Showing papers on "Petri net published in 2008"

Semantics and analysis of business process models in BPMN

Abstract: The Business Process Modelling Notation (BPMN) is a standard for capturing business processes in the early phases of systems development. The mix of constructs found in BPMN makes it possible to create models with semantic errors. Such errors are especially serious, because errors in the early phases of systems development are among the most costly and hardest to correct. The ability to statically check the semantic correctness of models is thus a desirable feature for modelling tools based on BPMN. Accordingly, this paper proposes a mapping from BPMN to a formal language, namely Petri nets, for which efficient analysis techniques are available. The proposed mapping has been implemented as a tool that, in conjunction with existing Petri net-based tools, enables the static analysis of BPMN models. The formalisation also led to the identification of deficiencies in the BPMN standard specification.

Semantics and analysis of business process models in BPMN

Abstract: The Business Process Modelling Notation (BPMN) is a standard for capturing business processes in the early phases of system development. The mix of constructs in BPMN makes it possible to define models with a range of semantic errors. But the static analysis of BPMN models to detect such errors is hindered by ambiguities in the standard specification and the complexity of the language. The fact that BPMN integrates constructs from graph-oriented process definition languages with features for concurrent execution of multiple instances of a subprocess and exception handling, makes it challenging to provide a formal semantics of BPMN. Even more challenging is to provide a semantics that can be used to analyse BPMN models. This paper proposes a formalisation of BPMN in terms a mapping to Petri nets, for which efficient analysis techniques exist. The mapping has been implemented as a tool that generates code in the Petri Net Markup Language. The formalisation has led to the identification of deficiencies in the BPMN specification.

Comparing the Expressiveness of Timed Automata and Timed Extensions of Petri Nets

Abstract: Time dependant models have been intensively studied for many reasons, among others because of their applications in software verification and due to the development of embedded platforms where reliability and safety depend to a large extent on the time features. Many of the time dependant models were suggested as real-time extensions of several well-known untimed models. The most studied formalisms include Networks of Timed Automata which extend the model of communicating finite-state machines with a finite number of real-valued clocks, and timed extensions of Petri nets where the added time constructs include e.g. time intervals that are assigned to the transitions (Time Petri Nets) or to the arcs (Timed-Arc Petri Nets). In this paper, we shall semi-formally introduce these models, discuss their strengths and weaknesses, and provide an overview of the known results about the relationships among the models.

Petri nets for systems and synthetic biology

Abstract: We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which unifies the qualitative, stochastic and continuous paradigms. Each perspective adds its contribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how qualitative descriptions are abstractions over stochastic or continuous descriptions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks.

Soundness of workflow nets : classification, decidability, and analysis

Abstract: Workflow nets, a particular class of Petri nets, have become one of the standard ways to model and analyze workflows. Typically, they are used as an abstraction of the workflow that is used to check the so-called soundness property. This property guarantees the absence of livelocks, deadlocks, and other anomalies that can be detected without domain knowledge. Several authors have proposed alternative notions of soundness and have suggested to use more expressive languages, e.g., models with cancellations or priorities. This paper provides an overview of the different notions of soundness and investigates these in the presence of different extensions of workflow nets. We will show that the eight soundness notions described in the literature are decidable for workflow nets. However, most extensions will make all of these notions undecidable. These new results show the theoretical limits of workflow verification. Moreover, we discuss some of the analysis approaches described in the literature.

Measuring Similarity between Business Process Models

Abstract: Quality aspects become increasingly important when business process modeling is used in a large-scale enterprise setting. In order to facilitate a storage without redundancy and an efficient retrieval of relevant process models in model databases it is required to develop a theoretical understanding of how a degree of behavioral similarity can be defined. In this paper we address this challenge in a novel way. We use causal footprintsas an abstract representation of the behavior captured by a process model, since they allow us to compare models defined in both formal modeling languages like Petri nets and informal ones like EPCs. Based on the causal footprint derived from two models we calculate their similarity based on the established vector space model from information retrieval. We validate this concept with an experiment using the SAP Reference Model and an implementation in the ProM framework.

A Survey and Comparison of Petri Net-Based Deadlock Prevention Policies for Flexible Manufacturing Systems

Abstract: Over the last two decades, a great deal of research has been focused on solving deadlock problems in resource allocation systems such as computer communication systems, workflow systems, and flexible manufacturing systems, resulting in a wide variety of approaches. As a well-defined problem in resource allocation systems, deadlock prevention based on a Petri net formalism has received an enormous amount of attention in the literature. This paper intends to review and compare a variety of Petri net-based deadlock prevention policies reported in the literature. Their comparison is done in terms of structural complexity, behavior permissiveness, and computational complexity. This paper should facilitate engineers in choosing a suited method for their industrial application cases.

A Maximally Permissive Deadlock Prevention Policy for FMS Based on Petri Net Siphon Control and the Theory of Regions

Abstract: This paper addresses the deadlock problems in flexible manufacturing systems (FMS) by using a Petri net siphon control method and the theory of regions. The proposed policy consists of two stages. The first one, called siphons control, is to add, for every siphon that we identify, a monitor to the original net model such that it is optimally invariant controlled. In the second stage, the theory of regions is utilized to derive the net supervisors such that deadlocks can be prevented. The first-stage work significantly lowers the computational cost compared with the approach where the theory of regions is used alone. An FMS example is presented to illustrate the technique. By varying the markings of given net structures, this paper shows its computational advantages.

Selective Siphon Control for Deadlock Prevention in Petri Nets

Abstract: Deadlock prevention is a crucial step in the modeling of flexible manufacturing systems. In the Petri net framework, deadlock prevention policies based on siphon control are often employed, since it is easy to specify generalized mutual exclusion constraints that avoid the emptying of siphons. However, such policies may require an excessive computational load and result in impractical oversized control subnets. This is often a consequence of the redundancy in the control conditions derived from siphons. In this paper, a novel method is proposed that provides small size controllers, based on a set covering approach that conveniently relates siphons and markings. Some examples are provided to demonstrate the feasibility of the approach and to compare it with other methods proposed in the literature.

Resource-Oriented Petri Net for Deadlock Avoidance in Flexible Assembly Systems

Abstract: In many flexible assembly systems, base components are transported with pallets; parts to be mounted onto the base ones are transported by trays with no pallets. When an assembly operation is performed by using some parts in a tray but not all, the tray with the remaining parts still occupies a buffer space. In this way, an assembly/disassembly material flow is formed. In such a material flow, deadlock can occur both in the base component and part flow. Furthermore, the assembly operations can also result in a deadlock. Thus, it is a great challenge to tackle deadlocks in such processes. This paper models them using resource-oriented Petri nets. Based on the models, a deadlock control policy is proposed and proved to be computationally efficient and less conservative than the existing policies in the literature. An industrial case study is used to show the results.

Opacity generalised to transition systems

Abstract: Recently, opacity has proved a promising technique for describing security properties. Much of the work has been couched in terms of Petri nets. Here, we extend the notion of opacity to the model of labelled transition systems and generalise opacity in order to better represent concepts from the literature on information flow. In particular, we establish links between opacity and the information flow concepts of anonymity and non-inference. We also investigate ways of verifying opacity when working with Petri nets. Our work is illustrated by two examples, one describing anonymity in a commercial context, and the other modelling requirements upon a simple voting system.

Control of Elementary and Dependent Siphons in Petri Nets and Their Application

Abstract: The importance of siphons is well recognized in the analysis and control of deadlocks in a Petri net. To minimize the number of siphons that have to be explicitly controlled, siphons in a net are divided in a net into elementary and dependent ones. The concepts of token-rich, token-poor, and equivalent siphons are newly presented. More general conditions under which a dependent siphon can be always marked are established. The existence of dependent siphons in a Petri net is investigated. An algorithm is developed to find the set of elementary siphons in a net system for deadlock control purposes. The application of the proposed elementary siphon concept to the existing deadlock control policies is discussed. A few different-sized manufacturing examples are used to demonstrate the advantages of elementary siphon-based policies. The significant value of the proposed theory via a particular deadlock control policy is shown. Finally, some interesting and open problems are discussed.

On Controllability of Dependent Siphons for Deadlock Prevention in Generalized Petri Nets

Abstract: A fair amount of research has shown the importance of siphons in the analysis and control of deadlocks in a variety of resource allocation systems by using a Petri net formalism. In this paper, siphons in a generalized Petri net are classified into elementary and dependent ones, as done for ordinary nets in our previous work. Conditions are derived under which a dependent siphon is controlled by properly supervising its elementary siphons, which indicates that the controllability of dependent siphons in an ordinary Petri net is a special case of that in a generalized one. The application of the controllability of dependent siphons is shown by considering the deadlock prevention problem for a class of resource allocation systems, namely, G-system that allows multiple resource acquisitions and flexible routings in a flexible manufacturing system with machining, assembly, and disassembly operations. We develop a monitor-based deadlock prevention policy that first adds monitors for elementary siphons only to a G-system plant model such that the resultant net system satisfies the maximal controlled-siphon property (maximal cs-property). Then, by linear programming, initial tokens in the additional monitors are decided such that liveness is enforced to the supervised system. Also, a simplified live marking relationship for a G-system between the initial tokens of the source places and those of the resource places is derived. Finally, the proposed deadlock prevention methods are illustrated by using an example.

A Petri Net Method for Schedulability and Scheduling Problems in Single-Arm Cluster Tools With Wafer Residency Time Constraints

Abstract: With wafer residency time constraints for some wafer fabrication processes, such as low pressure chemical-vapor deposition, the schedulability and scheduling problems are still open. This paper aims to solve both problems. A Petri net (PN) model is developed for the system. This model describes when the robot should wait and a robot wait is modeled as an event in an explicit way. Thus, to schedule a single-arm cluster tool with wafer residency time constraint is to decide how long a robot wait should be. Based on this model, for the first time, we present the necessary and sufficient conditions under which a single-arm cluster tool with residency time constraints is schedulable, which can be checked analytically. Meanwhile, a closed form scheduling algorithm is developed to find an optimal periodic schedule if it is schedulable. Also, a simple method is presented for the implementation of the periodic schedule for steady state, which is not seen in any previous work.

Modeling and Supervisory Control of Railway Networks Using Petri Nets

Abstract: In this paper, we deal with the problem of modeling railway networks with Petri nets so as to apply the theory of supervisory control for discrete event systems to automatically design the system controller. We provide a modular representation of railway networks in terms of stations and tracks including sensors and semaphores. We first ensure safeness and local liveness imposing both generalized mutual exclusion constraints and constraints also involving the firing vector. The detailed model used in this first step can be abstracted, considering a higher level description of a railway network that belongs to the class of ES PR (extended simple sequential process with resources) nets and show that global liveness may be enforced by adding appropriate monitor places designed using siphon analysis. In our approach, this can be done without an exhaustive computation of all siphons and we can characterize the cases in which the procedure can be recursively applied, giving a simple test for closed-loop net to remain an ES PR net.

Implementing Fuzzy Reasoning Petri-Nets for Fault Section Estimation

Abstract: Fuzzy reasoning Petri-nets (PNs) is a promising technique to tackle the complexities of power system fault section estimation. This paper addresses several key issues in implementing fuzzy reasoning PNs for fault section estimation, which include optimal design of structure of diagnosis models to avoid large matrix size, utilization of fuzzy logic parameters to effectively handle uncertainties, realization of matrix execution algorithm to achieve parallel reasoning and adaptability, and integration of more reliable input data to enhance estimation accuracy. Case studies are presented to demonstrate the estimation capability under complex scenarios. An implementation solution residing in a control center is proposed.

Quantifying process equivalence based on observed behavior

Abstract: In various application domains there is a desire to compare process models, e.g., to relate an organization-specific process model to a reference model, to find a web service matching some desired service description, or to compare some normative process model with a process model discovered using process mining techniques. Although many researchers have worked on different notions of equivalence (e.g., trace equivalence, bisimulation, branching bisimulation, etc.), most of the existing notions are not very useful in this context. First of all, most equivalence notions result in a binary answer (i.e., two processes are equivalent or not). This is not very helpful because, in real-life applications, one needs to differentiate between slightly different models and completely different models. Second, not all parts of a process model are equally important. There may be parts of the process model that are rarely activated (i.e., ''process veins'') while other parts are executed for most process instances (i.e., the ''process arteries''). Clearly, differences in some veins of a process are less important than differences in the main arteries of a process. To address the problem, this paper proposes a completely new way of comparing process models. Rather than directly comparing two models, the process models are compared with respect to some typical behavior. This way, we are able to avoid the two problems just mentioned. The approach has been implemented and has been used in the context of genetic process mining. Although the results are presented in the context of Petri nets, the approach can be applied to any process modeling language with executable semantics.

Nets with Tokens which Carry Data

Abstract: We study data nets, a generalisation of Petri nets in which tokens carry data from linearlyordered infinite domains and in which whole-place operations such as resets and transfers are possible. Data nets subsume several known classes of infinite-state systems, including multiset rewriting systems and polymorphic systems with arrays. We show that coverability and termination are decidable for arbitrary data nets, and that boundedness is decidable for data nets in which whole-place operations are restricted to transfers. By providing an encoding of lossy channel systems into data nets without whole-place operations, we establish that coverability, termination and boundedness for the latter class have non-primitive recursive complexity. The main result of the paper is that, even for unordered data domains (i.e., with only the equality predicate), each of the three verification problems for data nets without whole-place operations has non-elementary complexity.

Schedulability Analysis of Time-Constrained Cluster Tools With Bounded Time Variation by an Extended Petri Net

Abstract: Cluster tools for some wafer fabrication processes such as low-pressure chemical vapor deposition have strict wafer delay constraints. A wafer that completes processing in a processing chamber should leave the chamber within a specified time limit. Otherwise, the wafer suffers from severe quality troubles due to residual gases and heat within the chamber. An important engineering problem is to verify whether for given task times there exists a tool operation schedule that satisfies the wafer delay limit. There have been studies on the problem, which all assume deterministic task times. However, in reality, the task times are subject to random variation. In this paper, we develop a systematic method of determining schedulability of time-constrained decision-free discrete-event systems, where time variation can be confined within finite intervals. To do this, we propose an extended Petri net for modeling such systems. We then develop a necessary and sufficient condition for which there always exists a feasible schedule and one for which there never exists any feasible schedule. We develop a graph-based computational procedure for verifying the schedulability conditions and determining the worst-case task delay. We demonstrate how the procedure can be used for cluster tool engineering to control wafer delays against wafer alignment failures and time variation.

Translating unstructured workflow processes to readable BPEL: Theory and implementation

Abstract: The Business Process Execution Language for Web Services (BPEL) has emerged as the de facto standard for implementing processes. Although intended as a language for connecting web services, its application is not limited to cross-organizational processes. It is expected that in the near future a wide variety of process-aware information systems will be realized using BPEL. While being a powerful language, BPEL is difficult to use. Its XML representation is very verbose and only readable for the trained eye. It offers many constructs and typically things can be implemented in many ways, e.g., using links and the flow construct or using sequences and switches. As a result only experienced users are able to select the right construct. Several vendors offer a graphical interface that generates BPEL code. However, the graphical representations are a direct reflection of the BPEL code and not easy to use by end-users. Therefore, we provide a mapping from Workflow Nets (WF-nets) to BPEL. This mapping builds on the rich theory of Petri nets and can also be used to map other languages (e.g., UML, EPC, BPMN, etc.) onto BPEL. In addition to this we have implemented the algorithm in a tool called WorkflowNet2BPEL4WS.

Conformance checking of service behavior

Abstract: A service-oriented system is composed of independent software units, namely services, that interact with one another exclusively through message exchanges. The proper functioning of such system depends on whether or not each individual service behaves as the other services expect it to behave. Since services may be developed and operated independently, it is unrealistic to assume that this is always the case. This article addresses the problem of checking and quantifying how much the actual behavior of a service, as recorded in message logs, conforms to the expected behavior as specified in a process model. We consider the case where the expected behavior is defined using the BPEL industry standard (Business Process Execution Language for Web Services). BPEL process definitions are translated into Petri nets and Petri net-based conformance checking techniques are applied to derive two complementary indicators of conformance: fitness and appropriateness. The approach has been implemented in a toolset for business process analysis and mining, namely ProM, and has been tested in an environment comprising multiple Oracle BPEL servers.

On Siphon Computation for Deadlock Control in a Class of Petri Nets

Abstract: As a structural object, siphons are well recognized in the analysis and control of deadlocks in resource allocation systems modeled with Petri nets. Many deadlock prevention policies characterize the deadlock behavior of the systems in terms of siphons and utilize this characterization to avoid deadlocks. This paper develops a novel methodology to find interesting siphons for deadlock control purposes in a class of Petri nets, i.e., a system of simple sequential processes with resources . Resource circuits in an are first detected, from which, in general, a small portion of emptiable minimal siphons can be derived. The remaining emptiable ones can be found by their composition. A polynomial-time algorithm for finding the set of elementary siphons is proposed, which avoids complete siphon enumeration. It is shown that a dependent siphon can always be controlled by properly supervising its elementary siphons. A computationally efficient deadlock control policy is accordingly developed. Experimental study shows the efficiency of the proposed siphon computation approach.

Analyzing interacting WS-BPEL processes using flexible model generation

Abstract: We address the problem of analyzing the interaction between WS-BPEL processes. We present a technology chain that starts out with a WS-BPEL process and translates it into a Petri net model. On the model we decide controllability of the process (the existence of a partner process, such that both can interact properly) and compute its operating guideline (a characterization of all properly interacting partner processes). To manage processes of realistic size, we present a concept of a flexible model generation which allows the generation of compact Petri net models. A case study demonstrates the value of this technology chain.

A Region-Based Algorithm for Discovering Petri Nets from Event Logs

Abstract: The paper presents a new method for the synthesis of Petri nets from event logs in the area of Process Mining. The method derives a bounded Petri net that over-approximates the behavior of an event log. The most important property is that it produces a net with the smallest behavior that still contains the behavior of the event log. The methods described in this paper have been implemented in a tool and tested on a set of examples.

Intuitive Mapping of UML 2 Activity Diagrams into Fundamental Modeling Concept Petri Net Diagrams and Colored Petri Nets

Abstract: This paper describes how UML 2 Activity diagrams can be intuitively translated into Petri net notations. The UML2 specification states that activities are based on Petri net semantics. The transformation of UML 2 Activity diagrams into Petri net semantics have been researched for various reasons. Translating UML activities into Petri nets creates new problems. The Petri net diagrams are (i) more complex (ii) contain more nodes and edges, (iii) unsuitable for visualization by stakeholders. A solution to this problem is to translate the UML activity diagram into a Fundamental Modeling Concepts Petri net diagram compact notation. This can be converted to a colored Petri net (CPN) for execution and validation. A case study taken from a web ordering system activity is used for explaining and illustrating this concept.

A Constrained Probabilistic Petri Net Framework for Human Activity Detection in Video

Abstract: Recognition of human activities in restricted settings such as airports, parking lots and banks is of significant interest in security and automated surveillance systems. In such settings, data is usually in the form of surveillance videos with wide variation in quality and granularity. Interpretation and identification of human activities requires an activity model that a) is rich enough to handle complex multi-agent interactions, b) is robust to uncertainty in low-level processing and c) can handle ambiguities in the unfolding of activities. We present a computational framework for human activity representation based on Petri nets. We propose an extension-Probabilistic Petri Nets (PPN)-and show how this model is well suited to address each of the above requirements in a wide variety of settings. We then focus on answering two types of questions: (i) what are the minimal sub-videos in which a given activity is identified with a probability above a certain threshold and (ii) for a given video, which activity from a given set occurred with the highest probability? We provide the PPN-MPS algorithm for the first problem, as well as two different algorithms (naive PPN-MPA and PPN-MPA) to solve the second. Our experimental results on a dataset consisting of bank surveillance videos and an unconstrained TSA tarmac surveillance dataset show that our algorithms are both fast and provide high quality results.

Modularization of biochemical networks based on classification of Petri net t-invariants

Abstract: Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior. With increasing system complexity, the basic behavior can only be expressed by a huge number of t-invariants. According to our validation criteria for biochemical Petri nets, the necessary verification of the biological meaning, by interpreting each subnetwork (t-invariant) manually, is not possible anymore. Thus, an automated, biologically meaningful classification would be helpful in analyzing t-invariants, and supporting the understanding of the basic behavior of the considered biological system. Here, we introduce a new approach to automatically classify t-invariants to cope with network complexity. We apply clustering techniques such as UPGMA, Complete Linkage, Single Linkage, and Neighbor Joining in combination with different distance measures to get biologically meaningful clusters (t-clusters), which can be interpreted as modules. To find the optimal number of t-clusters to consider for interpretation, the cluster validity measure, Silhouette Width, is applied. We considered two different case studies as examples: a small signal transduction pathway (pheromone response pathway in Saccharomyces cerevisiae) and a medium-sized gene regulatory network (gene regulation of Duchenne muscular dystrophy). We automatically classified the t-invariants into functionally distinct t-clusters, which could be interpreted biologically as functional modules in the network. We found differences in the suitability of the various distance measures as well as the clustering methods. In terms of a biologically meaningful classification of t-invariants, the best results are obtained using the Tanimoto distance measure. Considering clustering methods, the obtained results suggest that UPGMA and Complete Linkage are suitable for clustering t-invariants with respect to the biological interpretability. We propose a new approach for the biological classification of Petri net t-invariants based on cluster analysis. Due to the biologically meaningful data reduction and structuring of network processes, large sets of t-invariants can be evaluated, allowing for model validation of qualitative biochemical Petri nets. This approach can also be applied to elementary mode analysis.