New Class Of Petri Nets Research Articles

Petri transport networks

This paper presents a new class of Petri nets - Petri transport networks, used to simulate the transport’s systems. This class can be attributed to hierarchical temporal colored probabilistic Petri nets. The paper gives a definition, basic concepts, structure and functioning rules of Petri transport networks. The relevance of the topic raised in the article is due to increasing attention to the development of transport systems, their evolution and modernization. Modern management methods, various mechanisms for regulating traffic flows, infrastructural extensions, all this does not meet the challenges posed by modern transport infrastructure. Moreover, the problem is increasing every year. Petri transport networks introduced in the work, are a convenient tool ohms to simulate the transport’s systems of any complexity and scale. A new class of Petri transport networks is characterized by a hierarchical structure, in which the first level displays the entire system as a whole, the second - the internal structure of each object. Distinctive features are also the adjustment of the activation of traffic flows by means of a control marker, inter-level synchronization, separation of positions and transitions to types having different functions.

Signal set tissue systems and overlapping localities

In signal set tissue systems with overlapping localities (ssolt-systems) evolution rules can be associated with several cells. Rules may influence each other through instant signalling and, moreover, they are synchronised when sharing activated cells. The latter is a new feature. We study the behaviour of ssolt-systems in the form of labelled step transition systems. This allows to compare ssolt-systems with and without signalling and overlapping localities. Next the synthesis problem is considered, i.e., the question when given a step transition system, how to effectively construct an ssolt-system exhibiting this behaviour. To this end, ssolt-systems are related to a new class of Petri nets, that are behaviourally equivalent to ssolt-systems. It is shown how certain region based synthesis techniques can be applied to these nets and hence are also available for ssolt-systems.

A model based approach to assess the performance of production systems in degraded mode

Nowadays production systems are asked to perform their activities in a high uncertainty environment and to guarantee their performance in this environment. Therefore, they are asked to master risks that are part of their daily activities, to maintain the performance which is considered as their key success factor. Risks may cause serious effects that threaten the production systems and degrade their performance. Nevertheless, we cannot estimate the degradation that a risk may cause to system performance, since risk analysis methods found in the literature do not allow simulating the behaviour of the system in degraded mode. In order to help production systems to assess their performance in risk situations, we propose in this paper a model-based approach that enables assessing the performance of production systems in degraded mode. Our approach is based on function, interaction, structure (FIS) modelling framework that enables modelling complex system and its failures. The resulting model is converted into an executable simulation model based on a new class of Petri Nets (PNs) called predicate-transition, prioritised, synchronous (PTPS) PN. The obtained simulation model is then executed in order to obtain performance indicators in degraded mode. This tool is used during the system design, in order to study the impact of risks on the designed production system performance. It is also used to study an existing production system in order to analyse and optimise its behaviour in degraded mode. In this article, we present our tool and apply it to a special case of production systems which is a hospital sterilisation system.

Composition Colored Petri Nets for the Refinement of Reaction-based Models

Model refinement is an important step in the model building process. For reaction-based models, data refinement consists in replacing one species with several of its variants in the refined model. We discuss in this paper the implementation of data refinement with Petri nets such that the size of the model (in terms of number of places and transitions) does not increase. We capture the compositional structure of species by introducing a new class of Petri nets, composition Petri nets (ComP-nets), and their colored counterpart, colored composition Petri nets (ComCP-nets). Given a reaction-based model with known compositional structure, represented as a ComP-net, we propose an algorithm for building a ComCP-net which implements the data refinement of the model and has the same network structure as the initial ComP-net.

A New Class of Petri Nets for Modeling and Property Verification of Switched Stochastic Systems

Switched stochastic systems (SSS) can be used to describe hybrid systems with randomness. However, the languages to describe their discrete switching logic and stochastic dynamic processes are different, and this difference makes their design and analysis hard. This paper proposes a new Petri net model, namely stochastic-differential Petri net (S-DPN), to describe both discrete switching logic, represented by a Markov chain, and stochastic dynamic processes, represented by a set of stochastic differential equations. We then apply a model checking technique to S-DPN to check the correctness of the requirements of SSS. A temperature control system is used to demonstrate the effectiveness of our method.

Modeling Internet Host Reliability using Higher-Order Time Petri Net

The Higher-Order Petri Net is a new class of Petri Nets that exploit the properties of higher-order neural networks. Adding time to HOPN produces a new class called Higher-Order Time Petri Net, this is the subject of our study .In this paper, a method to model the internet host reliability with Higher-Order Time Petri Net is proposed. Analysis of HOTPN model is presented. A reachability graph is defined in a discrete way by using an enumeration procedure and the reachable states of the Time Petri Net and HOTPN. Finally, we compare between TPN and HOTPN by using the behavior properties and reachability graph.

Petri net-based modeling and control of the multi-elevator systems

This paper extends the Petri net (PN)-based modeling of multi-elevator control system for M floors and N elevators which provides the generic PN model of the system. A new class of Petri nets is in...

A New Class of Fuzzy Petri Nets for Knowledge Representation and Reasoning

This paper presents a new class of Petri nets called generalised fuzzy Petri nets. The new class extends the existing fuzzy Petri nets by introducing three operators in the form of triangular norms, which are supposed to function as substitute for the min, max and * algebraic product operators. To demonstrate the power and the usefulness of this model, an application of the generalised fuzzy Petri nets in the domain of train traffic control is provided. The new model is more flexible than the classical one as in the former class the user has the chance to define the input/output operators. The proposed approach can be used for knowledge representation and reasoning in decision support systems.

A New Class of Fuzzy Petri Nets for Knowledge Representation and Reasoning

This paper presents a new class of Petri nets called generalised fuzzy Petri nets. The new class extends the existing fuzzy Petri nets by introducing three operators in the form of triangular norms...

Concurrency bugs in multithreaded software: modeling and analysis using Petri nets

In this paper, we apply discrete-event system techniques to model and analyze the execution of concurrent software. The problem of interest is deadlock avoidance in shared-memory multithreaded programs. We employ Petri nets to systematically model multithreaded programs with lock acquisition and release operations. We define a new class of Petri nets, called Gadara nets, that arises from this modeling process. We investigate a set of important properties of Gadara nets, such as liveness, reversibility, and linear separability. We propose efficient algorithms for the verification of liveness of Gadara nets, and report experimental results on their performance. We also present modeling examples of real-world programs. The results in this paper lay the foundations for the development of effective control synthesis algorithms for Gadara nets.

Membrane Systems with Qualitative Evolution Rules

In membrane systems, biochemical reactions taking place in the compartments of a cell are abstracted to evolution rules that specify which and how many objects are consumed and produced. The recently proposed reaction systems also investigate processes carried by biochemical reactions, but the resulting computational model is remarkably different. A key difference is that in reaction systems, biochemical reactions are modeled using a qualitative rather than a quantitative approach. In this paper, we introduce so-called set membrane systems, a variant of membrane systems with qualitative evolution rules inspired by reaction systems. We then relate set membrane systems to Petri nets which leads to a new class of Petri nets: set-nets with localities. This Petri net model provides a faithful match with the operational semantics of set membrane systems.

Combined Petri net modelling and AI based heuristic hybrid search for flexible manufacturing systems—part 1. Petri net modelling and heuristic search

This two-part paper presents modelling and scheduling approaches for flexible manufacturing systems (FMS) using Petri nets (PNs) and artificial intelligence (AI) based heuristic search methods. In part I, the description of FMS formulation that will be considered throughout the paper is presented. A new class of PNs, Buffer-nets, for defining FMS is proposed, which enhances the modelling techniques for manufacturing systems with features that are considered difficult to model. An input language for automatic synthesis of these nets is developed. A scheduling architecture, which integrates PN models and AI techniques, is proposed. Finally, the complexity issues of manufacturing systems are addressed.

Process nets with resources for manufacturing modeling and their analysis

This paper presents a new class of Petri nets, called process nets with resources (PNRs), for modeling manufacturing systems where only parts can interact with resources, and resources alone cannot interact with one another. PNRs properly include S/sup 3/PR, augmented marked graphs, and some subclasses of resource control net (RCN) merged nets and ERCN merged nets. As a result, PNRs can model far more complex manufacturing process flows and resource sharing than these nets. To construct a PNR, we first build a process net to specify the process flow for each part type. A process net is a consistent, conservative, strongly connected, and live Petri net that satisfies three conditions, including strong reversibility. Then resource places denoting the availability of resource types are added to the process nets. We generalize strong reversibility for PNRs in order to check a sufficient condition for reversibility of PNRs. It is shown that strong reversibility and reversibility of a PNR depends on the siphons. Liveness of a PNR can be verified by checking the potential firing ability of all transitions of each isolated process net, which is, informally speaking, a process net with all resources allocated to it. A manufacturing example is given to show the applicability of PNRs.

Petri nets with k simultaneously enabled generally distributed timed transitions

Stochastic Petri nets have been used to analyze the performance and reliability of complex systems comprising concurrency and synchronization. Various extensions have been proposed in literature in order to broaden their field of application to an increasingly larger range of real situations. In this paper we extend the class of Markov regenerative stochastic Petri nets ∗ (MRSPNs ∗), removing the restriction that at most one generally distributed timed transition can be enabled in any marking. This new class of Petri nets, which we call concurrent generalized Petri nets (CGPNs), allows simultaneous enabling of immediate, exponentially and generally distributed timed transitions, under the hypothesis that the latter are all enabled at the same instant. The stochastic process underlying a CGPN is shown to be still an MRGP. We evaluate the kernel distribution of the underlying MRGP and define the steps required to generate it automatically. The methodology described is used to assess the behavior of a system in both steady-state and transient functioning conditions.

Two theoretical and practical aspects of knitting technique: invariants and a new class of Petri net

We present two aspects of knitting technique, the structural properties (especially the P- and T-invariants), and the synchronized choice net (a new class of Petri net), that are of both theoretical importance and practical uses to the verification of structural correctness of a Petri net or to detect the structural problem of a Petri net. This work first proves that the ordinary Petri nets synthesized with knitting technique are structurally bounded, consistent, conservative and safe (when each home place holds one token) using the well-known linear algebra approach. It also provides a procedure for finding P- and T-invariants for Petri net synthesized using the knitting technique. We present examples for P-invariants and show that we can synthesize Petri nets more general than the "asymmetric-choice nets". The algorithm for finding P-invariants of ordinary Petri nets is extended to find the P-invariants for a general Petri net synthesized with knitting technique and the arc-ratio rules. We present a new class of Petri nets, called synchronized choice nets, which are the largest set of Petri nets that can be covered by both T-components and P-components. An algorithm is proposed to find its T-components and the P-components, respectively. The complexity of this algorithm is also presented. The theory of synchronized choice nets has the potential to simplify that for free choice nets.

Higher-order Petri net models based on artificial neural networks

In this paper, the properties of higher-order neural networks are exploited in a new class of Petri nets, called higher-order Petri nets (HOPN). Using the similarities between neural networks and Petri nets this paper demonstrates how the McCullock-Pitts models and the higher-order neural networks can be represented by Petri nets. A 5-tuple HOPN is defined, a theorem on the relationship between the potential firability of the goal transition and the T-invariant (HOPN) is proved and discussed. The proposed HOPN can be applied to the polynomial clause subset of first-order predicate logic. A five-clause polynomial logic program example is also included to illustrate the theoretical results.

Petri net models of fuzzy neural networks

Artificial neural networks (ANN's) are highly parallel and distributed computational structures that can learn from experience and perform inferences. Petri nets, on the other hand, provide an effective modeling framework for distributed systems. The basic concepts of Petri net are utilized to develop ANN-like multilayered Petri net architectures of distributed intelligence having learning ability. A Petri net model of single neuron is presented. A two-layer Petri net model-neural Petri net (NPN)-that uses this neuron model as a building block is described. A new class of Petri nets called the fuzzy neural Petri net (FNPN) is defined. The FNPN can be used for representing a fuzzy knowledge base and for fuzzy reasoning. Some application examples for the two Petri net based models are given. >

Parameterized Petri nets and their application to planning and coordination in intelligent systems

A new class of Petri nets (PNs), called parameterized Petri Nets (PPNs), is proposed and applied for planning and coordination of intelligent systems. The PPN approach uses a hierarchical organization to deal with the complexity characteristic of net representations, through parameterization of transitions and the use of generalized or parameterized places in higher level nets. A unique useful characteristic of PPNs is that they can be used to generate a high level, abstract plan, even in the absence of complete information, which may be mapped into a specific plan at a lower level of the hierarchy. The PPN system model structural properties are verified based on the corresponding PN model. >

Modeling, controlling, and simulation of local area networks for flexible manufacturing systems using Petri nets

Flexible manufacturing systems (FMSs) are advanced manufacturing systems comprising machining cells, robots, a automated guided vehicles (AGVs) that function under the hierarchical control of computers. The flexibility of an FMS primarily imparted by integrating the functions of different system elements such as machining cells, robots, AGVs usig computers. In this paper, the role of local area networks (LANs) in FMSs is explicated. The contribution of this paper is twofold. First, the differences between the LANs in conventional systems (CLANs) to that of LANs in FMSs (FLANs) are explicated. Secondly, a new class of Petri nets (PNs) called augmented timed PNs are introduced as a modeling tool designing, simulating, analyzing, and finally implementing the LAN in FMS. A software package has been developed to simulate the Petri net models (PNMs). The software package developed aids system designers by simulating the PNM and generating certain performance criteria.

A petri net model for system design and refinement

This paper considers the use of Petri nets in the system design process. It proposes a new class of Petri nets called Information Flow Nets (IFNs) which are particularly suitable for performing refinement in the system design. We first define the class of IFNs and describe their behavior and some of their useful properties, such as clean termination. The notion of a “well-behaved IFN” is then defined and a top-down refinement technique is presented which allows us to construct arbitrary sized well-behaved IFNs. The conditions required for the refinement technique to preserve the properties of a well-behaved IFN are derived. We formally prove that a refined IFN N″, obtained by substituting a well-behaved IFN N' in a well-behaved IFN N, is itself well-behaved. The significance of such a technique is that it can be used, in a top-down approach to system design, to build systems that are automatically well-behaved. This in turn helps to avoid the difficulty of analyzing large and complex nets.