Rewriting Logic as a Unifying Framework for Petri Nets

The paper is a partial synthesis of the work that a team within the Faculty of Managerial and Technological Engineering has in the field of modeling and simulation of systems with Petri nets. The paper deals with three issues. The first part is Modeling and simulation of manufacturing systems with timed Petri nets. The first part presents the way in which the performances of some manufacturing systems are evaluated using timed Petri nets. The first example is a manufacturing system specific to the textile industry. The system has three production lines. In this case, the modeling with timed Petri nets allows the analysis of the operation of the flow lines and highlights the bottleneck. Another modeled manufacturing system is specific to a series production, more precisely it refers to the manufacture of gas cookers within a company from Oradea. The model with Petri nets also describes the supply sequences of the stocks of parts and subassemblies. The next modeled system is an automated manufacturing system for the packaging of detergents. The complexity of the Detergent Packing System and the high level of automation, require the use of efficient modeling and simulation methods to verify the validity of the solutions adopted. In this chapter is present the model of a robotic welding cell. The second part of the paper, the transition from timed Petri nets to hierarchical colored Petri nets, shows how Petri nets were developed for a robotic cell for metallographic analysis. The third part is dedicated to modeling with colored Petri nets timed with complex colors of the flexible manufacturing cell A007 within the Department of Industrial Engineering.

It had been shown that Merlin's Time Petri Nets are a special case of Time Stream Petri Nets. In this paper, we show that there does not exist a time equivalence between both models. We extend first this result to the non equivalence of Timed Automata and Time Petri Nets and second to the non equivalence of Timed Link Petri Net and Timed Transition Petri Net.

Petri net (PN) is a classical tool for modeling, simulation, and analysis. With the emergence of distributed manufacturing system (DMS), PN has been evolved into different forms such as colored PN (CPN) and timed PN (TPN). To fulfill the practical requirements, CPN has been extended to a larger and more complex model. Meanwhile, DMS becomes an important issue for industry, and how to model a complex manufacturing network for better throughput needs further investigation. A simple single type of PN only cannot fulfill all contemporary requirements at the same time. This paper proposes a new concept for a new PN-hierarchical timed CPN (HTCPN), which can be a powerful tool for modeling, simulation, and analysis for current large complex distributed manufacturing system. This paper presents a general structure of DMS and uses HTCPN to model the manufacturing system as discrete event with dynamic behavior. The proposed approach shows superiority on modeling large complex manufacturing system as it represents the material flow and transitions clearly and provides overview and detailed description for DMS.

Local time membrane systems and time Petri nets

With the aim of solving the problems of the Petri nets to the place/transition nets automatic conversion and realization of Petri nets parallel control and running, the algorithm is proposed to transform Color Petri net systems transform into P/T nets. The algebraic model of colored Petri nets and P/T nets, and its intrinsic mechanism is analyzed, the process and theory verification of the colored Petri nets into P/T nets are given. The colored Petri nets into P/T network algorithm is proposed, through the network model of formal, colored Petri nets correlation matrix pretreatment. Experimental results show that it is an effective method to solve Color Petri Net systems transform into P/T nets, lay the foundation for various senior Petri nets system transformation into P/T nets and achieve the parallelism and simulation of running.

Specification and properties of a cache coherence protocol model.- GAMERU: A language for the analysis and design of human communication pragmatics within organizational systems.- Recent results on the complexity of problems related to Petri nets.- Algebraic structure of flows of a regular coloured net.- On equivalent execution semantics of concurrent systems.- Mathematical methods for calculating invariants in Petri nets.- On Petri nets with deterministic and exponentially distributed firing times.- An accurate performance model of CSMA/CD bus LAN.- Petri net models for the ?-calculus.- Fair processes.- Operational Petri net semantics for CCSP.- Infinitary languages of Petri nets and logical sentences.- A strong part of concurrency.- Concurrency and continuity.- Parallel systems specifications with coloured Petri nets and algebraic specifications.- Bibliography of Petri nets.

Performance analysis can be carried out in several ways, especially in case of Markovian models. In order to interpret high level of abstraction, we often use modeling tools like timed Petri nets (TPNs). Although some subclasses of TPNs (e.g. stochastic Petri nets (SPNs) [17, 19]) can be handled analytically, a general timed Petri net is hard to evaluate via numerical analysis. However, the simulation of SPNs or deterministic and stochastic Petri nets (DSPNs) [16] are supported by many known tools (see, e.g. [3, 20]), it is hard to find a simulation tool for timed Petri nets with generally distributed (i.e., particular but arbitrarily chosen) firing times. In this paper, we present TiPeNeSS (Timed Petri Net Simulator Software) which supports the simulation of timed Petri nets containing transitions with generally distributed firing delays. The input of the software (the Petri net and the parameters) is defined in an XML file, what allows us to generate results in batch mode. Besides, we describe a case study in which we optimize the frequency of the regular maintenance in a manufacturing process.

The context of our work is the complex systems simulation. Complex systems modelling and simulation require to take into account the interactions between the different components. For instance, an airport ground traffic simulation requires to model the planes with the pilots, the control tower, the

Behaviour Equivalent Max-Plus Automata for a Class of Timed Petri Nets

In this paper, we propose the new method for the parallel system design based on expanded the logical coloured Petri net (LCPN). An LCPN is an extended Petri net that solves the problem of system description in previously proposed place/transition nets and coloured Petri nets. This extension of Petri nets is suitable for designing complex control systems and for discussing methods of evaluating such systems realistically. In order to study the behaviour of the server system modelled with this net we simulated a Java program. This program confirmed that this extended Petri net is an effective tool for modelling the parallel system.

A correct and rapid inference is required for practical use of expert system for fault section estimation in power systems. This paper proposes a new model-based expert system for fault section estimation using colored and timed Petri nets. The Petri nets simplify the inference procedure greatly because it can represent the causalities among faults of power system components, protective actions of relays and circuit breakers. They can also represent the operating states of these protective devices explicitly, or, more precisely, whether a relay has been actuated correctly or falsely, etc. In addition, time sequence information on actuated relays and tripped circuit breakers can be handled by using the colored and timed Petri nets. Therefore, the operating states of relays and circuit breakers can be inferred more correctly. Petri nets are suited for parallel processing so well that there is a possibility of reducing the inference time considerably. In the proposed system, the inference is executed by setting the initial states in the Petri nets using the information on the actuated relays and the tripped circuit breakers and then operating the Petri nets. There have been several test cases which used a prototype system on the Macintosh computer employing Object Common Lisp, and good results have been obtained.

The recently introduced method, which was called ldquostretching,rdquo is extended to timed Petri nets which may have both controllable and uncontrollable transitions. Using this method, a new Petri net, called ldquostretched Petri net,rdquo which has only unit firing durations, is obtained to represent a timed-transition Petri net. Using this net, the state of the original timed Petri net can be represented easily. This representation also makes it easy to design a supervisory controller for a timed Petri net for any purpose. In this paper, supervisory controller design to avoid deadlock is considered in particular. Using this method, a controller is first designed for the stretched Petri net. Then, using this controller, a controller for the original timed Petri net is obtained. Algorithms to construct the reachability sets of the stretched and original timed Petri nets, as well as algorithms to obtain the controller for the original timed Petri net are presented. These algorithms are implemented using Matlab. Examples are also presented to illustrate the introduced approach.

Timed Petri nets can be used to model and analyse scheduling problems. To support the modelling of scheduling problems, we provide a method to map tasks, resources and constraints onto a timed Petri net. By mapping scheduling problems onto Petri nets, we are able to use standard Petri net theory. In this paper we will show that we can use Petri net based tools and techniques to find conflicting and redundant precedences, upper- and lower-bounds for the makespan, etc. This is illustrated by a Petri net based analysis of the notorious 10×10 problem due to Fisher & Thompson (1963)

Basic graph models of processes, such as Petri nets, have usually omitted the concept of time as a parameter. Time has been added to the Petri net model in two ways. The timed Petri net (TPN) uses a fixed number of discrete time intervals. The stochastic Petri net (SPN) uses an exponentially distributed random variable. In this paper, a discrete time stochastic Petri model is described. These discrete time SPN's fill the gap between TPN and normal SPN. However, the use of discrete time complicates the SPN model in that more than one transition may fire at a time step. Finally, an example of a live and bounded Petri net which has nonempty, disjoint, recurrent subsets of markings is given.

Petri Nets provide a graphical notation for modeling systems and performing analysis. Colored Petri Nets (CPNs) combine the strengths of ordinary Petri Nets with a high level programming language, making them more suitable for modeling large systems. A CPN model is an executable representation of a system that can be analyzed through simulation. CPN models are built using CPN Tools, a graphical software tool and interface used to create, edit, simulate, and analyze models. This tutorial is meant to introduce the reader to the vocabulary and constructs of CPNs and illustrate the use of CPN Tools in creating and simulating models by means of a familiar, simple example. In particular, we show how to create a CPN model of the call center example presented by White and Ingalls in their tutorial Introduction to Simulation.