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Hybrid Petri nets
 European Control Conference Grenoble
, 1991
"... Abstract. Petri nets (PNs) are widely used to model discrete event dynamic systems (computer systems, manufacturing systems, communication systems, etc). Continuous Petri nets (in which the markings are real numbers and the transition firings are continuous) were defined more recently; such a PN ma ..."
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Cited by 131 (2 self)
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Abstract. Petri nets (PNs) are widely used to model discrete event dynamic systems (computer systems, manufacturing systems, communication systems, etc). Continuous Petri nets (in which the markings are real numbers and the transition firings are continuous) were defined more recently; such a PN may model a continuous system or approximate a discrete system. A hybrid Petri net can be obtained if one part is discrete and another part is continuous. This paper is basically a survey of the work of the authors ’ team on hybrid PNs (definition, properties, modeling). In addition, it contains new material such as the definition of extended hybrid PNs and several applications, explanations and comments about the timings in Petri nets, more on the conflict resolution in hybrid PNs, and connection between hybrid PNs and hybrid automata. The paper is illustrated by many examples.
Fluid stochastic Petri nets: Theory applications and solution techniques
 European Journal of Operational Research
, 1998
"... In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold uid rather than discrete tokens. We de ne a class of uid stochastic Petri nets in such awaythat the discrete and continuous portions may a ect each other. Following this de nition we provide equation ..."
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Cited by 67 (11 self)
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In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold uid rather than discrete tokens. We de ne a class of uid stochastic Petri nets in such awaythat the discrete and continuous portions may a ect each other. Following this de nition we provide equations for their transient and steadystate behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.
Discreteevent simulation of Fluid Stochastic Petri Nets
 IEEE Transactions on Software Engineering
, 1999
"... The purpose of this paper is to describe a method for simulation of recently introduced fluid stochastic Petri nets. Since such nets result in rather complex set of partial differential equations, numerical solution becomes a formidable task. Because of a mixed, discrete and continuous state space, ..."
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Cited by 36 (6 self)
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The purpose of this paper is to describe a method for simulation of recently introduced fluid stochastic Petri nets. Since such nets result in rather complex set of partial differential equations, numerical solution becomes a formidable task. Because of a mixed, discrete and continuous state space, simulative solution also poses some interesting challenges, which are addressed in the paper. 1
Firstorder hybrid Petri nets: A model for optimization and control
 IEEE Trans. on Robotics and Automation
, 2000
"... Abstract—We consider in this paper firstorder hybrid Petri Nets, a model that consists of continuous places holding fluid, discrete places containing a nonnegative integer number of tokens, and transitions, either discrete or continuous. We set up a linear algebraic formalism to study the firstor ..."
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Cited by 34 (2 self)
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Abstract—We consider in this paper firstorder hybrid Petri Nets, a model that consists of continuous places holding fluid, discrete places containing a nonnegative integer number of tokens, and transitions, either discrete or continuous. We set up a linear algebraic formalism to study the firstorder continuous behavior of this model and show how its control can be framed as a conflict resolution policy that aims at optimizing a given objective function. The use of linear algebra leads to sensitivity analysis that allows one to study of how changes in the structure of the model influence the optimal behavior. As an example of application, we show how the proposed formalism can be applied to flexible manufacturing systems with arbitrary layout and different classes of products. Index Terms—Flexible manufacturing systems, hybrid Petri nets, optimization, performance evaluation, sensitivity analysis.
Architecturebased software reliability analysis: Overview and limitations
 IEEE Transactions on Dependable and Secure Computing
"... Abstract—With the growing size and complexity of software applications, research in the area of architecturebased software reliability analysis has gained prominence. The purpose of this paper is to provide an overview of the existing research in this area, critically examine its limitations, and s ..."
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Cited by 29 (0 self)
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Abstract—With the growing size and complexity of software applications, research in the area of architecturebased software reliability analysis has gained prominence. The purpose of this paper is to provide an overview of the existing research in this area, critically examine its limitations, and suggest ways to address the identified limitations. Index Terms—Software reliability, software architecture. Ç 1
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.
On reachability in autonomous continuous Petri net systems
 24 th International Conference on Application and Theory of Petri Nets (ICATPN 2003). Volume 2679 of Lecture
, 2003
"... Abstract. Fluidification is a common relaxation technique used to deal in a more friendly way with large discrete event dynamic systems. In Petri nets, fluidification leads to continuous Petri nets systems in which the firing amounts are not restricted to be integers. For these systems reachability ..."
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Cited by 13 (4 self)
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Abstract. Fluidification is a common relaxation technique used to deal in a more friendly way with large discrete event dynamic systems. In Petri nets, fluidification leads to continuous Petri nets systems in which the firing amounts are not restricted to be integers. For these systems reachability can be interpreted in several ways. The concepts of reachability and limreachability were considered in [7]. They stand for those markings that can be reached with a finite and an infinite firing sequence respectively. This paper introduces a third concept, the δreachability. A marking is δreachable if the system can get arbitrarily close to it with a finite firing sequence. A full characterization, mainly based on the state equation, is provided for all three concepts for general nets. Under the condition that every transition is fireable at least once, it holds that the state equation does not have spurious solutions if δreachability is considered. Furthermore, the differences among the three concepts are in the border points of the spaces they define. For mutual limreachability and δreachability among markings, i.e., reversibility, a necessary and sufficient condition is provided in terms of liveness. 1
PetriNets And HybridState Markov Processes In A PowerHierarchy Of Dependability Models
, 2003
"... This paper extends the power hierarchy of dependability models developed by Malhotra and Trivedi (1994) and Muppala et al. (2000) to include Piecewise Deterministic Markov Processes (PDP) and PDPrelated Petri Nets. PDPs are ..."
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Cited by 12 (2 self)
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This paper extends the power hierarchy of dependability models developed by Malhotra and Trivedi (1994) and Muppala et al. (2000) to include Piecewise Deterministic Markov Processes (PDP) and PDPrelated Petri Nets. PDPs are
Hybrid HighLevel Nets
 In Proc. of the 1996 Winter Simulation Conference
, 1996
"... This paper presents a new methodology for modeling and simulation of hybrid systems which is called Hybrid Highlevel Nets (HYNETs). The new methodology integrates three established modeling approaches into one language. Highlevel Petri Nets represent the basic discrete framework, differential alge ..."
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Cited by 10 (0 self)
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This paper presents a new methodology for modeling and simulation of hybrid systems which is called Hybrid Highlevel Nets (HYNETs). The new methodology integrates three established modeling approaches into one language. Highlevel Petri Nets represent the basic discrete framework, differential algebraic equations (DAEs) are used to describe continuous systems behavior and objectoriented concepts improve the expressiveness and compactness of models. The paper explains basic ideas of the language and illustrates its usefulness with a small example. 1 INTRODUCTION Modeling and simulation of hybrid systems, i. e. systems consisting of a mixture of discrete and continuous components, is a research area that becomes more and more interesting. This is due to the fact that most systems of real world applications are not purely discrete nor purely continuous and often both parts influence each other. Consider for instance the small example in Figure 1: A level of liquid in a tank changes co...