for the server side is introduced. A Java platform that implement such applications is described and a complete system to manage the operations of the data structures is discussed with an example.

The paper addresses the fault detection problem for discrete event systems modeled by Petri nets (PN). Assuming that the PN structure and initial marking are known, faults are modeled by unobservable transitions. The paper recalls a previously proposed diagnoser that works online and employs an algorithm based on the definition and solution of some integer linear programming problems to decide whether the system behavior is normal or exhibits some possible faults. To reduce the on-line computational effort, we prove some results showing that if the unobservable subnet enjoys suitable properties, the algorithm solution may be obtained with low computational complexity. We characterize the properties that the PN modeling the system fault behavior has to fulfill and suitably modify the proposed diagnoser.

Public bicycle sharing systems control and performance evaluation: A Petri net-based approach

This paper presents the toolkit SNAKES that is aimed at providing a flexible solution to the problem of quickly prototyping Petri nets tools. In particular, SNAKES is expected to have as few built-in limitations as possible with respect to the particular variant of Petri net to be used. The goal is to make SNAKES suitable for any kind of Petri net model, including new ones for which there exists no available tool. For this purpose, SNAKES is designed as a very general Petri net core library enriched with a set of extension modules to provide specialised features. On the one hand, the core library is versatile in that it defines a general Petri net structure where all the computational aspects are delegated to an interpreted programming language. On the other hand, the extension modules provide with enough flexibility to allow to redefine easily any part of the base Petri net model. SNAKES is released under the GNU LGPL, it can be downloaded at 〈http://www.univ-paris12.fr/lacl/pommereau/soft/snakes〉 with the API documentation and a tutorial.

Aim To research the application of Petri net's theoretical method in the concurrent asynchronous communications control, find out the detect arithmetic of system's deadlock, and analyze the system's liveness. Methods A detect method of deadlock for information net based Petri net is proposed in this paper. The main method is as follows: After standardize the information systems and extract its mathematical model used the Petri net theory, and then standardize this model. On the basis of model's analysis, find out the loca where system is deadness. Results After the statistical analysis of application result, this method can be effectively applied in the information systems' plan, it will reduce the times of deadlock number above 89%. Conclusion This method can be applied in the system which have the transmission of concurrent asynchronous information, provide the theory basis which have important reference value for finding the fault and repair system. The main problem is the search ergodic process of Petri net's data structure is quite time consuming, so it can be combined with experience and man-machine interactive in application, to improve the efficiency.

Many tools for online collaboration, information and file sharing are currently employed to facilitate the process of online education. However, as stated in [14] the existing E-learning environments are not mature enough and only a small set of them provide functionality for defining reusable learning entities, reliable publishing and republishing mechanisms and possibilities for the teachers to give feedback to or receive feedback from the E-students. In order to improve E-learning experience [14] presents PeU 2.0, a system that enables the graphical representation and editing of the learning workflow without the execution environment of a workflow management system. The present paper examines the current executability of Petri Nets and gives a mapping of the visual elements in the PeU 2.0 graphs onto Petri Net structures. An interesting approach is introduces for the physical execution of the Petri Nets.

A new heuristic search approach for scheduling two classes of flexible manufacturing systems (FMSs) that contains assembly operations is proposed. The FMSs are modeled by two classes of Petri nets, called generalized symmetric and asymmetric nets. In the paper, the problem of minimizing makespan is transformed into searching the reachability graph for the optimal (minimal time) firing sequence from the initial marking (state) to the goal marking. A solution of the state equation constitutes a part of the heuristic function. The dynamic information of the nets, such as concurrency and synchronization, is used to adjust the heuristic function since the solution of the state equation may over-estimate the real cost.

Petri Nets (PNs) are an effective structure for modeling and analyzing asynchronous systems with concurrent and parallel activities. A Petri net models the static properties of a discrete event system concentrating on two basic concepts: events and conditions. Most of the theoretical work on Petri nets is a formal definition of Petri nets structures, which consist of a set of places, representing conditions, a set of transitions, representing events, an input function and an output function. For practical purposes, a graphical representation is more useful. Two types of nodes portray places and transitions. A circle is a place and a bar is a transition. There is no inherent measure of time in a classical Petri net. To approach time-based evaluation of system performances, Timed Petri Nets (TPNs) were introduced. Modeling the notion of time is not straightforward. There are several possibilities for introducing time in PNs, among them timed transitions and timed places. This paper reviews several published examples where Petri Nets were used in different circumstances such as estimating expected utilization of processing resources at steady state in open queueing networks, verifying computerized simulations and batch planning in textile industry.

Nowadays, Petri net models have been used as a very promising modelling tool for systems and it presents randomness, concurrency, and synchronisation. Many researchers give attention to Petri nets because of its wide utilization. Therefore, reusability, sharing, and standardization are three functions that Petri nets must have. To actualized this concept, Semantic Web technologies can be implemented. One of the Semantic Web technologies is Ontology. In this paper, a formal approach for representing a business process in Petri nets into Ontologies is proposed. Firstly, a business process in Petri nets is presented. Then, formal definitions of Petri nets and OWL DL ontologies are introduced. Next step, converting a business process in Petri nets into OWL DL ontologies. Finally, using SPARQL Query in OWL DL ontologies to make sure that the relations of the business process in Petri nets are the same as the relations of the business process in OWL DL ontologies.