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Journal ArticleDOI

Inhibitor D-Timed Petri Nets And Pereormance Analysis Of Communication Protocols

01 Jan 1986-Infor (Taylor & Francis)-Vol. 24, Iss: 3, pp 231-249
TL;DR: It is shown that the behaviour of inhibitor free-choice Petri nets with deterministic firing times can be represented by probabilistic state graphs, and stationary descriptions can be obtained by standard techniques used for analysis of Markov chains.
Abstract: It is shown that the behaviour of inhibitor free-choice Petri nets with deterministic firing times can be represented by probabilistic state graphs. For bounded petri nets the corresponding state graphs are finite, and stationary descriptions can thus be obtained by standard techniques used for analysis of Markov chains. An immediate application of such a model is jseri^ormance analysis of systems of asynchronous concurrent processes and, in particular, communicatioii protocols. Places of Petri nets model queues of messages, transitions represent events in communication networks, inhibitor arcs are used to indicate priorities of simultaneous events, and probabilities associated with free-choice classes correspond to relative frequencies of random events. The alternating bit protocol is used as an illustration of analysis.
Citations
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Journal ArticleDOI
TL;DR: In this article, a flexible manufacturing cell (FMC) is defined and a set of specifications for the FMC is established, then a suitable model is developed to analyse and control the performance of FMC.
Abstract: A flexible manufacturing cell (FMC) is part of a flexible manufacturing system (FMS). In general, a FMC consists of versatile workstations and storage buffers connected by a versatile material handling system. Owing to its versatile configurations and material routeing alternatives, effective modelling and control of the FMC is a complex and challenging problem. In order to resolve these difficulties, it is desired to establish a set of specifications for the FMC, then to develop a suitable model to analyse and control the performance of the FMC. Since the cell control is distributed in nature, the cell controller specifications are established in terms of cell functionality, software, hardware, and environment aspects. On the basis of the cell controller specification, a coloured timed Petri net (CTPN) is developed for modelling and control of the FMC. A cell controller including CNC controller, robot controller will be developed on the basis of the CTPN model. Finally, a FMC example is given to illustra...

50 citations

Journal Article
TL;DR: Several classes of D–timed Petri nets are discussed to show a hierarchy of models with increasing “modelling power”, and many performance characteristics can be obtained using an approach similar to operational analysis.
Abstract: D–timed Petri nets are Petri nets with deterministic firing times assigned to transitions of a net. Several classes of D–timed are discussed in this paper to show a hierarchy of models with increasing “modelling power”. Conflict–free inhibitor nets are sufficient to model communication protocols with timeouts used to recover from lost and/or distorted messages but they introduce intermediate states which can be removed without any significant effect on the model’s behaviour. Extended nets with interrupt arcs (or generalized inhibitor arcs) eliminate all such states. Finally, enhanced nets with two classes of transitions, immediate and timed transitions, are introduced to further reduce the state space. For each class a discrete–time description is provided which represents the behaviour of a net by a homogeneous semi–Markov discrete process. Many performance characteristics can thus be obtained using an approach similar to operational analysis.

25 citations


Cites background or result from "Inhibitor D-Timed Petri Nets And Pe..."

  • ...Some further state reductions are discusses in [Zuberek 1986]....

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  • ...Some other results are given in [Zuberek 1986]....

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01 Jan 1988

18 citations


Cites background or methods from "Inhibitor D-Timed Petri Nets And Pe..."

  • ...Readers are referred to [69] and [103] for more discus­ sions....

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  • ...More recently, Zuberek extended and applied the model to do performance analysis of protocols [100], [103], [104], [105]....

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  • ...The techniques presented here resemble those proposed in [69] and [103]....

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Journal ArticleDOI
TL;DR: The method's theoretical foundation, which is based on analysing the embedded Markov chain of a derived decision reachability graph for the TPN model that is considered, is presented and the methodology is demonstrated by analysing two simple models.

11 citations

Proceedings ArticleDOI
01 Feb 1988
TL;DR: Because of scarcity of nets as well as corresponding systems of equilibrium equations, list structure representations are proposed, and a general procedure for generation of the state space is outlined to show the required processing of list structures.
Abstract: It is shown that the behavior of timed Petri nets with deterministic firing times (D-timed nets) and with exponentially distributed random firing times (M-timed nets) can be described within one uniform formalism. Moreover, for both classes of nets the state spaces are homogeneous semi-Markov chains, the stationary probabilities of states and many performance measures can thus be obtained by standard techniques developed for analysis of Markov processes. Because of scarcity of nets as well as corresponding systems of equilibrium equations, list structure representations are proposed, and a general procedure for generation of the state space is outlined to show the required processing of list structures.

7 citations

References
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Journal ArticleDOI
TL;DR: It is shown that GSPN are equivalent to continuous-time stochastic processes, and solution methods for the derivation of the steady state probability distribution are presented.
Abstract: Generalized stochastic Petri nets (GSPNs) are presented and are applied to the performance evaluation of multiprocessor systems. GSPNs are derived from standard Petri nets by partitioning the set of transitions into two subsets comprising timed and immediate transitions. An exponentially distributed random firing time is associated with each timed transition, whereas immediate transitions fire in zero time. It is shown that GSPN are equivalent to continuous-time stochastic processes, and solution methods for the derivation of the steady state probability distribution are presented. Examples of application of gspn models to the performance evaluation of multiprocessor systems show the usefulness and the effectiveness of this modeling tool. 15 references.

1,394 citations

Journal ArticleDOI
TL;DR: The time-Petri net (TPN) appears to be a suitable model for the study of practical recoverable processes and several practical communication protocols are formally designed and analyzed using this new model.
Abstract: A study is presented which permits the formal analysis and synthesis of recoverable computer communication protocols. This study is based on a formal representation of processes by a model of computation, the Petri nets (PN's). The PN model is generalized to include a representation of the possible failures, and then, the concept of "recoverability" is formally defined. A set of necessary and sufficient conditions which a process must satisfy in order to be recoverable is derived. In the PN model, the processes that satisfy these conditions are shown to have some practical limitations. A new model, the time-Petri net (TPN), is introduced to remove these limitations. This new model allows the introduction of constraints in the execution times of its part. As shown in this paper, the TPN appears to be a suitable model for the study of practical recoverable processes. Several practical communication protocols are formally designed and analyzed using this new model, and some interesting properties of these protocols are formally derived.

917 citations

Proceedings ArticleDOI
06 May 1980
TL;DR: It is shown that the behavior of a certain class of timed Petri nets can be represented by a finite labeled directed graph in which the labels describe times and probabilities of transitions between vertices of the graph.
Abstract: It is shown that the behavior of a certain class of timed Petri nets can be represented by a finite labeled directed graph in which the labels describe times and probabilities of transitions between vertices of the graph. Further analysis of such a graph can be done by techniques known for Markov chains. The method is applied to evaluation of some performance indices for two simple processor architectures. The timed Petri nets modeling the processors are shown and the resulting performance indices are compared. Some other architectures are discussed shortly.

204 citations

Journal ArticleDOI
Agerwala1
TL;DR: Today's modeling tools, appropriate for conventional sequential systems, will be inadequate for the complex concurrent systems of the 80's, and petri nets may offer a solution.
Abstract: Today's modeling tools, appropriate for conventional sequential systems, will be inadequate for the complex concurrent systems of the 80's. Petri nets may offer a solution.

174 citations