Petri Net Analysis Research Articles

Petri net model for supply‐chain quality conflict resolution of a complex product

PurposeThis paper aims to develop a Petri net model for analyzing the quality conflict and its resolution of a complex product. The result aims to assist decision makers (DMs) to properly select their activities when a quality conflict has happened.Design/methodology/approachAccording to the features of Petri net and conflict analysis theory, a novel Petri net for conflict analysis (PNCA) is designed which contains transition and preference labels to describe DMs' decision activities and profit comparisons. Additionally, a generating approach is proposed, which can help DMs to construct a PNCA. Furthermore, based on players' bounded rationality, the equilibrium of PNCA is studied to provide scientific supports for DMs' decision‐making. A case study on an aircraft production system is conducted to demonstrate the feasibility and effectiveness of the new model, which furnishes a fresh perspective on the supply chain quality management of a complex product.FindingsA new methodology is proposed for the domain of conflict analysis, which is easier to understand and improves the operation efficiency. What is more important, DMs can clearly be aware of their following choices according to the corresponding transition information.Originality/valueThe paper contributes to conflict analysis theory by designing a new model and develops a new graph model for managing the supply chain quality of a complex product.

Analysis of stochastic Petri nets with signals

Product-form models facilitate the efficient analysis of large stochastic models and have been sought after for some three decades. Apart from the dominating work on queueing networks, some product-forms were found for stochastic Petri nets (SPNs) that allow fork-join constructs and for queueing networks extended to include special customers called signals, viz. G-networks. We appeal to the Reversed Compound Agent Theorem (RCAT) to prove new product-form solutions for SPNs in which there are special transitions, the firings of which act in a similar way to signals in G-networks, but which may be generated by synchronised firings (or service completions) and may affect several places simultaneously. We show that SPNs with signals are strict generalisations of G-networks with negative customers, triggers and catastrophes, and illustrate with copious examples.

Waste electronics and electrical equipment disassembly and recycling using Petri net analysis: Considering the economic value and environmental impacts

The Industry Council for Electronic Equipment Recycling (ICER) has published estimates of waste generation based on both assumptions and analysis regarding the relationship between the market sales of Electrical and Electronic Equipment (EEE) in a given year and the expected lifetime of products as well as by employing market saturation factors. Waste EEE (WEEE) has an adverse impact on the environment. Therefore, it is important to reduce the quantity of WEEE through recycling. While attempting to improve the recycling rate of WEEE by enhancing the disassembly processes, two issues must be considered simultaneously—economy and safety. In this paper, a Petri Net (PN) based analysis approach is proposed to deal with the disassembly and recycling problems in End-Of-Life (EOL) WEEE. By using the PN analysis, the optimal tradeoff between the cost and environmental effectiveness of the disassembly processes is determined. A case study is used to illustrate the proposed analysis method.

Petri Net Modeling for Probabilistic Safety Assessment and its Application in the Air Lock System of a CANDU Nuclear Power Plant

Abstract Historically, fault trees are extensively used in Probabilistic Safety Assessment (PSA) to model and evaluate the probability and consequence of failures of complex engineering systems, such as nuclear power plants. Scenarios of hypothetical accidents resulting in severe core damage can be developed. Petri net is another modeling technique that offers many advantages when comparing with fault trees, such as is ability to represent the time sequence of the events along with their duration. In this research, Petri net theory is extended to model system failures. The transformations required to model logic gates by Petri nets are explored and examples provided. Methods for qualitative analysis for Petri nets are presented. The application of Petri net in the airlock system of a Canada Deuterium Uranium (CANDU) reactor is explored. It is further demonstrated that Petri net can be used in both coherent and non-coherent systems.

A Survey on the Object-Oriented Petri Net Modeling

With the larger and more complex of the size and function of software products，choosing an efficient modeling technique for analyzing complicated and ever-changing system plays a vital role．Object-Oriented Petri nets for its unique characteristics which are simple and laconic modeling method and strong mathematical analysis capacity becomes a hot research．In this paper，it explain that the object-oriented technology how to combine with Petri nets．The typical Object-Oriented Petri net modeling steps and analysis methods are expounded. Up-to-date research about OOPN and its main improved models OOCPN, OOAPN and OOTPN are summarized, the pros and cons of each modeling are analyzed．The interrelated topics and the future development about OOPN are also mentioned．

English

This paper provides Petri net (PN) modeling and performance analysis of a surface mount device (SMD) electronics manufacturing assembly line for an automated remanufacturing of printed circuit boards. Concentrating on the operational aspects, PN models for an automated assembly stations were constructed. These models enable designers to have a better understanding of the system control and analysis from the graphical representations of PNs. In this context, the selection of the particular buffer size and its effects on the production rate of the transferline are explored. PN models are designed to analyze two different transferlines and to find out when local gains propagate to the end of the transferline. Furthermore, artificial neural networks (ANN) are proposed as a fast function approximation tool for a rapid re-analysis of the remanufacturing system. ANN can easily predict the output of the transferline for unknown input patterns when the input and output relation is monotonically increasing or decreasing. This capability of the ANN proves to be useful to analyze the transferline when there is no further information available. The approaches as presented in this paper can be generalized and applied to many other applications of multi-robot assembly systems.   Key words: Electronics remanufacturing, stochastic Petri nets, artificial neural networks, surface mount device, performance analysis.

Reachability determination in acyclic Petri nets by cell enumeration approach

Reachability is one of the most important behavioral properties of Petri nets. We propose in this paper a novel approach for solving the fundamental equation in the reachability analysis of acyclic Petri nets, which has been known to be NP-complete. More specifically, by adopting a revised version of the cell enumeration method for an arrangement of hyperplanes in discrete geometry, we develop an efficient solution scheme to identify firing count vector solution(s) to the fundamental equation on a bounded integer set, with a complexity bound of O((nu)n−m), where n is the number of transitions, m is the number of places and u is the upper bound of the number of firings for all individual transitions.

A verifiable low-level concurrent programming model based on colored Petri nets

Concurrent programs written in a machine-level language are being used in many areas, but the verification of such programs brings various new challenges to the programming language community. Most of existing contributions on verifying the safety properties of concurrent programs are for high-level languages, specifications, or calculi in the literature. Due to the lack of abstraction at a low level, additional work is needed to extend these methods to machine-level language. This paper describes an approach to integrate Petri nets into low-level concurrent programs to form a new programming model (abstract machine). A program in the programming model is a restricted version of colored Petri net, with transitions colored by assembly codes for machine-level threads, and places colored by shared data consisting of memory locations or registers. Existing analysis and verification approaches for usual Petri nets can be applied indirectly for such a low-level concurrent program.

OOSPN-Based Modeling and Simulation of Tridimensional Rail Net Transmission System in Container Terminal

Object-Oriented Stochastic Petri Net (OOSPN) is utilized concerning the complexity of container terminal tridimensional rail transmission system network. It simplifies the structure and modeling with object-oriented and hierarchy idea, while the efficiency of each state is detected based on Stochastic Petri Net performance analysis. Thereby, it finds the system bottleneck which also provides reference for the improvement of the program. The efficiency indicators are obtained by analysis and construction of container terminal transmission system as well.

Sensitivity analysis on causal chains of Bayesian networks

To analyze the key path of Bayesian network in complex systems, this study proposes to analyze the sensitivity of causal chains of Bayesian networks using the Petri net structural analysis approach to obtain the key chain through which the cause influences the consequence. First, the Bayesian network is transformed into Petri net, the structural analysis approach of which is employed to analyze structural nature of the Bayesian network, ensuring correctness of the constructed Bayesian network structure. Then based on the above fact that the structure is correct, S-invariants of a Petri net is used to search for simple causal chains of the Bayesian network. Finally, the causal effect is defined and sensitivity analysis is made on the causal chains. The said method is applied to MDS causal chain analysis. Results show that the proposed method is direct viewing and practical. This method has some reference value for decision making in complex systems. © 2011 Wiley Periodicals, Inc.

Constraint graph-based approach for the analysis and the control of time critical systems

The increasing complexity of manufacturing systems gives rise to the development of new formal methods allowing to handle their particularities. Petri nets are a powerful formalism for the specification and verification of concurrent systems including sequential systems and manufacturing systems. To deal with systems whose time issues become fundamental, different time Petri nets extensions have been developed in the literature, each one being dependent on the application considered. For the time critical systems, their correctness depends not only on the logic correctness but also on the time constraints. Timing issues are essential. In this paper, a new method of analysis and control for P-time Petri nets is proposed. It is based on the firing instant notion and exploits a constraint graph approach.

Relevant Timed Schedules/Clock Vectors for Constructing Time Petri Net Reachability Graphs

We consider here the time Petri nets (the TPN model) and its state space abstractions. We show that only some timed schedules/clock vectors (one per enabled transition) of the clock/firing domains are relevant to construct reachability graphs for the TPN. Moreover, we prove formally that the resulting graphs are smaller than the TPN reachability graphs proposed in the literature. Furthermore, these results establish a relation between dense time and discrete time analysis of time Petri nets and allow also improving discrete time analysis by considering only some elements of the clock/firing domains.

Robustness analysis of non-ordinary Petri nets for flexible assembly/disassembly processes based on structural decomposition

Design of robust supervisory controllers for manufacturing systems with unreliable resources has received significant attention recently. Robustness analysis provides an alternative way to analyse a perturbed system to quickly respond to resource failures. Although we have analysed the robustness properties of several subclasses of ordinary Petri nets (PNs), analysis for non-ordinary PNs has not been done. Non-ordinary PNs have weighted arcs and have the advantage to compactly model operations requiring multiple parts or resources. In this article, we consider a class of flexible assembly/disassembly manufacturing systems and propose a non-ordinary flexible assembly/disassembly Petri net (NFADPN) model for this class of systems. As the class of flexible assembly/disassembly manufacturing systems can be regarded as the integration and interactions of a set of assembly/disassembly subprocesses, a bottom-up approach is adopted in this article to construct the NFADPN models. Due to the routing flexibility in NFADPN, there may exist different ways to accomplish the tasks. To characterise different ways to accomplish the tasks, we propose the concept of completely connected subprocesses. As long as there exists a set of completely connected subprocesses for certain type of products, the production of that type of products can still be maintained without requiring the whole NFADPN to be live. To take advantage of the alternative routes without enforcing liveness for the whole system, we generalise the concept of persistent production proposed to NFADPN. We propose a condition for persistent production based on the concept of completely connected subprocesses. We extend robustness analysis to NFADPN by exploiting its structure. We identify several patterns of resource failures and characterise the conditions to maintain operation in the presence of resource failures.

Object-Oriented Petri Net Modeling and Analysis of China Railway Container Freight Yard Logistic System

The railway container freight yard logistic system is a typical discrete event dynamic system (DEDS) and has the feature of high randomness, low flexibility, uncertainty of operation time and high coordination demand of facilities. Object-oriented petri net (OPN) inherits the petri net (PN) advantages for efficiently describing the asynchronism, concurrency, distributivity, parallel DEDS and overcomes the disadvantages when faces complex discrete element dynamic system. We choose object-oriented petri net to model and analyze China railway container freight yard logistic system and get the object OPN model and communication relation net.

Timing-Failure Risk Assessment of UML Design Using Time Petri Net Bound Techniques

Software systems that do not meet their timing constraints can cause risks. In this work, we propose a comprehensive method for assessing the risk of timing failure by evaluating the software design. We show how to apply best practises in software engineering and well-known Time Petri Net (TPN) modeling and analysis techniques, and we demonstrate the effectiveness of the method with reference to a case study in the domain of real-time embedded systems. The method customizes the Australian standard risk management process, where the system context is the UML-based software specification, enriched with standard MARTE profile annotations to capture nonfunctional system properties. During the risk analysis, a TPN is derived, via model transformation, from the software design specification and TPN bound techniques are applied to estimate the probability of timing failure. TPN bound techniques are also exploited, within the risk evaluation and treatment steps, to identify the risk causes in the software design.

Control and data flow compatibility in the interaction between dynamic business processes

AbstractIn the coming years, one of the challenges for business processes is to obtain a high degree of flexibility and ability to adapt to the changing contexts. Two key elements for achieving this are the use of Semantic Web technologies and the possibility of decoupling the business and the interaction aspects in a business process. Nevertheless, these solutions open up new challenges related to the necessity of checking whether a set of processes can successfully cooperate. Compatibility questions should be considered from a control flow point of view (the order of the interactions should be appropriate) and also from a data flow point of view (the information exchanged should be—semantically—adequate). In this paper, we concentrate on the compatibility of a set of processes executed in DENEB, a platform for the Development and ExecutioN of wEB processes based on the Net‐within‐Nets formalism and that follows a conversational approach. More specifically, this paper examines whether a set of interactions among a set of processes is compatible and also whether a given (imposed) interaction logic is compatible with a given business logic. Processes and their interactions have been semantically enhanced by means of domain ontologies and compatibility questions are studied using standard Petri net analysis techniques. Copyright © 2010 John Wiley & Sons, Ltd.

Application of multiroot decision diagrams for integer functions

New data structures for representation of integer functions and matrices are proposed, namely, multiroot binary decision diagrams (MRBDD). Algorithms for performing standard operations on functions and matrices represented by MRBDDs are presented. Thanks to the more efficient reuse of structural elements, representation by multiroot binary decision diagrams is more efficient than the widely used multiterminal binary decision diagrams (MTBDD). Experimental results are given, which show that multiroot binary decision diagrams are a promising alternative to multiterminal binary decision diagrams, in particular, in probabilistic verification, manipulation of probability distributions, analysis of Petri nets, and other computational models.

Oris: a tool for modeling, verification and evaluation of real-time systems

Oris is a tool for qualitative verification and quantitative evaluation of reactive timed systems, which supports modeling and analysis of various classes of timed extensions of Petri Nets. As most characterizing features, Oris implements symbolic state space analysis of preemptive Time Petri Nets, which enable schedulability analysis of real-time systems running under priority preemptive scheduling; and stochastic Time Petri Nets, which enable an integrated approach to qualitative verification and quantitative evaluation. In this paper, we present the current version of the tool and we illustrate its application to two different case studies in the areas of qualitative verification and quantitative evaluation, respectively.

Polynomial algebra of discrete models in systems biology

An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.

Coupled Petri nets for computer network risk analysis

This paper presents a framework for quantifying the risk induced by the potential for cyber attacks levied against network-supported operations. It also permits a formal assessment of candidate risk management policies that address network host vulnerabilities and host-process coupling. The framework incorporates a novel application of Petri net state coverability analysis coupled with process failure mode analysis. It extends previous work on Petri nets for attack analysis in three ways: (i) new metrics that quantify risk as a function of Petri net state and techniques for evaluating the metrics based on the minimal coverability set of a Petri net; (ii) a new method for coupling a Petri net representation of a computer network attack to a process failure modes model; and (iii) a new method for identifying high-value risk management opportunities. The paper concludes by presenting an application of the analysis techniques to evaluate risk in process control networks.