Showing papers on "Petri net published in 1985"

Petri Nets: An Introduction

Abstract: 1. Introductory Examples and Basic Definitions.- 1.1 Examples from Different Areas.- 1.2 Examples from Logic Circuits and Operating Systems.- 1.3 Non-Sequential Programs.- 1.4 An Example for Systems Analysis.- 1.5 Some Basic Definitions.- 1.6 Summary and Overview.- Exercises for Chapter 1.- 1. Condition/Event-Systems.- 2. Nets Consisting of Conditions and Events.- 2.1 Cases and Steps.- 2.2 Condition/Event-Systems.- 2.3 Cyclic and Live Systems.- 2.4 Equivalence.- 2.5 Contact-Free C/E-Systems.- 2.6 Case Graphs.- Exercises for Chapter 2.- 3. Processes of Condition/Event-Systems.- 3.1 Partially Ordered Sets.- 3.2 Occurrence Nets.- 3.3 Processes.- 3.4 The Composition of Processes.- 3.5 Processes and Case Graphs.- Exercises for Chapter 3.- 4. Properties of Systems.- 4.1 Synchronic Distances.- 4.2 Some Quantitative Properties of Synchronic Distances.- 4.3 Synchronic Distances in Sequential Systems.- 4.4 Synchronic Distances in Cyclic Systems.- 4.5 Facts.- Exercises for Chapter 4.- 2. Place/Transition-Nets.- 5. Nets Consisting of Places and Transitions.- 5.1 Place/Transition-Nets.- 5.2 Linear Algebraic Representation.- 5.3 Coverability Graphs.- 5.4 Decision Procedures for Some Net Properties.- 5.5 Liveness.- Exercises for Chapter 5.- 6. Net Invariants.- 6.1 S-Invariants.- 6.2 Nets Covered by S-Invariants.- 6.3 The Verification of System Properties Using S-Invariants.- 6.4 Properties of a Sender-Receiver Model.- 6.5 A Seat-Reservation System.- 6.6 The Verification of Facts in C/E-Systems by Means of S-Invariants.- 6.7 T-Invariants.- Exercises for Chapter 6.- 7. Liveness Criteria for Special Classes of Nets.- 7.1 Marked Nets, Deadlocks and Traps.- 7.2 Free Choice Nets.- 7.3 Marked Graphs.- Exercises for Chapter 7.- 3. Nets with Individual Tokens.- 8. Predicate/Event-Nets.- 8.1 An Introductory Example.- 8.2 Predicate/Event-Nets.- 8.3 An Organization Scheme for Distributed Databases.- 8.4 Facts in P/E-Nets.- 8.5 A Normal Form for P/E-Nets.- Exercises for Chapter 8.- 9. Relation Nets.- 9.1 Introductory Examples.- 9.2 Relation Nets.- 9.3 The Translation of P/E-Nets into Relation Nets.- 9.4 Calculation with Multirelations.- 9.5 A Matrix Representation for Relation Nets.- 9.6 S-Invariants for Relation Nets.- 9.7 An Example for Applying S-Invariants: The Verification of Facts.- 9.8 Relation Net Schemes.- Appendix. Mathematical Notions and Notation.- I. Sets.- II. Relations.- III. Mappings, Functions.- IV. Partial Orders.- VII. Vectors and Matrices.- Further Reading.- 1. Some Landmarks in the Development of Net Theory.- 2. Conferences on Petri Nets.- 3. Text Books.- 4. Bibliographies.- 5. References to Chapter 2.- 6. References to Chapter 3.- 7. References to Chapter 4.- 8. References to Chapter 5.- 9. References to Chapter 6.- 10. References to Chapter 7.- 11. References to Chapter 8.- 12. References to Chapter 9.- 13. Modifications and Generalizations of Place/Transition-Nets.- 14. Applications.- 15. Implementation and Automatic Analysis of Nets.- 16. Related System Models.

A Generalized Timed Petri Net Model for Performance Analysis

Abstract: We have developed a Generalized Timed Petri Net (GTPN) model for evaluating the performance of computer systems. Our model is a generalization of the TPN model proposed by Zuberek [1] and extended by Razouk and Phelps [2]. In this paper, we define the GTPN model and present how performance estimates are obtained from the GTPN. We demonstrate the use of our automated GTPN analysis techniques on the dining philosophers example. This example violates restrictions made in the earlier TPN models. Finally, we compare the GTPN to the stochastic Petri net (SPN) models. We show that the GTPN model has capabilities for modeling and analyzing parallel systems lacking in existing SPN models. The GTPN provides an efficient, easily used method of obtaining accurate performance estimates for models of computer systems which include both deterministic and geometric holding times.

Checking properties of nets using transformation

Abstract: In order to make easier the verification of parallel systems, we present a set of transformations which preserve several classical properties of nets: boundednes, safety, covering by S-invariants, proper termination, home states, unavoidable states, liveness and abstraction. These transformations are powerful enough to construct all other transformations defined before. We conclude with examples of possible utilisations.

A petri net approach to the modelling and analysis of flexible manufacturing systems

Abstract: In this paper we present an approach for modelling and analyzing flexible manufacturing systems (FMSs) using Petri nets. In this approach, we first build a Petri net model (PNM) of the given FMS in a bottom-up fashion and then analyze important qualitative aspects of FMS behaviour such as existence/absence of deadlocks and buffer overflows. The basis for our approach is a theorem we state and prove for computing the invariants of the union of a finite number of Petri nets when the invariants of the individual nets are known. We illustrate our approach using two typical manufacturing systems: an automated transfer line and a simple FMS.

Discrete Time Stochastic Petri Nets

Abstract: 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.

Hierarchical reduction method for analysis and decomposition of Petri nets

Abstract: A hierarchical reduction method for Petri nets is proposed. After a brief survey on the existing methods of Petri net reduction, concepts such as reducible subnet, degree of subnet, and macronode are defined. The subnets are partially ordered by the degree of subnet, and thus the reducible subnets can be reduced into the macronodes. A reduced net can be obtained without changing the properties (for example, liveness and boundedness). A sequence of reduction results in a hierarchy of reduced Petri nets that allow easy verification and hierarchical decomposition of the system.

An overview of evaluative models for flexible manufacturing systems

Abstract: Flexible manufacturing systems (FMSs) are a class of automated systems which can be used to improve productivity in discrete parts manufacturing. Due to the complexity of these systems, it is useful to have models that can aid in the design and operation of FMSs. We specifically differentiate here betweengenerative (or prescriptive) models, whichfind candidate decisions, andevaluative (or descriptive) models, whichevaluate a given set of decisions. We briefly cover, in a practical context, the pros and cons of these two classes of models. Then we focus on the latter class of models. Evaluative models for FMSs fall into five main classes, based on the technique used, namely: static allocation, queueing network theory, simulation, perturbation analysis, and Petri nets. Each of these approaches is briefly described, advantages and disadvantages mentioned, and references given to more detailed papers.

Some equivalence notions for concurrent systems. An overview

Abstract: String-equivalence, Behaviour-equivalence, Observation-equivalence, Exhibited-Behaviour-equivalence, Failure-equivalence and Testing equivalence are re-defined and discussed on Petri Net models of concurrent systems. Since the previous notions, being based on sequences of events, do not distinguish real concurrency from its sequential non-deterministic simulation, they are refined, in order to capture the concurrency degree of the systems, in terms of the subset languages approach. The equivalence notions introduced are then compared w.r.t. their strength.

Towards reachability trees for high-level Petri nets

Abstract: High-level Petri nets have been introduced as a powerful net type, by which it is possible to handle rather complex systems in a succinct and manageable way. The success of high-level Petri nets is undebatable when we speak about description, but there is still much work to be done to establish the necessary analysis methods. It has already been shown how to generalize the concept of place-invariants and transition-invariants, from place-transition-nets to high-level Petri nets. Our present paper constitutes the first steps towards a generalization of reachability trees, which is one of the other important analysis methods known for PT-nets. The central idea in our paper is the observation, that HL-nets often possess classes of equivalent markings. As an example an HL-net describing the five dining philo\-sophers has an equivalence-class consisting of those five markings in which exactly one philosopher is eating. These five markings are interchangeable, in the sense that their subtrees represent equivalent behaviours, where the only difference is the identity of the involved philosophers and forks. If we analyze one of these subtrees, we also understand the behaviour of the others. We describe an algorithm which constructs the HL-tree. The algorithm can easily be automated and we will soon start the work on an implementation. The constructed HL-trees turn out to be considerably smaller than the corresponding PT-trees (reachability trees for the equivalent PT-nets).

Petri net representation of decision models

Abstract: Models of decision-making organizations supported by command, control, and communication systems are represented using the Petri net formalism. A small set of primitives, defining the correspondence between decision models, signals, and functions and their Petri net counterparts, is proposed. A new decision signal-routing demultiplexer is added to the Petri net formalism to represent internal decision-making in the model. Using the above primitives, any decision-making structure can be modeled by a Petri net diagram. An array is introduced that describes the interactions between decision-makers, and an algorithm is presented for the calculation of delay when synchronous protocols are used.

The residue of vector sets with applications to decidability problems in Petri nets

Abstract: A set K of integer vectors is called right-closed, if for any elementmeK all vectors m′≧m are also contained in K. In such a case K is a semilinear set of vectors having a minimal generating set res(K), called the residue of K. A general method is given for computing the residue set of a right-closed set, provided it satisfies a certain decidability criterion. Various right-closed sets wich are important for analyzing, constructing, or controlling Petri nets are studied. One such set is the set CONTINUAL(T) of all such markings which have an infinite continuation using each transition infinitely many times. It is shown that the residue set of CONTINUAL(T) can be constructed effectively, solving an open problem of Schroff. The proof also solves problem 24 (iii) in the EATCS-Bulletin. The new methods developed in this paper can also be used to show that it is decidable, whether a signal net is prompt [23] and whether certain ω-languages of a Petri net are empty or not. It is shown, how the behaviour of a given Petri net can be controlled in a simple way in order to realize its maximal central subbehaviour, thereby solving a problem of Nivat and Arnold, or its maximal live subbehaviour as well. This latter approach is used to give a new solution for the bankers problem described by Dijkstra. Since the restriction imposed on a Petri net by a fact [11] can be formulated as a right closed set, our method also gives a new general approach for „implementations” of facts.

The Design of a Unified Package for the Solution of Stochastic Petri Net Models

Abstract: : This paper describes the philosophical differences between three current Stochastic Petri Net models in an attempt to merge the most important (and non-contradictory) aspects into one. It previews the design of a package for the solution of this unified model.

PSI: A Petri net based simulator for flexible manufacturing systems

Abstract: Petri nets and related specification tools such as the Grafcet are more and more used to express the operation constraints (i.e. the synchronisation mechanisms imposed by the mechanical part of the system), however no Petri net based discrete event simulator was available. ~o PSI, a prototype of such a package, has been realized [V~ in order to complement the comparison of the existing packages by an evaluation of such an approach.

Coordination technology and Petri nets

Abstract: This paper introduces a new approach to Petri net interpretation. With this approach, properly interpreted Petri nets yield new insights about the mechanics of human work organizations. Furthermore, these insights take technically useful form. In the last few years, the approach has led to the development of an industrial software technology — Coordination technology — for the construction of electronic work environments. The technological and scientific background are described enough to provide motivation for the new approach to Petri net interpretation.

Modelling scheduling problems with timed Petri nets

Abstract: In this paper, we show how to model with a timed Petri net, tasks, resources and constraints of a scheduling problem.

Combining Queueing Network and Generalized Stochastic Petri Net Models for the Analysis of a Software Blocking Phenomenon

Abstract: Much work has been done on the modeling of hardware resources; far fewer studies have been conducted on the impact of software systems on the underlying hardware. The authors address one such case in which blocking is present because of critical sections of code; this cannot be treated within the framework of product-form queuing network models. They show how a combination of generalized stochastic petri nets and queuing networks can easily model the situation under consideration. In addition, they show how a simple extension of this model can be applied to studying realistic systems with several domains.

Some equivalence notions for concurrent systems. An overview

Abstract: String-equivalence, Behaviour-equivalence, Observation-equivalence, Exhibited-Behaviour-equivalence, Failure-equivalence and Testing equivalence are re-defined and discussed on Petri Net models of concurrent systems. Since the previous notions, being based on sequences of events, do not distinguish real concurrency from its sequential non-deterministic simulation, they are refined, in order to capture the concurrency degree of the systems, in terms of the subset languages approach. The equivalence notions introduced are then compared w.r.t. their strength.

M-timed Petri nets, priorities, preemptions, and performance evaluation of Petri nets

Abstract: In M-timed Petri nets, firing times are exponentially distributed random variables associated with transitions of a net. Several classes of M-timed Petri nets are discussed in this paper to show increasing “modelling power” of different nets. Conflict-free nets can model M- and E k -type queueing systems. Free-choice nets can also represent H k -type systems. Systems with several classes of users and with service priorities assigned to user classes require nets with inhibitor arcs. Preemption of service can be represented by extended nets with escape (or generalized inhibitor) arcs. Finally, to provide flexible modelling of scheduling and decision strategies, enhanced Petri nets are introduced with two classes of transitions, immediate and timed ones, and with (exponentially distributed) firing times associated with the timed transitions. It is shown that the behavior of bounded M-timed Petri nets can be represented by finite “state” graphs which are finite-state continuous-time homogeneous Markov processes. Stationary probabilities of states can thus be obtained by standard techniques used for analysis of Markov chains, and then operational analysis can be applied for performance evaluation. Simple models of interactive systems are used as an illustration of modelling.

Analyzing safety and fault tolerance using time Petri nets

Abstract: The application of Time Petri net modelling and analysis techniques to safety-critical real-time systems is explored and procedures described which allow analysis of safety, recoverability, and faulttolerance. These procedures can be used to help determine software requirements, to guide the use of fault detection and recovery procedures, to determine conditions which require immediate mitigating action to prevent accidents, etc. Thus it is possible to establish important properties during the synthesis of the system and software design instead of using guesswork and costly a posteriori analysis.

CSP-programs with individual tokens

Abstract: We define a subclass of predicate/transition-nets and show how to translate CSP-programs into such nets. We consider a subset of CSP for which Hennessy, Li and Plotkin have given an operational semantics in [HLP]. We show that the firing sequences of our net translation correspond to this operational semantics. Additionally, we also give a non-interleaving semantics to CSP by considering unfoldings and processes of the net translation.