Petri Nets and Timed Petri Nets in Modeling and Analysis of Concurrent Systems – An Overview

Petri nets are formal models of systems which exhibit concurrent activities. Communication networks, multiprocessor systems, manufacturing systems and dis- tributed databases are simple examples of such systems. As formal models, Petri nets are bipartite directed graphs, in which the two types of vertices represent, in a very gen- eral sense, conditions and events. An event can occur only when all conditions associated with it (represented by arcs directed to the event) are satisfied. An occurrence of an event usually satisfies some other conditions, indicated by arcs directed from the event. So, an occurrence of one event causes some other event to occur, and so on. In order to study performance aspects of systems modeled by Petri nets, the durations of modeled activities must also be taken into account. This can be done in different ways, resulting in different types of temporal nets. In timed Petri nets, occurrence times are associated with events, and the events occur in real–time (as opposed to instantaneous oc- currences in other models). For timed nets with constant or exponentially distributed occurrence times, the state graph of a net is a Markov chain, in which the stationary prob- abilities of states can be determined by standard methods. These stationary probabilities are used for the derivation of many performance characteristics of the model. Analysis of net models based on exhaustive generation of all possible states is called reachability analysis; it provides detailed characterization of model’s behavior, but often re- quires generation and analysis of huge state spaces (in some models the number of states increases exponentially with some model parameters, which is known as “state explo- sion”). Structural analysis determines the properties of net models on the basis of connections among model elements; structural analysis is usually much simpler than reachability analysis, but can be applied only to models satisfying certain properties. If neither reachability nor structural analysis is feasible, discrete–event simulation of timed nets can be used to study the properties of net models. This paper overviews basic concepts of Petri nets, intro- duces timed Petri nets, and provides brief summaries of sev- eral case studies of performance analysis which are discussed in greater detail in other publications of the author

PETRI NETS AND TIMED PETRI NETS BASIC CONCEPTS AND PROPERTIES

Petri nets are formal models of systems which exhibit concurrent activities. Communication networks, multiprocessor systems, manufacturing systems and distributed databases are simple examples of such systems. As formal models, Petri nets are bipartite directed graphs, in which the two types of vertices represent, in a very general sense, conditions and events. An event can occur only when all conditions associated with it (represented by arcs directed to the event) are satisfied. An occurrence of an event usually satisfies some other conditions, indicated by arcs directed from the event. So, an occurrence of one event causes some other event to occur, and so on. In order to study performance aspects of systems modeled by Petri nets, the durations of modeled activities must also be taken into account. This can be done in different ways, resulting in different types of temporal nets. In timed Petri nets, occurrence times are associated with events, and the events occur in real-time (as opposed to instantaneous occurrences in other models). For timed nets with constant or exponentially distributed occurrence times, the state graph of a net is a Markov chain, in which the stationary probabilities of states can be determined by known methods. These stationary probabilities can be used for the derivation of many performance characteristics of the model. Analysis of net models based on exhaustive generation of all possible states is called reachability analysis; it provides detailed characterization of model's behavior, but often requires analysis of huge state spaces (the number of states can increase exponentially with some model parameters which is known as "state explosion"). Structural analysis determines the properties of net models on the basis of connections among model elements; structural analysis is usually much simpler than reachability analysis, but can be applied only to models satisfying certain properties. If neither reachability nor structural analysis is feasible, discrete event simulation of timed nets can be used to study the properties of net models. This report introduces basic concepts of Petri nets and timed Petri nets, discusses some of their properties, and presents several straightforward applications. It also includes a comprehensive list of references

A petri-net based methodology for modeling, simulation, and control of flexible manufacturing systems

Global competition has made it necessary for manufacturers to introduce such advanced technologies as flexible and agile manufacturing, intelligent automation, and computer-integrated manufacturing. However, the application extent of these technologies varies from industry to industry and has met various degrees of success. One critical barrier leading to successful implementation of advanced manufacturing systems is the ever-increasing complexity in their modeling, analysis, simulation, and control. The purpose of this work is to introduce a set of Petri net-based tools and methods to address a variety of problems associated with the design and implementation of flexible manufacturing systems (FMSs). More specifically, this work proposes Petri nets as an integrated tool for modeling, simulation, and control of flexible manufacturing systems (FMSs). The contributions of this work are multifold. First, it demonstrates a new application of PNs for simulation by evaluating the performance of pull and push diagrams in manufacturing systems. Second, it introduces a class of PNs, Augmented-timed Petri nets (ATPNs) in order to increase the power of PNs to simulate and control flexible systems with breakdowns. Third, it proposes a new class of PNs called Realtime Petri nets (RTPNs) for discrete event control of FMS s. The detailed comparison between RTPNs and traditional discrete event methods such as ladder logic diagrams is presented to answer the basic question \u27Why is a PN better tool than ladder logic diagram?\u27 and to justify the PN method. Also, a conversion procedure that automatically generates PN models from a given class of logic control specifications is presented. Finally, a methodology that uses PNs for the development of object-oriented control software is proposed. The present work extends the PN state-of-the-art in two ways. First, it offers a wide scope for engineers and managers who are responsible for the design and the implementation of modem manufacturing systems to evaluate Petri nets for applications in their work. Second, it further develops Petri net-based methods for discrete event control of manufacturing systems

The use of Petri nets for modeling pipelined processors

This paper discusses the use of Petri Nets for modeling and analyzing pipelined processors. Petri Nets are particularly well-suited to modeling the synchronization, buffering, resource contention and delicate timing so common in pipelined processors. Tools for simulating, animating and analyzing the behavior of the models are described. The usefulness of the tools and the analysis methods they support in evaluating the performance and analyzing the detailed timing of pipelined microprocessors is illustrated through an example

Parallel Graph Transformation for Model Simulation applied to Timed Transition Petri Nets

Proceedings of the Workshop on Graph Transformation and Visual Modelling Techniques (GT-VMT 2004)This work discusses the use of parallel graph transformation systems for (multi-formalism) modeling and simulation and their implementation in the meta-modeling tool AToM3. As an example, a simulator for Timed Transition Petri Nets (TTPN) is modeled using parallel graph transformation.This work has been partially sponsored by the SEGRAVIS network and the Spanish Ministry of Science and Technology (TIC2002-01948)

Model based fault diagnosis for hybrid systems : application on chemical processes

The complexity and the size of the industrial chemical processes induce the monitoring of a growing number of process variables. Their knowledge is generally based on the measurements of system variables and on the physico-chemical models of the process. Nevertheless, this information is imprecise because of process and measurement noise. So the research ways aim at developing new and more powerful techniques for the detection of process fault. In this work, we present a method for the fault detection based on the comparison between the real system and the reference model evolution generated by the extended Kalman filter. The reference model is simulated by the dynamic hybrid simulator, PrODHyS. It is a general object-oriented environment which provides common and reusable components designed for the development and the management of dynamic simulation of industrial systems. The use of this method is illustrated through a didactic example relating to the field of Chemical Process System Engineering

A Simulation Model Articulation of the REA Ontology

This paper demonstrates how the REA enterprise ontology can be used to construct simulation models for business processes, value chains and collaboration spaces in supply chains. These models support various high-level and operational management simulation applications, e.g. the analysis of enterprise sustainability and day-to-day planning. First, the basic constructs of the REA ontology and the ExSpect modelling language for simulation are introduced. Second, collaboration space, value chain and business process models and their conceptual dependencies are shown, using the ExSpect language. Third, an exhibit demonstrates the use of value chain models in predicting the financial performance of an enterprise

Integration of an object formalism within a hybrid dynamic simulation environment

PrODHyS is a general object-oriented environment which provides common and reusable components designed for the development and the management of dynamic simulation of systems engineering. Its major characteristic is its ability to simulate processes described by a hybrid model. In this framework, this paper focuses on the "Object Differential Petri Net" (ODPN) formalism integrated within PrODHyS. The use of this formalism is illustrated through a didactic example relating to the field of Chemical Process System Engineering (PSE)

Integration of a failure monitoring within a hybrid dynamic simulation environment

The complexity and the size of the industrial chemical processes induce the monitoring of a growing number of process variables. Their knowledge is generally based on the measurements of system variables and on the physico-chemical models of the process. Nevertheless this information is imprecise because of process and measurement noise. So the research ways aim at developing new and more powerful techniques for the detection of process fault. In this work, we present a method for the fault detection based on the comparison between the real system and the reference model evolution generated by the extended Kalman filter. The reference model is simulated by the dynamic hybrid simulator, PrODHyS. It is a general object-oriented environment which provides common and reusable components designed for the development and the management of dynamic simulation of industrial systems. The use of this method is illustrated through a didactic example relating to the field of Chemical Process System Engineering