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25
SPNP: Stochastic Petri Net Package
, 1989
"... We present SPNP, a powerful GSPN package developed at Duke University. SPNP allows the modeling of complex system behaviors. Advanced constructs are available, such as marking dependent arc multiplicities, enabling functions, arrays of places or transitions, and subnets; in addition, the full expres ..."
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Cited by 198 (38 self)
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We present SPNP, a powerful GSPN package developed at Duke University. SPNP allows the modeling of complex system behaviors. Advanced constructs are available, such as marking dependent arc multiplicities, enabling functions, arrays of places or transitions, and subnets; in addition, the full expressive power of the C programming language is available to increase the flexibility of the net description.
A Characterization of the Stochastic Process Underlying a Stochastic Petri Net
 IEEE Transactions on Software Engineering
, 1994
"... Petri net ..."
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.
Branching cells as local states for event structures and nets: Probabilistic applications
 In Proceedings of 8th FoSSaCS, volume 3441 of LNCS
, 2005
"... Abstract. We study the concept of choice for true concurrency models such as prime event structures and safe Petri nets. We propose a dynamic variation of the notion of cluster previously introduced for nets. This new object is defined for event structures, it is called a branching cell. Our aim is ..."
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Cited by 15 (9 self)
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Abstract. We study the concept of choice for true concurrency models such as prime event structures and safe Petri nets. We propose a dynamic variation of the notion of cluster previously introduced for nets. This new object is defined for event structures, it is called a branching cell. Our aim is to bring an interpretation of branching cells as a right notion of “local state”, for concurrent systems. We illustrate the above claim through applications to probabilistic concurrent models. In this respect, our results extends in part previous work by VaraccaVölzerWinskel on probabilistic confusion free event structures. We propose a construction for probabilities over socalled locally finite event structures that makes concurrent processes probabilistically independent—simply attach a dice to each branching cell; dices attached to concurrent branching cells are thrown independently. Furthermore, we provide a true concurrency generalization of Markov chains, called Markov nets. Unlike in existing variants of stochastic Petri nets, our approach randomizes Mazurkiewicz traces, not firing sequences. We show in this context the Law of Large Numbers (LLN), which confirms that branching cells deserve the status of local state. Our study was motivated by the stochastic modeling of fault propagation and alarm correlation in telecommunications networks and services. It provides the foundations for probabilistic diagnosis, as well as the statistical distributed learning of such models. 1
Stochastic Process Semantics for Dynamical Grammar Syntax
 UCI ICS TR
, 2005
"... We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to semantics given in terms of a ring of operators, so that grammatic ..."
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Cited by 13 (8 self)
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We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to semantics given in terms of a ring of operators, so that grammatical composition corresponds to operator addition or multiplication. The operators are generators for the timeevolution of stochastic processes. Within this modeling framework one can express data clustering models, logic programs, ordinary and stochastic differential equations, graph grammars, and stochastic chemical reaction kinetics. This mathematical formulation connects these apparently distant fields to one another and to mathematical methods from quantum field theory and operator algebra. 1
Steady State Solution of MRSPN with Mixed Preemption Policies
 In International Computer Performance and Dependability Symposium  IPDS96
, 1996
"... Markov Regenerative Stochastic Petri Nets (MRSPN) have been recently recognized as a valuable tool to model systems with nonexponential timed activities. The usual assumption in the implementation of such models is that at most a single nonexponential transition, with associated enabling memory ..."
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Cited by 8 (4 self)
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Markov Regenerative Stochastic Petri Nets (MRSPN) have been recently recognized as a valuable tool to model systems with nonexponential timed activities. The usual assumption in the implementation of such models is that at most a single nonexponential transition, with associated enabling memory policy, can be enabled in each marking. More recently, new memory policies have been studied in order to represent more complex and effective preemption mechanisms in real systems. Closedform solutions in the Laplace transform domain have been provided also in this case. This paper concentrates on the steadystate analysis of MRSPN and provides an unified analytical approach to include mixed memory policies into a single model. A numerical example concludes the paper. Key words: Stochastic Petri Nets, Markov regenerative processes, preemptive policies, steadystate analysis. 1 Introduction There is an increasing interest in the implementation of tools for performance/dependabilit...
Dynamical systems and stochastic programming: To ordinary differential equations and
 Biology
"... Abstract. In this paper we focus on the relation between models of biological systems consisting of ordinary differential equations (ODE) and models written in a stochastic and concurrent paradigm (sCCP stochastic Concurrent Constraint Programming). In particular, we define a method to associate a s ..."
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Cited by 8 (4 self)
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Abstract. In this paper we focus on the relation between models of biological systems consisting of ordinary differential equations (ODE) and models written in a stochastic and concurrent paradigm (sCCP stochastic Concurrent Constraint Programming). In particular, we define a method to associate a set of ODE’s to an sCCP program and a method converting ODE’s into sCCP programs. Then we study the properties of these two translations. Specifically, we show that the mapping from sCCP to ODE’s preserves rate semantics for the class of biochemical models (i.e. chemical kinetics is maintained) and we investigate the invertibility properties of the two mappings. Finally, we concentrate on the question of behavioral preservation, i.e if the models obtained applying the mappings have the same dynamics. We give a convergence theorem in the direction from ODE’s to sCCP and we provide several wellknown examples in which this property fails in the inverse direction, discussing them in detail. 1
Trueconcurrency Probabilistic Models: Markov Nets and a Law of Large Numbers
, 2005
"... We introduce the model of Markov nets, a probabilistic extension of safe Petri nets under the trueconcurrency semantics. This model builds upon our previous work on probabilistic event structures. We use the notion of branching cell for event structures and show that the latter provides the adequa ..."
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Cited by 6 (0 self)
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We introduce the model of Markov nets, a probabilistic extension of safe Petri nets under the trueconcurrency semantics. This model builds upon our previous work on probabilistic event structures. We use the notion of branching cell for event structures and show that the latter provides the adequate notion of local state, for nets. We prove a Law of Large Numbers (LLN) for Markov nets—this constitutes the main contribution of the paper. This LLN allows characterizing in a quantitative way the asymptotic behavior of Markov nets.
and E.Glavas. “Performance evaluation of twopriority network schema for singlebuffered Delta Network
 Proceedings of the 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'07), 2007
"... In this paper a novel twopriority network schema is presented, and exemplified through its application on singlebuffered Delta Networks in packet switching environments. Network operations considered include conflict resolution and communication strategies. The proposed scheme is evaluated and co ..."
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Cited by 5 (4 self)
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In this paper a novel twopriority network schema is presented, and exemplified through its application on singlebuffered Delta Networks in packet switching environments. Network operations considered include conflict resolution and communication strategies. The proposed scheme is evaluated and compared against the singlepriority scheme. Performance evaluation was conducted through simulation, due to the complexity of the model, and uniform traffic conditions were considered. Metrics were gathered for the two most important network performance factors, namely packet throughput and the mean time a packet needs to traverse the network. The model can also be uniformly applied to several representative networks providing a basis for fair comparison and the necessary data for network designers to select optimal values for network operation parameters. I.