Road Traffic Models Using Petri Nets and Minplus Algebra

The synthesis problem of concurrent systems is the problem of synthesizing a concurrent system model from sequential observations. The paper studies the synthesis problem for elementary Petri nets and transition systems. A characterization of the class of transition systems which correspond to elementary Petri nets is proven. It is shown how to generate all elementary Petri nets corresponding to a given transition system. If there is any such elementary Petri net, it is proven that there always exists a small one which has only polynomially many elements in the size of the transition system.

In this paper we present a survey on methods for the synthesis of Petri nets from behavioral descriptions given as languages. We consider place/transition Petri nets, elementary Petri nets and Petri nets with inhibitor arcs. For each net class we consider classical languages, step languages and partial languages as behavioral description. All methods are based on the notion of regions of languages. We identify two different types of regions and two different principles of computing from the set of regions of a language a finite Petri net generating this language. For finite or regular languages almost each combination of Petri net class, language type, region type and computation principle can be considered to compute such a net. Altogether, we present a framework for region-based synthesis of Petri nets from languages which integrates almost all known approaches and fills several remaining gaps in literature.

Using elementary Petri nets, it is difficult to mixturely model the discrete, continuous and other complicated events, for example, DNA, RNA and amino acid sequence events. Therefore, Hybrid Functional Petri Net with extension (HFPNe) was introduced to overcome this difficulty and also to allow representation of pathway models without loss of biological details. First, this book chapter explains how modeling with Petri net is done. After which, a full definition of HFPNe is given, along with its relation to hybrid Petri net and other related Petri net extension. Finally, to demonstrate the elegance of HFPNe architecture in handling complex pathway modeling, we chose a biological pathway that involves discrete, continuous and sequence events (gene regulatory network of the cell fate determination in C. elegans). We provide the biological mechanisms of this network and show how intuitively it could be modeled on HFPNe architecture using a software tool, Cell Illustrator.KeywordsGene Regulatory NetworkCell Fate DeterminationInput PlaceOutput PlaceContinuous PlaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Petri net is said to be elementary if every place can contain no more than one token. In this paper, it is studied topological properties of the elementary Petri net for a pipeline consisting of n functional devices. If the work of the functional devices is considered continuous, we can come to some topological space of “intermediate” states. In the paper, it is calculated the homology groups of this topological space. By induction on n, using the Addition Sequence for homology groups of semicubical sets, it is proved that in dimension 0 and 1 the integer homology groups of these nets are equal to the group of integers, and in the remaining dimensions are zero. Directed homology groups are studied. A connection of these groups with deadlocks and newsletters is found. This helps to prove that all directed homology groups of the pipeline elementary Petri nets are zeroth.

In the area of Petri nets, many different developments have taken place within the last 30 years, in academia as well as in practice. For an adequate use in practice, a coherent and application oriented combination of various types and techniques for Petri nets is necessary. In order to attain a formal basis for different classes of Petri nets we introduce the concept of abstract Petri nets. The essential point of abstract Petri nets is to allow different kinds of net structures as well as the combination of various kinds of data types. This means that in abstract Petri nets the data type and the net structure part can be considered as abstract parameters which can be instantiated to different concrete net classes. We show that several net classes, like place/transition nets, elementary nets, S-graphs, algebraic high-level nets, and predicate/transitions nets are instantiations of abstract Petri nets. Moreover, we discuss coloured Petri nets in this context.KeywordsPredicate LogicForgetful FunctorUniform ApproachSpeci CationSignature Morphism

Presently, the number, types, and distribution of resources in a resource allocation system (RAS), may change frequently and dynamically due to fluctuant customer demands. Such changes in a resource allocation (RA) specification mean different production or service behaviors yielded by the providers. This new situation gives rise to a challenging problem, namely, how to switch smoothly the provider systems to support different production. This paper tries to address this problem from the viewpoint of discrete event system (DES) supervisory control. A Petri net (PN) controller of an RAS can be designed from a resource allocation specification using P-invariant. Once the RA specification is changed, the controller is updated following it. Moreover, if the changed specification is unreasonable, the whole control system, are reconfigured to reach a legal system state and a newly reasonable resource allocation solution is re-calculated. Specifically, the paper proposed a reconfiguration method of a PN control system that is transformed into PN reachability analysis problem using a mathematic programming approach. In our method, not only the transition firing costs but also the steps of concurrent firing are taken into account to achieve an optimal reconfiguration solution. Finally, an example is provided for illustrating the application of the mentioned methods.

This paper describes the fundamental concepts and characteristics of Petri nets (PNs) that make them a significant tool for modeling and analyzing asynchronous systems with concurrent and parallel activities and follows the extensions that improved the implementation capabilities of the original PNs. Their first and most relevant extension was time modeling, a vital aspect of system performances not considered in the original version. There are several possibilities for introducing time in PNs. Among them, a technique that associates time with places is presented in some detail. As PNs tend to become cumbersome and time consuming when large and complex systems are involved, a method for decomposing timed PNs of open queuing networks is reviewed here. Though initially developed as an information/computer-based technique, PNs were immediately adopted in a variety of application areas, such as manufacturing, design, planning and control. Viewed through a more recently developed programming perspective, the ordinary PNs became “high level” PNs suitable for defining different data types and for applying hierarchical approaches. It is expected that the robust theoretical basis of this tool coupled with its visual and flexibility features will continue to appeal to researchers and practitioners alike in a variety of domains and as a result will continue to evolve and expand.

The Petri Net Toolbox (PN Toolbox) for MATLAB is a software package that offers instruments for the simulation, analysis and design of untimed, deterministic and stochastic P-/T-timed and stochastic Petri nets (PNs). The facilities available in this toolbox are appropriate for studying the dynamics of many classes of discrete-event systems. The Petri Net Simulink Block (PNSB) allows the modeling and analysis of hybrid systems whose event-driven part(s) is (are) modeled based on the PN formalism. The current paper focuses on the exploitation of the PN Toolbox for illustrating the usage of the PN theory in Control Engineering from the pedagogic point of view, the discussion being supported by example problems and comments on the teaching goals. The PN Toolbox is included in the Connections Program of The MathWorks Inc., as a third party product.

The aim of this invited survey is to introduce Computer science/Petri nets specialists to the basic system level issues brought up by the development of Flexible Manufacturing and how Petri nets are used to aid the production engineers in their work. After some terminology concerning production engineering, the hierarchical decision and control level is briefly reviewed. Finally, the role and the presence of nets in CAE (Computer Aided Engineering) and in CAM (Computer Aided Manufacturing) for FMSs (Flexible Manufacturing Systems) are considered. From the design point of view, the use of nets have many advantages in modeling, qualitative analysis, performance evaluation and code generation. From the control of the plant perspective, scheduling on nets models, the coordination of the plant (global and partial) and the presence of nets in the local control level are discussed.Petri nets theory presents a relatively mature body, nevertheless efficient performance evaluation (even for P/T net models) and qualitative analysis of high-level net models still requires important developments. Moreover, the impression that the Petri net newcomer may have looking at the many variants of high-level-nets formalisms may initially produce some kind of rejection. In any case, it is our opinion that Petri nets appears as a key formalism to describe, analyze and implement the control of FMSs. The merging of Petri nets and knowledge based techniques seems to be very promising to deal with large complex discrete event dynamic systems such as FMSs.KeywordsFlexible Manufacture SystemDiscrete Event SystemProgrammable Logic ControllerComputer Integrate ManufactureMarked GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Most studies employing Petri nets in semiconductor manufacturing model only one specific area (e.g. etching) in detail, and model the rest of the manufacturing process, e.g. by abstract input/output behavior. In our study, we show the feasibility of using Petri nets for modeling the complete production process. We use the first set of test data provided by the MASM-LAB, Arizona State University. It is a process of a two-product system making non-volatile memory chips. For modeling, we use our own tool PSim, which is based on a combined queuing and Petri net formalism. The integration of queues makes the modeling of parts waiting in front of a machine quite concise and intuitive. PSim offers a hierarchical and modular modeling approach, which is especially feasible for large and complex systems. We use the modular approach by once defining the structure of a machine as Petri net and then instantiating as many machines as needed. Then we model the operators, resources and the movement of parts between the machines as specified in the production plan. As a result, we can state that Petri nets are feasible for modeling a complete semiconductor manufacturing process.

The specification and distributed control of discrete event robotic manufacturing systems using Petri nets are considered, and a methodology of decomposition and coordination is presented for hierarchical and distributed control. First, a task specification is defined as a Petri net model at the conceptual level, and then transformed to the detailed Petri net representation of the subtasks. Finally, the overall Petri net is decomposed and the constituent subnets are assigned to local Petri net based controllers. The controllers are coordinated by the coordinator so that the decomposed transitions fire at the same time. System coordination algorithm through communication between the coordinator and the controllers, is presented. By the proposed method, modeling, simulation and control of large and complex manufacturing systems can be performed consistently using Petri nets.

Petri nets have proved their effectiveness in modeling and formal verification of a large number of applications: control systems, communication protocols, application workflows, hardware design, etc. In the present days, one important focus of computer science is on security and secure communications. The use of Petri nets for verifying security properties is not a mature field due to a lack of convenient modeling and verification capabilities. So far, in the Petri Net field there is only CPN Tools that is mature enough for modeling, using the colored Petri nets formalism. Nevertheless such verifications cannot be performed on large systems as CPN Tools is based on an exhaustive way of computing the semantics of a model. In this paper we present the use of AlPiNA, another candidate for this task. AlPiNA is a symbolic model checker that uses the formalism of algebraic Petri nets. We have used it successfully for modeling ad hoc networks and for verifying security protocols designed for this type of networks. As a case study and benchmark we have chosen the ARAN secure routing protocol. We managed to find all the attacks that were already reported for this protocol. To our knowledge this work is also the first successful attempt to use Petri nets for model checking the security properties of ad hoc networks protocols.

Compositional analysis aims to reveal the underlying structures of a large-scale system or network by analyzing its constituent components and their relationships. Today’s mathematical modeling languages, such as Petri nets, are useful for describing distributed systems and complex networks. However, the flat model architecture of Petri nets makes it difficult for them to depict the compositional structures of a large-scale model. Therefore, an enhanced compositionality feature has become a significant demand in large-scale modeling with Petri nets. This paper explores the underlying compositional structures of a given Petri net model by using a proposed sorting algorithm. The algorithm analyses compositional structures by sorting an incidence matrix that is generated from the Petri net model. Finally, the proposed sorting algorithm is applied to a traffic network model that was built with Petri nets to analyze its compositional structures, which represent different traffic lines, with the aim of optimizing the traffic network.

Graph Rewriting Systems are a powerful formalism for the specification of parallel and distributed systems, and the corresponding theory is rich of results concerning parallelism and concurrency. I will review the main results of the theory of concurrency for the algebraic approach to graph rewriting, emphasizing the relationship with the theory of Petri nets. In fact, graph rewriting systems can be regarded as a proper generalization of Petri nets, where the current state of a system is described by a graph instead of by a collection of tokens. Recently, this point of view allowed for the generalization to graph rewriting of some interesting results and constructions of the concurrent semantics of nets, including processes, unfoldings, and categorical semantics based on pair of adjoint functors.KeywordsDirect DerivationGraph TransformationGraph GrammarAdjoint FunctorHost GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The use of shared resources is a major problem occurring in discrete event (DE) systems, including manufacturing systems, computer systems, communication systems, highway/vehicle systems, and others. The issues involve problems of assignment of resources when the same resources are simultaneously requested by more than one job. Failure to suitably assign, or dispatch, resources in such situations can have serious deleterious effects on system performance, resulting in extreme cases in system deadlock [7]. Computer operating systems engineers and industrial engineers have used the concepts of circular wait (CW) and circular blocking in analysis of such phenomena [41, 24]. Various concepts in Petri nets (PN) are extremely useful for dealing with deadlock and a great deal of research has been done from the PN point of view (see references, especially [11, 14, 19]). The PN approaches are often based on the notion of the siphon, which indeed is called a “deadlock” in some works [26]. Unfortunately, it is known that many problems in scheduling, dispatching, and deadlock analysis are NP-hard [12], so that significant increases in computing power do not significantly improve computational ability. Neither PN nor CW approaches have addressed this issue.