Showing papers on "Petri net published in 2013"

Understanding Petri Nets

Abstract: s of type t o k e n . It also has a precondition saying that the value of the token in c o 1 must be y e 11 ow. If the precondition is satisfied, the processor may fire, consuming the token in the store. Upon firing, it produces two tokens, one in c o l with value r e d , and one in s with value t okenval. Informally, the processor may fire only when the traffic light is yellow. As a result of firing the processor, the traffic light turns red, a t the same time signaling the other light that it may turn green. T h e specification of the other processors is very similar and so is omitted. T h e specification of y2 r does not contain a conditional statement. This means that its behavior does not depend on the values of the consumed tokens. Consequently, it is very similar to the transitions in P/T nets. For this reason, a processor whose behavior is not conditional is often called a transition. This class of processors is important because we can apply analysis techniques like Sand T-invariants to ExSpect specifications only if the specification consists entirely of transitions. ExSpect has a tool to transform any specification into such a transitions-only specification with the same dynamic behavior.

Petri Net Modeling and Cycle-Time Analysis of Dual-Arm Cluster Tools With Wafer Revisiting

Abstract: There are wafer fabrication processes in cluster tools that require wafer revisiting. If a swap strategy is applied to dual-arm cluster tools handling wafer revisiting, a three-wafer periodical process is formed with three wafers completed in each period. Such a period contains three cycles in a revisiting process and three cycles in a nonrevisiting one. Hence, analysis and scheduling of such tools become very complicated. In this paper, a Petri net (PN) model is developed to describe their operations. Based on it, it is found that, if a swap strategy is applied, such tools are always in a transient state. A systematic method is then presented to analyze their performance. With the help of the proposed PN model, this work, for the first time, derives the optimality conditions of three-wafer period scheduling. Industrial application examples are given to show the results.

Decomposing Petri nets for process mining: A generic approach

Abstract: The practical relevance of process mining is increasing as more and more event data become available. Process mining techniques aim to discover, monitor and improve real processes by extracting knowledge from event logs. The two most prominent process mining tasks are: (i) process discovery: learning a process model from example behavior recorded in an event log, and (ii) conformance checking: diagnosing and quantifying discrepancies between observed behavior and modeled behavior. The increasing volume of event data provides both opportunities and challenges for process mining. Existing process mining techniques have problems dealing with large event logs referring to many different activities. Therefore, we propose a generic approach to decompose process mining problems. The decomposition approach is generic and can be combined with different existing process discovery and conformance checking techniques. It is possible to split computationally challenging process mining problems into many smaller problems that can be analyzed easily and whose results can be combined into solutions for the original problems.

Prediction of Remaining Service Execution Time Using Stochastic Petri Nets with Arbitrary Firing Delays

Abstract: Companies realize their services by business processes to stay competitive in a dynamic market environment. In particular, they track the current state of the process to detect undesired deviations, to provide customers with predicted remaining durations, and to improve the ability to schedule resources accordingly. In this setting, we propose an approach to predict remaining process execution time, taking into account passed time since the last observed event. While existing approaches update predictions only upon event arrival and subtract elapsed time from the latest predictions, our method also considers expected events that have not yet occurred, resulting in better prediction quality. Moreover, the prediction approach is based on the Petri net formalism and is able to model concurrency appropriately. We present the algorithm and its implementation in ProM and compare its predictive performance to state-of-the-art approaches in simulated experiments and in an industry case study.

Knowledge Acquisition and Representation Using Fuzzy Evidential Reasoning and Dynamic Adaptive Fuzzy Petri Nets

Abstract: The two most important issues of expert systems are the acquisition of domain experts' professional knowledge and the representation and reasoning of the knowledge rules that have been identified. First, during expert knowledge acquisition processes, the domain expert panel often demonstrates different experience and knowledge from one another and produces different types of knowledge information such as complete and incomplete, precise and imprecise, and known and unknown because of its cross-functional and multidisciplinary nature. Second, as a promising tool for knowledge representation and reasoning, fuzzy Petri nets (FPNs) still suffer a couple of deficiencies. The parameters in current FPN models could not accurately represent the increasingly complex knowledge-based systems, and the rules in most existing knowledge inference frameworks could not be dynamically adjustable according to propositions' variation as human cognition and thinking. In this paper, we present a knowledge acquisition and representation approach using the fuzzy evidential reasoning approach and dynamic adaptive FPNs to solve the problems mentioned above. As is illustrated by the numerical example, the proposed approach can well capture experts' diversity experience, enhance the knowledge representation power, and reason the rule-based knowledge more intelligently.

On the Implementation of Industrial Automation Systems Based on PLC

Abstract: Industrial automation is largely based on PLC-based control systems. PLCs are today mostly programmed in the languages of the IEC 61131 standard which are not ready to meet the new challenges of widely distributed automation systems. Currently, an extension of IEC 61131 which includes object oriented programming as well as the new standard IEC 61499 are available. Moreover, service-oriented paradigms where autonomous and interoperable resources provide their functionalities in the form of services that can be accessed externally by clients without knowing the underlining implementation have been presented in the literature. In the supervisory control theory, methodologies based on formal models have been developed to improve the coordination of concurrent and distributed systems. In this paper, an event-driven approach is proposed to improve the design of industrial control systems using commercial PLCs. At a lower level, basic sequences are coded in elementary software objects, called function blocks, providing their functionalities as services. At an upper level, a Petri Net (PN) controller forces the execution of such services according to desired sequences, while by a PN supervisor constraints on the sequences are satisfied.

A modelling approach to railway track asset management

Abstract: The UK railway network contains around 20,000 miles of track and is now carrying more, faster and heavier trains than previously. The effective management of this ageing and increasingly utilised system with limited financial resources is a significant challenge. Modelling tools are required to investigate the alternative strategies to manage such assets. The models available to date are very limited in their capability. A fundamental problem is their inability to adequately account for the underlying degradation process which is strongly dependent upon the history of the previous maintenance carried out. They also lack the complexity to enable the detailed maintenance and renewal options to be explored. This paper describes a modelling approach which first of all analyses the available data on the track geometry, and by implication the condition of the ballast, gathered at regular intervals by a measurement train. The analysis produces distributions of times for the track geometry to degrade to a specified state. Degradation distributions are therefore of relevance to the railway network under consideration, avoiding the need to use generic and possibly inappropriate data. With the degradation distributions available, a track section model is formed which incorporates the maintenance and renewal processes and provides a means of predicting the condition of the ballast section over time. The model uses a Petri net formulation with a Monte Carlo solution routine and enables the effectiveness of different maintenance strategies to be investigated. Ways in which the complexity of the model can be increased if desired is discussed and a case study is provided to indicate the use of the model.

Time and Petri Nets

Abstract: At first glance the concepts of time and of Petri nets are quite contrary: while time determines the occurrences of events in a system, classic Petri nets consider their causal relationships and they represent events as concurrent systems. But if we take a closer look at how time and causality are intertwined we realize that there are many possible ways in which time and Petri nets interact. This book takes a closer look at three time-dependent Petri nets: Time Petri nets, Timed Petri nets, and Petri nets with time windows. The author first explains classic Petri nets and their fundamental properties. Then the pivotal contribution of the book is the introduction of different algorithms that allow us to analyze time-dependent Petri nets. For Time Petri nets, the author presents an algorithm that proves the behavioral equivalence of a net where time is designed once with real and once with natural numbers, so we can reduce the state space and consider the integer states exclusively. For Timed Petri nets, the author introduces two time-dependent state equations, providing a sufficient condition for the non-reachability of states, and she also defines a local transformation for converting these nets into Time Petri nets. Finally, she shows that Petri nets with time-windows have the ability to realize every transition sequence fired in the net omitting time restrictions. These classes of time-dependent Petri nets show that time alone does not change the power of a Petri net, in fact time may or may not be used to force firing. For Time Petri nets and Timed Petri nets we can say that they are Turing-powerful, and thus more powerful than classic Petri nets, because there is a compulsion to fire at some point in time. By contrast, Petri nets with time-windows have no compulsion to fire, their expressiveness power is less than that of Turing-machines. This book derives from advanced lectures, and the text is supported throughout withexamples and exercises. It issuitable for graduate courses in computer science, mathematics, engineering, and related disciplines, and as a reference for researchers.

Scheduling Cluster Tools With Ready Time Constraints for Consecutive Small Lots

Abstract: In the semiconductor manufacturing industry, the lot size currently tends to be extremely small, even being only 5-8 wafers, whereas conventional lots have 25 identical wafers. The smaller lot size is made because customers demand extremely small lots, and the number of chips in a large 300 mm wafer has increased. Cyclic scheduling is not applicable for such small lot production because the number of identical work cycles accounts for a small proportion of scheduling as compared to the lengths of the starting and closing transient periods. We therefore examine a new noncyclic scheduling problem of cluster tools for small lot production that considers ready time constraints on the chambers and the robot. The ready times are the epochs when the resources are freed from processing the preceding lot. To solve the scheduling problem, we develop a Petri net model which is a graphical and mathematical method for discrete event dynamic systems. Based on the Petri net model, we also develop a mixed integer programming (MIP) model and a branch and bound (B&B) algorithm for determining an optimal schedule. The B&B algorithm solves lots with up to 25 wafers and eight wafers within 500 s for a single-armed cluster tool and a dual-armed cluster tool, respectively, when three process steps are considered. Therefore, we propose an approximation method for the dual-armed cluster tool that schedules only the first few wafers with the B&B algorithm and the succeeding wafers with a well-known cyclic sequence. From experiments, we conclude that the difference between the approximation method and an optimal makespan is less than 1%. The methods we propose can be used for general noncyclic scheduling problems that can be modeled by Petri nets.

Deadlock-Free Control of Automated Manufacturing Systems With Flexible Routes and Assembly Operations Using Petri Nets

Abstract: In the context of automated manufacturing systems (AMS), Petri nets are widely adopted to solve the modeling, analysis, and control problems. So far, nearly all known approaches to liveness enforcing supervisory control investigate AMS with either flexible routes or assembly operations, whereas little work investigates them with both. In this paper, we propose a novel class of systems, which can well deal with both features so as to facilitate the control of more complex AMS. Using structural analysis, we show that liveness of their Petri net model can be attributed to the absence of undermarked siphons, which is realizable by synthesizing a proper supervisory controller. Moreover, an efficient method is developed and verified via AMS examples.

All for the Price of Few

Abstract: We present a simple and efficient framework for automatic verification of systems with a parameteric number of communicating processes The processes may be organized in various topologies such as words, multisets, rings, or trees Our method needs to inspect only a small number of processes in order to show correctness of the whole system It relies on an abstraction function that views the system from the perspective of a fixed number of processes The abstraction is used during the verification procedure in order to dynamically detect cut-off points beyond which the search of the state space need not continue We show that the method is complete for a large class of well quasi-ordered systems including Petri nets Our experimentation on a variety of benchmarks demonstrate that the method is highly efficient and that it works well even for classes of systems with undecidable verification problems

Modeling and Analysis of State-of-the-art VM-based Cloud Management Platforms

Abstract: Virtualization is a key aspect to achieve scalability and flexibility in a cloud. Many solutions have been proposed to monitor and deploy Virtual Machines (VM) in resource pool of cloud. However, most of the cloud management systems, such as Amazon EC2 are proprietary. In the said perspective, many open source VM-based platforms have tossed for general users to research. The existing work has mainly focused on the discussion of architecture, feature-set, and performance analysis. Other important aspects, such as formal analysis, modeling, and verification are usually ignored. In this paper, we provide formal analysis, modeling, and verification of three open source state-of-the-art VM-based cloud platforms: (a) Eucalyptus, (b) Open Nebula, and (c) Nimbus. We used High-Level Petri Nets (HLPN) to model and analyze the structural and behavioral properties of the systems. Moreover, to verify the models, we have used Satisfiability Modulo Theories Library (SMT-Lib) and Z3 Solver. We modeled about 100 VM to verify the correctness and feasibility of our models. The results reveal that the models are functioning correctly. Moreover, the increase in the number of VM does not affect the working of the models that indicates the practicability of the models in a highly scalable and flexible environment.

MARCIE: model checking and reachability analysis done efficiently

Abstract: MARCIE is a tool for the analysis of generalized stochastic Petri nets which can be augmented by rewards. The supported analysis methods range from qualitative and quantitative standard properties to model checking of established temporal logics. MARCIE's analysis engines for bounded Petri net models are based on Interval Decision Diagrams. They are complemented by simulative and approximative engines to allow for quantitative reasoning on unbounded models. Most of the quantitative analyses benefit from a multi-threaded implementation. This paper gives an overview on MARCIE's functionality and architecture and reports on the recently added feature of CSRL and PLTLc model checking.

A semantics for every GSPN

Abstract: Generalised Stochastic Petri Nets (GSPNs) are a popular modelling formalism for performance and dependability analysis. Their semantics is traditionally associated to continuous-time Markov chains (CTMCs), enabling the use of standard CTMC analysis algorithms and software tools. Due to ambiguities in the semantic interpretation of confused GSPNs, this analysis strand is however restricted to nets that do not exhibit non-determinism, the so-called well-defined nets. This paper defines a simple semantics for everyGSPN. No restrictions are imposed on the presence of confusions. Immediate transitions may be weighted but are not required to be. Cycles of immediate transitions are admitted too. The semantics is defined using a non-deterministic variant of CTMCs, referred to as Markov automata. We prove that for well-defined bounded nets, our semantics is weak bisimulation equivalent to the existing CTMC semantics. Finally, we briefly indicate how every bounded GSPN can be quantitatively assessed.

A Petri Net-Based Novel Scheduling Approach and Its Cycle Time Analysis for Dual-Arm Cluster Tools With Wafer Revisiting

Abstract: For some wafer fabrication processes, such as an atomic layer deposition (ALD) process, the wafers need to visit some process modules for a number of times. Using the existing swap-based strategy scheduling method in such systems leads to a 3-wafer cyclic schedule. Unfortunately, it is not optimal in the sense of cycle time. Aiming at searching for a better schedule, this paper models the system by a timed Petri net. With this model, the properties of the 3-wafer schedule are analyzed. Then, based on the analysis, it is found that, to improve the performance, it is necessary to reduce the number of wafers completed in a cycle. Hence, a 1-wafer schedule is developed by using a new swap-based strategy. By using the Petri net model, its cycle time is analyzed and shown to be optimal. Also, an effective method is presented to implement it. Illustrative examples are given to verify the research results obtained in this paper.

Cross-organizational collaborative workflow mining from a multi-source log

Abstract: Today's enterprise business processes become increasingly complex given that they are often executed by geographically dispersed partners or different organizations. Designing and modeling such a cross-organizational workflow is a complicated, time-consuming process and requires that a designer has extensive experience. Workflow logs captured by different cross-organizational systems provide a very valuable source of information on how business processes are executed in reality and thus can be used to derive workflow models through process mining. In this paper, we investigate the application of process mining for workflow integration based on the concept of RM_WF_Net, a type of Petri net extended with resource and message factors. Four coordination patterns are defined for workflow integration. A process mining approach is presented to discover the coordination patterns between different organizations and the workflow models in different organizations from the running logs containing the information about resource allocation. A process integration approach is then presented to obtain the model for a cross-organizational workflow based on the model mined for each organization and the coordination patterns between different organizations.

A Review on the Applications of Petri Nets in Modeling, Analysis, and Control of Urban Traffic

Abstract: Urban traffic systems that possess system states that are distributed, parallel, deterministic, stochastic, discrete, and continuous are well suited for a Petri net (PN) approach The literature survey conducted in this paper shows the vast applications of PNs in modeling and simulation, analyzing and evaluating performances, intelligent control and optimization, and congestion management in urban traffic systems This paper outlines the related works conducted using PNs and discusses its viability, such as its contributions and limitations Extendibility and future research potential to further the successful applications of PNs in traffic systems are discussed and proposed in this paper

Adaptive Moving-Target Tracking Control of a Vision-Based Mobile Robot via a Dynamic Petri Recurrent Fuzzy Neural Network

Abstract: In this study, an adaptive moving-target tracking control (AMTC) scheme via a dynamic Petri recurrent fuzzy neural network (DPRFNN) is constructed for a vision-based mobile robot with a tilt camera. In this study, the dynamic model of a vision-based mobile robot system, including a nonholonomic mobile robot and a tilt camera based on the concepts of mechanical geometry and motion dynamics, is developed first. Then, a continuously adaptive mean shift algorithm is adopted for the moving-object detection, and a model-based conventional sliding-mode control (CSMC) strategy is introduced. In order to relax the control design dependent on detailed system information and alleviate chattering phenomena caused by the inappropriate selection of uncertainty bounds, it further designs a model-free AMTC scheme with a DPRFNN to imitate the CSMC strategy. In the DPRFNN, the concept of a Petri net and the recurrent frame of internal feedback loops are incorporated into a traditional fuzzy neural network to alleviate the computation burden of parameter learning and to enhance the dynamic mapping of network ability. This five-layer DPRFNN is utilized for the major role in the proposed AMTC scheme. The corresponding adaptation laws of network parameters are established in the sense of projection algorithm and Lyapunov stability theorem to ensure the network convergence, as well as robust control performance without detailed system information and the compensation of auxiliary controllers. In addition, the effectiveness of the proposed AMTC scheme is verified by numerical simulations under different target tracking, and its superiority is indicated in comparison with the CSMC system. Furthermore, experimental results are also provided to verify the validity of the proposed AMTC scheme in practical applications.

Petri Net-Based Optimal One-Wafer Scheduling of Single-Arm Multi-Cluster Tools in Semiconductor Manufacturing

Abstract: In operating a multi-cluster tool, it needs to coordinate the activities of multiple robots. Thus, it is very challenging to schedule it. This paper conducts a study on one-wafer cyclic scheduling for multi-cluster tools whose bottleneck cluster tool is process-bound. The system is modeled by a Petri net. With this model, conditions under which a one-wafer cyclic schedule exists are developed. Based on them, it is shown that, for any multi-cluster tool whose bottleneck cluster tool is process-bound, there is always a one-wafer cyclic schedule. Then, a method is presented to find the minimal cycle time and the optimal one-wafer cyclic schedule. It is computationally efficient. Illustrative examples are used to show the applications and effectiveness of the proposed method.

Dynamic Adaptive Fuzzy Petri Nets for Knowledge Representation and Reasoning

Abstract: Although a promising tool for knowledge representation and reasoning, fuzzy Petri nets (FPNs) still suffer from some deficiencies. First, the parameters in current FPN models, such as weight, threshold, and certainty factor do not accurately represent increasingly complex knowledge-based expert systems and do not capture the dynamic nature of fuzzy knowledge. Second, the fuzzy rules of most existing knowledge inference frameworks are static and cannot be adjusted dynamically according to variations of antecedent propositions. To address these problems, we present a new type of FPN model, dynamic adaptive fuzzy Petri nets, for knowledge representation and reasoning. We also propose a max-algebra based parallel reasoning algorithm so that the reasoning process can be implemented automatically. As illustrated by a numerical example, the proposed model can well represent the experts' diverse experience and can implement the knowledge reasoning dynamically.

Performance Analysis of Device-to-Device Communications with Dynamic Interference Using Stochastic Petri Nets

Abstract: In this paper, we study the performance of Device-to-Device (D2D) communications with dynamic interference. In specific, we analyze the performance of frequency reuse among D2D links with dynamic data arrival setting. We first consider the arrival and departure processes of packets in a non-saturated buffer, which result in varying interference on a link based on the change of its backlogged state. The packet-level system behavior is then represented by a coupled processor queuing model, where the service rate varies with time due to both the fast fading and the dynamic interference effects. In order to analyze the queuing model, we formulate it as a Discrete Time Markov Chain (DTMC) and compute its steady-state distribution. Since the state space of the DTMC grows exponentially with the number of D2D links, we use the model decomposition and some iteration techniques in Stochastic Petri Nets (SPNs) to derive its approximate steady state solution, which is used to obtain the approximate performance metrics of the D2D communications in terms of average queue length, mean throughput, average packet delay and packet dropping probability of each link. Simulations are performed to verify the analytical results under different traffic loads and interference conditions.

A Petri-Net-Based Scheduling Strategy for Dual-Arm Cluster Tools With Wafer Revisiting

Abstract: There are wafer fabrication processes in cluster tools that require wafer revisiting. The adoption of a swap strategy for such tools forms a 3-wafer cyclic (3-WC) period with three wafers completed in each period. It has been shown that, by such a scheduling strategy, the minimal cycle time cannot be reached for some cases. This raises a question of whether there is a scheduling method such that the performance can be improved. To answer this question, a dual-arm cluster tool with wafer revisiting is modeled by a Petri net. Based on the model, the dynamical behavior of the process is analyzed. Then, a 2-wafer cyclic (2-WC) scheduling strategy is revealed for the first time. Cycle time analysis is conducted for the proposed strategy to evaluate its performance. It shows that, for some cases, the performance obtained by a 2-WC schedule is better than that obtained by any existing 3-WC ones. Thus, they can be used to complement each other in scheduling dual-arm cluster tools with wafer revisiting. Illustrative examples are given.

Strategies for Modeling Complex Processes Using Colored Petri Nets

Abstract: Colored Petri Nets (CPNs) extend the classical Petri net formalism with data, time, and hierarchy These extensions make it possible to model complex processes as CPNs without being forced to abstract from relevant aspects Moreover, CPNs are supported by CPN Tools—a powerful toolset that supports the design and analysis of such processes The expressiveness of the CPN language enables different modeling approaches Typically, the same process can be modeled in numerous ways As a result, inexperienced modelers may create CPNs that are unnecessarily convoluted and bulky Using a running example and a set of design patterns, we show how to solve typical design problems in terms of CPNs By following these guidelines, it is possible to create succinct, but also comprehensible, models In addition, we present some new features supported by CPN Tools 30 (eg, priorities and real time stamps) and show how the software can be used for performance analysis (ie, comparing design alternatives using simulation)

Automatic Verification of Erlang-Style Concurrency

Abstract: This paper presents an approach to verify safety properties of Erlang-style, higher-order concurrent programs automatically. Inspired by Core Erlang, we introduce λ Actor, a prototypical functional language with pattern-matching algebraic data types, augmented with process creation and asynchronous message-passing primitives. We formalise an abstract model of λ Actor programs called Actor Communicating System (ACS) which has a natural interpretation as a vector addition system, for which some verification problems are decidable. We give a parametric abstract interpretation framework for λ Actor and use it to build a polytime computable, flow-based, abstract semantics of λ Actor programs, which we then use to bootstrap the ACS construction, thus deriving a more accurate abstract model of the input program.

Reliability analysis of repairable systems using Petri nets and vague Lambda-Tau methodology.

Abstract: The main objective of the paper is to developed a methodology, named as vague Lambda-Tau, for reliability analysis of repairable systems. Petri net tool is applied to represent the asynchronous and concurrent processing of the system instead of fault tree analysis. To enhance the relevance of the reliability study, vague set theory is used for representing the failure rate and repair times instead of classical(crisp) or fuzzy set theory because vague sets are characterized by a truth membership function and false membership functions (non-membership functions) so that sum of both values is less than 1. The proposed methodology involves qualitative modeling using PN and quantitative analysis using Lambda-Tau method of solution with the basic events represented by intuitionistic fuzzy numbers of triangular membership functions. Sensitivity analysis has also been performed and the effects on system MTBF are addressed. The methodology improves the shortcomings of the existing probabilistic approaches and gives a better understanding of the system behavior through its graphical representation. The washing unit of a paper mill situated in a northern part of India, producing approximately 200 ton of paper per day, has been considered to demonstrate the proposed approach. The results may be helpful for the plant personnel for analyzing the systems' behavior and to improve their performance by adopting suitable maintenance strategies.

A Three-Level Strategy for the Design and Performance Evaluation of Hospital Departments

Abstract: The efficient management of hospital departments (HDs) has recently become an important issue. Indeed, the increased demand and design for hospital services have saturated the capacity of HD that requires suitable tools for the efficient use of resources and flow of patients, staff, and drugs. This paper proposes a model based on a three-level strategy to design at the tactical level in a concise and effective way the structure, the resources, and the dynamics of a critically congested HD. The design strategy is composed of three basic elements: the modeling module, the optimization module, and the simulation and decision module. The first module employs a Unified Modeling Language tool and a timed Petri net (PN) model to effectively capture the detailed flow and dynamics of patients, starting from their arrival to the HD until their discharge. The optimization module employs the fluid relaxation to concisely approximate in a continuous PN framework the HD model and optimize suitable performance indices. The simulation module verifies that the optimized parameters allow an effective workflow organization while maximizing the patient flow. In case of inconsistencies due to the fluid approximation between the continuous model used in the design phase by the optimization module and the discrete one used in the subsequent verification phase by the simulation module, the latter module revises the values of some HD model parameters. A real case study on the Emergency Cardiology Department of the General Hospital of Bari (Italy) shows the efficiency and accuracy of the proposed method.