Type Of Petri Nets Research Articles

Regular string token fuzzy Petri nets

Fuzzy Petri nets are a type of classical Petri nets designed to deal with imprecise and ambiguous data, that have been widely used to represent fuzzy production rules and fuzzy rule-based reasoning. In this paper, we introduce a new model called string token fuzzy Petri nets to generate fuzzy regular languages. Also, we study the equivalences of fuzzy regular grammar and regular string token fuzzy Petri net and establish some closure properties such as union, catenation, kleene closure, reversal, homomorphism and inverse homomorphism of the languages generated by the regular string token fuzzy Petri nets.

Acyclic and Cyclic Reversing Computations in Petri Nets

Reversible computations constitute an unconventional form of computing where any sequence of performed operations can be undone by executing in reverse order at any point during a computation. It has been attracting increasing attention as it provides opportunities for low-power computation, being at the same time essential or eligible in various applications. In recent work, we have proposed a structural way of translating Reversing Petri Nets (RPNs) – a type of Petri nets that embeds reversible computation, to bounded Coloured Petri Nets (CPNs) – an extension of traditional Petri Nets, where tokens carry data values. Three reversing semantics are possible in RPNs: backtracking (reversing of the lately executed action), causal reversing (action can be reversed only when all its effects have been undone) and out of causal reversing (any previously performed action can be reversed). In this paper, we extend the RPN to CPN translation with formal proofs of correctness. Moreover, the possibility of introduction of cycles to RPNs is discussed. We analyze which type of cycles could be allowed in RPNs to ensure consistency with the current semantics. It emerged that the most interesting case related to cycles in RPNs occurs in causal semantics, where various interpretations of dependency result in different net’s behaviour during reversing. Three definitions of dependence are presented and discussed.

The Complexity of Synthesis of b-Bounded Petri Nets

For a fixed type of Petri nets τ, τ-SYNTHESIS is the task of finding for a given transition system A a Petri net N of type τ(τ-net, for short) whose reachability graph is isomorphic to A if there is one. The decision version of this search problem is called τ-SOLVABILITY. If an input A allows a positive decision, then it is called τ-solvable and a sought net N τ-solves A. As a well known fact, A is τ-solvable if and only if it has the so-called τ-event state separation property (τ-ESSP, for short) and the τ-state separation property (τ-SSP, for short). The question whether A has the τ-ESSP or the τ-SSP defines also decision problems. In this paper, for all b ∈ ℕ, we completely characterize the computational complexity of τ-SOLVABILITY, τ-ESSP and τ-SSP for the types of pure b-bounded Place/Transition-nets, the b-bounded Place/Transitionnets and their corresponding ℤb+1-extensions.

Colouring fuzziness for systems biology

Snoopy is a powerful modelling and simulation tool for various types of Petri nets, which have been applied to a wide range of biochemical reaction networks. We present an enhanced version of Snoopy, now supporting coloured and uncoloured stochastic, continuous and hybrid Petri Nets with fuzzy kinetic parameters. Colour helps to cope with modelling challenges imposed by larger and more complex networks. Fuzzy parameters are specifically useful when kinetic parameter values can not be precisely measured or estimated. By running fuzzy simulation we obtain output bands of the variables of interest induced by the effect of the fuzzy kinetic parameters. Simulation is always done on the uncoloured level. For this purpose, coloured fuzzy Petri nets are automatically unfolded to their corresponding uncoloured counterparts. Combining the power of fuzzy kinetic parameters with the modelling convenience of coloured Petri nets provides a new quality in user support with sophisticated modelling and analysis features.

USE OF FUZZY PETRI NETWORKS FOR INFORMATION DESCRIPTION OF THE HOUSING ENVIRONMENT

The current state of comfort of an apartment building indicates many problems that exist in this area. First, there is a need for clear planning of comfortable housing, which should take into account the current socio – economic needs of the population. Secondly, there is no clear definition of comfort levels of an apartment building. Also, there is a need to identify the main factors that affect the life and comfort of the population. The article is based on two main areas of research. The first is to present a description of the information model of a hybrid intelligent system (GIS) for the comfort of the living environment of an apartment building. This tool allows you to model the effects of interaction, adaptation, which can be observed in the system when making decisions. The study also simulates complex systems based on the use of fuzzy Petri nets (FPs) to describe comfort. MP and its various types are one of the classes of models that provide an opportunity to present the structure of integrated organizational – information systems and complexes, as well as logical – temporal processes of system operation. Fuzzy Petri nets are divided into two parts. The first part describes the structure of the network, it is usually standard, the processes of initial marking and movement of markers on the network are determined by means and methods of fuzzy sets and fuzzy logic. The biggest area of their application is complex objects. Fuzzy logic is used to formalize fuzzy concepts in terms of semantics and provides efficient information processing along with clear data. With the help of this network the endurance of modeling systems and the optimality of its structure are investigated. To date, a large number of different types of Petri nets are known, which provide an opportunity to present the structure of the models in the absence of analytical representation of the influence of certain factors.

Event Circular Waits and Their Analysis via Petri Nets

Deadlock control of automated manufacturing systems has been widely investigated in recent decades. According to classical Coffman theory, resource circular wait (RW) is viewed as a necessary condition for deadlocks to occur. However, the fact is not as simple as so. Counterexamples are presented to show that RWs do not necessarily appear together with deadlocks. Event circular waits (EWs) are proposed as an alternative to represent a fundamental necessary condition of deadlocks. First, we present the formal definitions of EWs in a type of Petri nets, i.e., weighted augmented marked graphs (WAMGs), and show that EWs are more general and essential than RWs in describing the cause of deadlocks. Second, we show a new classification of siphons, i.e., types I, II, III, and IV, and illustrate the relationship between undermarked siphons and EWs in the WAMGs. Third, we show that EWs are more efficient than RWs for deadlock avoidance since deadlocks can be avoided earlier at a specified marking by using EWs rather than RWs. Several examples are given to clarify the theory throughout this paper.

A Mathematical Model Using Time Elements for Timed-Arc Petri Nets

In this work, a novel graphical and mathematical model is introduced for Timed-Arc Petri Nets. In this model, operation durations related to events are associated with arcs as firing durations. Time elements are introduced on the arcs of the model for monitoring tokens in operation durations (firing durations) of firing processes (events). In the model, the status of the system is represented as states consisting of remaining time vector for indicating the status of time elements and marking vector for indicating the status of places' state information. This feature of states allows to obtain reachability set enhanced with the time information and the timed reachability graph of the system. In this work, behavioral properties of the proposed model are also defined. Moreover, via considering real world systems, behavioral properties are analyzed and performance of the model is compared with Stretched Petri Nets which is a recently proposed type of Timed Petri Nets.

Equivalent and Efficient Optimization Models for an Industrial Discrete Event System with Alternative Structural Configurations

Discrete event systems in applications, such as industry and supply chain, may show a very complex behavior. For this reason, their design and operation may be carried out by the application of optimization techniques for decision making in order to obtain their highest performance. In a general approach, it is possible to implement these optimization techniques by means of the simulation of a Petri net model, which may require an intensive use of computational resources. One key factor in the computational cost of simulation‐based optimization is the size of the model of the system; hence, it may be useful to apply techniques to reduce it. This paper analyzes the relationship between two Petri net formalisms, currently used in the design of discrete event systems, where it is usual to count on a set of alternative structural configurations. These formalisms are a particular type of parametric Petri nets, called compound Petri nets, and a set of alternative Petri nets. The development of equivalent models under these formalisms and the formal proof of this equivalence are the main topics of the paper. The basis for this formal approach is the graph of reachable markings, a powerful tool able to represent the behavior of a discrete event system and, hence, to show the equivalence between two different Petri net models. One immediate application of this equivalence is the substitution of a large model of a system by a more compact one, whose simulation may be less demanding in the use of computational resources.

Determining Truth Degrees of Input Places in Fuzzy Petri Nets

Fuzzy Petri net (FPN), as one type of high-level Petri nets, has attracted a lot of attention over the recent decade due to its adequacy for knowledge representation and logic reasoning. However, in the FPN literature, the truth degrees of input places are usually given directly or supposed by researchers. No or little research has been performed on the determination of initial marking vector for a specific FPN. In this correspondence paper, we introduce a group decision-making model using hesitant 2-tuple linguistic term sets to obtain the initial truth values of FPNs based on domain experts’ knowledge and gathered data. As is illustrated by the numerical example, the proposed framework can well capture domain experts’ diversity judgements and derive initial truth degrees for an FPN under different types of uncertainties.

Holmes: a graphical tool for development, simulation and analysis of Petri net based models of complex biological systems

Model development and its analysis is a fundamental step in systems biology. The theory of Petri nets offers a tool for such a task. Since the rapid development of computer science, a variety of tools for Petri nets emerged, offering various analytical algorithms. From this follows a problem of using different programs to analyse a single model. Many file formats and different representations of results make the analysis much harder. Especially for larger nets the ability to visualize the results in a proper form provides a huge help in the understanding of their significance. We present a new tool for Petri nets development and analysis called Holmes. Our program contains algorithms for model analysis based on different types of Petri nets, e.g. invariant generator, Maximum Common Transitions (MCT) sets and cluster modules, simulation algorithms or knockout analysis tools. A very important feature is the ability to visualize the results of almost all analytical modules. The integration of such modules into one graphical environment allows a researcher to fully devote his or her time to the model building and analysis. Available at http://www.cs.put.poznan.pl/mradom/Holmes/holmes.html. piotr@cs.put.poznan.pl.

Assessment of maintenance strategies for railway vehicles using Petri-nets

Abstract The density of railway traffic has been steadily increasing over past years and decades. The developments have implicated a growing need for efficient operation and maintenance of railway rolling stock systems. Also the increased operation of articulated trains has induced new challenges on maintenance organization and planning. Selecting optimal maintenance strategies for each component does not only influence the availability of the railway vehicles but also the operational performance and the profitability of the operator. Suitable tools to analyse, compare and optimize different maintenance strategies are therefore required. Petri nets are such a mathematical tool that and have been applied for maintenance modeling and simulations of different applications. Several types of Petri nets with different properties have been introduced. One of the recently proposed extensions of Petri nets are the Abridged Petri Nets (APN) which fulfill the specific requirements of railway rolling stock maintenance. In this paper, we propose the application of APN in combination with the Monte-Carlo simulation for railway rolling stock maintenance evaluation. In a first step, the applicability of the APN approach was demonstrated on a theoretical case study comprising a condition based maintenance strategy for a system. In a second case study, several real application case studies were modeled and compared based on the processes and real application field data of three railway vehicle components. The tool can be further extended by pre-defining selected strategies that be easily implemented within an overall decision support system.

Optimal management of reconfigurable manufacturing system modeling with Petri nets developed three-dimensional - RPD3D

Modeling of reconfigurable manufacturing systems would have done using existing Petri net types, but the complexity and dynamics of the new manufacturing system, mainly data reconfiguration feature, required looking for a more compact representation with many variables that to model as accurately not only the normal operation of the production system but can capture and model and reconfiguration process.Thus, it was necessary to create a new class of Petri nets, called RPD3D (Developed Petri nets with three dimensional) showing the name of both lineage (new class derived from Petri nets developed, created in 2000 by Prof. Dr. Ing Vasile Marinescu in his doctoral thesis) [1], but the most important of the new features defining (transformation from one 2D model into a 3D model).The idea was to introduce the classical model of a Petri third dimension to be able to overlay multiple levels (layers) formed in 2D or 3D Petri nets that interact with each other (receiving or giving commands to enable or disable the various modules together simulating the operation of reconfigurable manufacturing systems). The aim is to present a new type of Petri nets called RPD3D - Developed Petri three-dimensional model used for optimal control and simulation of reconfigurable manufacturing systems manufacture of products such systems.

Fuzzy Stochastic Petri Nets for Modeling Biological Systems with Uncertain Kinetic Parameters.

Stochastic Petri nets (SPNs) have been widely used to model randomness which is an inherent feature of biological systems. However, for many biological systems, some kinetic parameters may be uncertain due to incomplete, vague or missing kinetic data (often called fuzzy uncertainty), or naturally vary, e.g., between different individuals, experimental conditions, etc. (often called variability), which has prevented a wider application of SPNs that require accurate parameters. Considering the strength of fuzzy sets to deal with uncertain information, we apply a specific type of stochastic Petri nets, fuzzy stochastic Petri nets (FSPNs), to model and analyze biological systems with uncertain kinetic parameters. FSPNs combine SPNs and fuzzy sets, thereby taking into account both randomness and fuzziness of biological systems. For a biological system, SPNs model the randomness, while fuzzy sets model kinetic parameters with fuzzy uncertainty or variability by associating each parameter with a fuzzy number instead of a crisp real value. We introduce a simulation-based analysis method for FSPNs to explore the uncertainties of outputs resulting from the uncertainties associated with input parameters, which works equally well for bounded and unbounded models. We illustrate our approach using a yeast polarization model having an infinite state space, which shows the appropriateness of FSPNs in combination with simulation-based analysis for modeling and analyzing biological systems with uncertain information.

Survey on Fuzzy Petri Nets for Classification

The aim of this study is based on Survey on fuzzy Petri nets for Classification. Petri Nets (PN) is excellent networks which have great characteristics of combining a well defined mathematical theory with a graphical representation of the dynamic behavior of systems. But, with the growth in the difficulty of modern industrial, and communication systems, PN found themselves inadequate to address the problems of vagueness, and imprecision in data. This gave rise to combination of Fuzzy logic with Petri nets and a new tool emerged with the name of Fuzzy Petri Nets (FPN). Much research has been done for FPN and a number of their applications have been expected, but their basic types and structure is still ambiguous. Result of this research, an effort is made to categorize the applications of FPN for classification according to their structure and algorithms. We identify the different types of Petri nets will improve future research on Petri nets. Hence in this study, due to these limitations we focus on establishing the FPN in the light of their classifications has been done.

An Algorithm for Generating Product’s Structure in a Simulation Framework

The paper is describing an algorithm for randomly generating the orders received by a simulated manufacturing system. Based on a previously defined Petri Net type representation of the product, there is presented the proposed structure generation algorithm.The algorithm was implemented in a graphical programming environment which will serve also for developing the manufacturing system simulator, so the paper is describing the procedures for generating the records from the proposed data structure.Running the implemented procedure generated a product’s structure with the main components graphically represented complying with the data definition to be used in the simulation framework.

A Survey of Control Structures for Reconfigurable Petri Nets

Software systems are increasingly executed in dynamic infrastructures. These infrastructures are dynamic as they are themselves subject to change as they support various applications that may or may not share some of the resources. Dynamic software systems become more and more important, but are difficult to handle. Modeling and simulating dynamic systems requires the representation of their processes and the system changes within one model. To that effect, reconfigurable Petri nets consist of a Petri net and a set of rules that can modify the Petri net. Their main feature is the capability to model complex coordination behavior in dynamically adapting infrastructures. The interplay of both levels of dynamic behavior requires a very precise description, so the specification when and which rules are to be applied plays a crucial role for the convenient use of reconfigurable nets. We differentiate several types of reconfigurable Petri nets and present a survey of control structure for these types, reconfigurable Petri nets. These control structures either concern the infrastructure, i.e., the rules and transformations or the system part, i.e., the firing behavior, or both. They are introduced by a short characterization and illustrated by examples. We state the results for various Petri net types and the tools supporting the different control structures.

Languages of Watson-Crick Petri Net

Watson-Crick automata are one of the automata types that are used for transitions with two reading heads. This automata work on double stranded sequencesrelated by a complementarity relation similar with the Watson-Crick complementarity of DNA molecules. Watson-Crick automata can be related to a Petri net, which is a graphical and mathematical formalism suitable for the modeling and analysis of concurrent, asynchronous and distributed systems.From the relation between Watson-Crick automata and Petri net, a new model namely Watson-Crick Petri net has been developed. In this paper, a new variant of Watson-Crick automata with Petri net as a control unit is introduced. We also presented various types of Watson-Crick Petri nets that are generated using transitions labelled with various labelling policies and finite sets of final markings.

Mapping AADL to Petri Net Tool-Sets Using PNML Framework

Architecture Analysis and Design Language (AADL) has been utilized to specify and verify nonfunctional properties of Real-Time Embedded Systems (RTES) used in critical application systems. Examples of such critical application systems include medical devices, nuclear power plants, aerospace, financial, etc. Using AADL, an engineer is enable to analyze the quality of a system. For example, a developer can perform performance analysis such as end-to-end flow analysis to guarantee that system components have the required resources to meet the timing requirements relevant to their communications. The critical issue related to developing and deploying safety critical systems is how to validate the expected level of quality (e.g., safety, performance, security) and functionalities (capabilities) at design level. Currently, the core AADL is extensively applied to analyze and verify quality of RTES embed in the safety critical applications. The notation lacks the formal semantics needed to reason about the logical properties (e.g., deadlock, livelock, etc.) and capabilities of safety critical systems. The objective of this research is to augment AADL with exiting formal semantics and supporting tools in a manner that these properties can be automatically verified. Toward this goal, we exploit Petri Net Markup Language (PNML), which is a standard acting as the intermediate language between different classes of Petri Nets. Using PNML, we interface AADL with different classes of Petri nets, which support different types of tools and reasoning. The justification for using PNML is that the framework provides a context in which interoperability and exchangeability among different models of a system specified by different types of Petri nets is possible. The contributions of our work include a set of mappings and mapping rules between AADL and PNML. To show the feasibility of our approach, a fragment of RT-Embedded system, namely, Cruise Control System has been used.

Using UML and Petri nets for visualization of business document flow

The article deals with two principles of business workflow modeling, Petri nets and UML notation, that are the acceptable approaches to business modeling and can be used also for business documents workflow. The special type of Petri nets, WF-nets and UML activity diagrams are used in this article and both modeling ways are presented on the concrete business workflow and then there are presented and specified their advantage and disadvantage for business documents flows. At beginning it is explained the word workflow in context business documents, its features, principles and using in business environment. After that it is clarified that the UML is OMG’s most-used specification, and the way the world models not only application structure, behavior, and architecture, but also business process, workflows and data structure. Activity diagram UML is good way to show how different workflows in the business are managed, how they start, go and stop. Diagrams also show many different decision paths that can be taken from start to finish. State charts can be used as a detail the transitions or changes of states when documents can go through in the business. They show how a documents moves from one state to another and the rules that govern that change. Petri-nets offer a graphical notation for stepwise processes that include choice, iteration, and concurrent execution. Unlike UML Petri nets have an exact mathematical definition of their execution semantics, with a well-developed mathematical theory for process analysis. In the article there are modeled a special type of Petri nets, the WF-nets. The practical part of article incorporates two models of concrete business documents workflows presented in these notations, their comparison and recommendation for using these diagrams in business process management.

Minimal cut sets of a coherent fault tree generation using reverse Petri nets

This paper proposes a new method for minimal cut sets generation of a coherent fault tree (FT) without repeated events. The approach is based on a special type of Petri nets – reverse Petri net (RPN) which can be generated directly from the FT. Using RPN properties and state equation, we have shown that the problem of finding all minimal cut sets becomes the following direct reachability problem: to find all dead markings reachable from marking of RPN. All minimal cut sets are then obtained as leaves of the reachability graph of a RPN. An algorithm to determine all leaves of the reachability graph is presented in the paper. The algorithm requires special numeration of the places and transitions of RPN which enables the generation of only one spanning tree of the reachability graph. Since the number of minimal cut sets in a complex system can be very large and a complexity problem occurs, we here propose an approach for solving this problem based on cutting the reachability tree of RPN.