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GreatSPN 1.7: GRaphical Editor and Analyzer for Timed and Stochastic Petri Nets
, 1995
"... This paper describes the GreatSPN 1.7 package for the modeling, validation, and performance evaluation of distributed systems using Generalized Stochastic Petri Nets and their colored extension. The tool provides a friendly framework to experiment with timed Petri net based modeling techniques. It i ..."
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Cited by 95 (17 self)
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This paper describes the GreatSPN 1.7 package for the modeling, validation, and performance evaluation of distributed systems using Generalized Stochastic Petri Nets and their colored extension. The tool provides a friendly framework to experiment with timed Petri net based modeling techniques. It implements efficient analysis algorithms to allow its use on "real" applications, not only toy examples. Developed in a University for non profit purposes, it is distributed free of charge to other universities for educational and research purposes. An overview of the complete architecture of the package is given together with examples of its application. Then the various analysis and simulation modules are described. 1 Introduction GreatSPN 1.7 is a tool for the modeling and analysis of systems, based on the Petri net formalism. In this paper we first briefly describe the historical evolution of the package, which explains the reasons for some implementation choices as well as the intended p...
Numerical Analysis of Superposed GSPNs
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 1996
"... The numerical analysis of various modeling formalisms profits from a structured representation for the generator matrix Q of the underlying continuous time Markov chain, where Q is described by a sum of tensor (Kronecker) products of much smaller matrices. In this paper we describe such a representa ..."
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Cited by 68 (10 self)
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The numerical analysis of various modeling formalisms profits from a structured representation for the generator matrix Q of the underlying continuous time Markov chain, where Q is described by a sum of tensor (Kronecker) products of much smaller matrices. In this paper we describe such a representation for the class of superposed generalized stochastic Petri nets (SGSPNs), which is less restrictive than in previous work. Furthermore a new iterative analysis algorithm is proposed. It pays special attention to a memory efficient representation of iteration vectors as well as to a memory efficient structured representation of Q. In consequence the new algorithm is able to solve models which have state spaces with several millions of states, where other exact numerical methods become impracticable on a common workstation.
Generalized stochastic Petri nets: A definition at the net level and its implications
 IEEE Transactions on Software Engineering
, 1993
"... Abstmct The original proposals of several stochastic Petri net modeling techniques and of generalized stochastic Petri nets (GSPN) in particular were based mainly on the characteristics of their underlying stochastic processes. This led to the use of GSPN only as a shortened notation for the descri ..."
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Cited by 62 (9 self)
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Abstmct The original proposals of several stochastic Petri net modeling techniques and of generalized stochastic Petri nets (GSPN) in particular were based mainly on the characteristics of their underlying stochastic processes. This led to the use of GSPN only as a shortened notation for the description of stochastic models. Although already quite useful in practice, this approach did not fully exploit the benefits of a Petri net description; in particular, it did not use any of the results of classical net theory. The integration of qualitative net theory results, together with the probabilistic analysis approach, requires a deep structural foundation of the GSPN definition. In this paper, the class of Petri nets obtained by eliminating timing from GSPN models while preserving the qualitative behavior is identified. Structural results for those nets are also derived, thus obtaining the first structural analysis of Petri nets with priority and inhibitor arcs. A revision of the GSPN definition based on the structural properties of the models is then presented. The main advantage is that for a (wide) class of nets, the definition of firing probabilities of conflicting immediate transitions does not require the information on reachable markings (which was, instead, necessary with the original definition). Identification of the class of models for which the netlevel specification is possible is also based on the structural analysis results. The new procedure for the model specification is illustrated by means of an example, which shows the usefulness of the new approach. A net level specification of the model associated with efficient structural analysis techniques can have a substantial impact on model analysis as well. Index TermsConflicts and concurrency, Markovian models, performance modeling, probabilistic specification, stochastic Petri nets, structural Petri net analysis, timed and immediate transitions, transition priorities. I.
Efficient computation of timebounded reachability probabilities in uniform continuoustime Markov decision processes
, 2004
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Stochastic wellformed colored nets and symmetric modeling applications
 IEEE Trans. on Comput
, 1993
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A Comparison of Performance Evaluation Process Algebra and Generalized Stochastic Petri Nets
 In Proc. 6th International Workshop on Petri Nets and Performance Models
, 1995
"... Generalized Stochastic Petri Nets (GSPN)and Performance Evaluation Process Algebra (PEPA) can both be used to study qualitative and quantitative behaviour of systems in a single environment. This paper presents a comparison of the two formalisms in terms of the facilities that they provide to the mo ..."
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Cited by 34 (8 self)
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Generalized Stochastic Petri Nets (GSPN)and Performance Evaluation Process Algebra (PEPA) can both be used to study qualitative and quantitative behaviour of systems in a single environment. This paper presents a comparison of the two formalisms in terms of the facilities that they provide to the modeller, considering both the definition and the analysis of the performance model. Our goal is to provide a better understanding of both formalisms, and to prepare a fertile ground for exchanging ideas and techniques between the two. To illustrate similarities and differences, we make the different issues more concrete by means of an example modelling resource contention. 1 Introduction In this paper we present a comparison of two formalisms which may be used to develop performance models as continuous time Markov chains (CTMC). Generalized stochastic Petri nets (GSPN) is a wellestablished high level modelling paradigm which has been widely applied in performance analysis. In contrast, Per...
DISCRETETIME MARKOVIAN STOCHASTIC PETRI NETS
, 1995
"... We revisit and extend the original definition of discretetime stochastic Petri nets, by allowing the firing times to have a “defective discrete phase distribution”. We show that this formalism still corresponds to an underlying discretetime Markov chain. The structure of the state for this process ..."
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Cited by 27 (8 self)
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We revisit and extend the original definition of discretetime stochastic Petri nets, by allowing the firing times to have a “defective discrete phase distribution”. We show that this formalism still corresponds to an underlying discretetime Markov chain. The structure of the state for this process describes both the marking of the Petri net and the phase of the firing time for of each transition, resulting in a large state space. We then modify the wellknown power method to perform a transient analysis even when the state space is infinite, subject to the condition that only a finite number of states can be reached in a finite amount of time. Since the memory requirements might still be excessive, we suggest a bounding technique based on truncation.
Recent Developments in NonMarkovian Stochastic Petri Nets
, 1998
"... Analytical modeling plays a crucial role in the analysis and design of computer systems. Stochastic Petri Nets represent a powerful paradigm, widely used for such modeling in the context of dependability, performance and performability. Many structural and stochastic extensions have been proposed in ..."
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Cited by 22 (4 self)
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Analytical modeling plays a crucial role in the analysis and design of computer systems. Stochastic Petri Nets represent a powerful paradigm, widely used for such modeling in the context of dependability, performance and performability. Many structural and stochastic extensions have been proposed in recent years to increase their modeling power, or their capability to handle large systems. This paper reviews recent developments by providing the theoretical background and the possible areas of application. Markovian Petri nets are first considered together with very well established extensions known as Generalized Stochastic Petri nets and Stochastic Reward Nets. Key ideas for coping with large state spaces are then discussed. The challenging area of nonMarkovian Petri nets is considered, and the related analysis techniques are surveyed together with the detailed elaboration of an example. Finally new models based on Continuous or Fluid Stochastic Petri Nets are briefly discussed.
Performance Analysis of Stochastic Timed Petri Nets using Linear Programming Approach
 IEEE Transactions on Software Engineering
, 1995
"... Stochastic timed Petri nets are a useful tool in performance analysis of concurrent systems such as parallel computers, communication networks and flexible manufacturing systems. In general, performance measures of stochastic timed Petri nets are difficult to obtain for problems of practical sizes. ..."
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Cited by 16 (0 self)
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Stochastic timed Petri nets are a useful tool in performance analysis of concurrent systems such as parallel computers, communication networks and flexible manufacturing systems. In general, performance measures of stochastic timed Petri nets are difficult to obtain for problems of practical sizes. In this paper, we provide a method to compute efficiently upper and lower bounds for the throughputs and mean token numbers in general Markovian timed Petri nets. Our approach is based on uniformization technique and linear programming.