The use of Petri nets for modeling pipelined processors

Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.INDEX TERMS Flexible manufacturing systems (FMS), deadlock, deadlock prevention, Petri Nets (PN), liveness enforcing supervisor (LES), PN computation tools.

The use of Petri nets for modelling, analysing and simulating complex distributed production systems meets serious problems when the size of the model grows. Therefore, it would be very useful to decompose a Petri net based model into smaller models linked with one another. The aim of this paper is to suggest and discuss some possible definitions of Modular Petri nets. This is accomplished by introducing the concept of Petri subnet. Two possible definitions are proposed and the meaning and the usefulness with respect to both model definition and model executability for simulation are pointed out. All definitions are given for the basic model of Petri nets. The extension of modularity concepts to high level Petri nets is shown to be possible in the second part of the paper, where an application is illustrated. In particular an algorithm is given which allows automatic composition of subnets into a larger model

Petri net-based modeling of a class of complex digital systems

Petri Nets are tools for the modelling and analysis of the behaviour of systems and analysis of the Petri Net can then reveal important information about the structure and dynamic behaviour of the modelled system. In this article, the author argues that Petri Net concepts (when used qualitatively) are not fundamentally different from those of ANT. For example, the ‘places’ from Petri Nets bear a strong resemblance to the actors in ANT, and the ‘triggers’ or ‘transitions’, are somewhat analogous to ANT’s translations. In modelling, places represent conditions and transitions represent events. Tokens may model the resources or data items that are associated with a place or places. The original research that this article is based on was undertaken using an actor-network framework to develop a model for e-Learning for students with Learning Difficulties. This article explores the qualitative use of Petri Nets to supplement this ANT treatment.

Petri Nets are tools for the modelling and analysis of the behaviour of systems and analysis of the Petri Net can then reveal important information about the structure and dynamic behaviour of the modelled system. In this article, the author argues that Petri Net concepts (when used qualitatively) are not fundamentally different from those of ANT. For example, the ‘places’ from Petri Nets bear a strong resemblance to the actors in ANT, and the ‘triggers’ or ‘transitions’, are somewhat analogous to ANT’s translations. In modelling, places represent conditions and transitions represent events. Tokens may model the resources or data items that are associated with a place or places. The original research that this article is based on was undertaken using an actor-network framework to develop a model for e-Learning for students with Learning Difficulties. This article explores the qualitative use of Petri Nets to supplement this ANT treatment.

In this paper we describe how the completion time distribution for short TCP connections can be computed using Deterministic Stochastic Petri Net (DSPN) models of TCP protocol. A DSPN model of TCP is a representation of the finite state machine description of the TCP transmitter behavior, and provides an accurate description of the TCP dynamics. The DSPN requires as input only the packet loss probability, and the average round trip time for the TCP connections being considered. The proposed model has been validated by comparing it against simulation results in various network scenarios, thus proving that the model is accurate. Numerical results are presented to prove the flexibility and the potentialities of the proposed methodology.KeywordsPerformance EvaluationCommunication Network PlanningTransport Control ProtocolDeterministic Stochastic Petri NetsCompletion Time Distribution

The article is devoted to the implementation of a method for modeling processes in complex educational systems based on the proposed variety of neuro-fuzzy temporal Petri nets. The article considers educational systems of the level of higher educational institutions, which, of course, belong to the class of complex systems. The need for a method, models and modeling tools is dictated by the fact that modern educational processes require constant modernization, due to the constantly growing volumes of information, changes in legislation, stricter requirements for specialists, rapid development of technologies, constant discoveries in various fields, as well as the influence of external factors. Requirements for the tools for modeling processes in complex systems are formulated, the use of Petri nets as the basis of such models is substantiated. The existing educational processes are considered on the example of the cycle of training in the master's program of the Belarusian-Russian University. The model of educational and information-analytical learning processes in the master's program based on the neuro-fuzzy temporal Petri net is presented. The proposed method allows to increase the flexibility of the choice of individual trajectories of training in the master's program, the effectiveness of elective disciplines and to make the transition to an integrated approach in the preparation of undergraduates. The proposed method can also be used as a basis for monitoring the state and control of information and analytical processes in educational systems. An approach to the construction of software-instrumental environment for the design and modification of information-analytical processes is described, aimed, among other things, at bridging the semantic gap between experts, architects and developers of information-analytical processes. A subsystem for the formation of a neuro-fuzzy temporal model of processes within the framework of a software-instrumental environment is considered.

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.

This paper deals with the modeling and control of discrete event robotic manufacturing cells using Petri nets, and proposes a methodology of model based design and implementation of hierarchical and distributed control. Hierarchical Petri net models are adopted; conceptual Petri net model and detailed Petri net model. The overall detailed Petri net model is decomposed into local Petri net models which are used by the local machine controllers. The upper level station controller coordinates the distributed local controllers so that the aggregate behavior of decomposed subnets is the same as that of the original Petri net. The overall control system is implemented using multithreaded programming based on Petri net based multitask processing. Simulation experiments show that the distributed Petri net model based control system can perform the overall multitask processing control by coincidence of the behavior of the real system with the local Petri net models.

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.

Modelling and analysis of kanban-controlled (just-in-time) production systems under realistic assumptions presents a number of challenges, including the ability to conduct both qualitative and quantitative analysis, and the ability to model control policies. These challenges are due, in part, to station interdependence, blocking and starvation due to limited buffer spaces, and the necessity of modelling both material and kanban flows. Petri nets (PNs) have recently emerged as a promising approach for modelling manufacturing systems. PNs are a graphical and mathematical technique useful for modelling concurrent, asynchronous, distributed, parallel, non-deterministic and stochastic systems. PN models can be analysed to determine both their qualitative and quantitative properties. In this paper, we develop stochastic, coloured PN (SCPN) models of a JIT system utilizing two different kanban control policies: a traditional kanban system (TKS) policy and a flexible kanban system (FKS) policy. The resulting models can be used to represent JIT systems of arbitrary size, producing single or multiple types of products, with fixed order points 1. The models are shown to be live and bounded, and can be simulated to produce quantitative results. Sample simulation results are presented to illustrate the models' capabilities.

The methods of modeling and control of discrete event robotic manufacturing cells using Petri nets are considered, and a methodology of decomposition and coordination is presented for hierarchical and distributed control. Based on task specification, a conceptual Petri net model is transformed into the detailed Petri net model, and then decomposed into constituent local Petri net based controller tasks. The local controllers are coordinated by the coordinator through communication between the coordinator and the controllers. Simulation and implementation of the control system for a robotic workcell are described. By the proposed method, modeling, simulation, and control of large and complex manufacturing systems can be performed consistently using Petri nets.

Half a century after Carl Adam Petri’s Ph.D. thesis: A perspective on the field

Petri nets have proven to be a valuable tool for modelling concurrent systems. As such, they should be suitable for modelling agent and multi-agent systems, as these are inherently concurrent. Nevertheless, there are not many systems that allow modelling of the whole multi-agent system in Petri nets. The use of Petri nets is usually limited to sub-problems, such as verification of interaction protocols. This paper describes the main concepts of PNagent - a tool for modelling BDI agents using the formalism of object oriented Petri nets (OOPN). PNagent allows development, testing and running software agents in a consistent graphical environment. The framework is suitable for prototyping and experiments with both multi-agent applications and the particular agent architecture itself. At the same time, thanks to the formal nature of its underlying paradigm, it provides means for verification of agentpsilas properties.

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.