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37
Stochastic petri nets: An elementary introduction
 In Advances in Petri Nets
, 1989
"... ABSTRACT Petri nets in which random firing delays are associated with transitions whose ..."
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Cited by 66 (0 self)
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ABSTRACT Petri nets in which random firing delays are associated with transitions whose
Fault detection and diagnosis in distributed systems: an approach by partially stochastic Petri nets
 special issue on Hybrid Systems
, 1998
"... We address the problem of alarm correlation in large distributed systems. The key idea is to make use of the concurrence of events in order to separate and simplify the state estimation in a faulty network. Petri nets and their causality semantics are used to model concurrency. Special partially ..."
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Cited by 64 (11 self)
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We address the problem of alarm correlation in large distributed systems. The key idea is to make use of the concurrence of events in order to separate and simplify the state estimation in a faulty network. Petri nets and their causality semantics are used to model concurrency. Special partially stochastic Petri nets are developed, that establish some kind of equivalence between concurrence and independence. The diagnosis problem is defined as the computation of the most likely history of the net given a sequence of observed alarms. Solutions are provided in four contexts, with a gradual complexity on the structure of observations.
Dependability Evaluation Using Composed SANBased Reward Models
, 1992
"... Dependability evaluation is an important, but difficult, aspect of the design of faulttolerant parallel and distributed computing systems. One possible technique is to use Markov models, but if applied directly to realistic designs, this often results in large and intractable models. Many authors h ..."
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Cited by 40 (9 self)
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Dependability evaluation is an important, but difficult, aspect of the design of faulttolerant parallel and distributed computing systems. One possible technique is to use Markov models, but if applied directly to realistic designs, this often results in large and intractable models. Many authors have investigated methods to avoid this explosive statespace growth, but have typically either solved the problem for a specific system design, or required manipulation of the model at the statespace level. Stochastic activity networks (SANs), a stochastic extension of Petri nets, together with recently developed reduced base model construction techniques, have the potential to avoid this state space growth at the SAN level for many parallel and distributed systems. This paper investigates this claim, by considering their application to three different systems: a faulttolerant parallel computing system, a distributed database architecture, and a multiprocessormultimemory system. We show that this method does indeed result in tractable Markov models for these systems, and argue that it can be applied to the dependability evaluation of many parallel and distributed systems.
A Formal Approach to the Integration of Performance Aspects in the Modeling and Analysis of Concurrent Systems
 Information and Computation
, 1998
"... A formal approach for modeling and analyzing concurrent systems is proposed which integrates performance characteristics in the early stages of the design process. The approach relies on both stochastically timed process algebras and stochastically timed Petri nets in order to exploit their compleme ..."
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Cited by 29 (13 self)
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A formal approach for modeling and analyzing concurrent systems is proposed which integrates performance characteristics in the early stages of the design process. The approach relies on both stochastically timed process algebras and stochastically timed Petri nets in order to exploit their complementary advantages. The approach is instantiated to the case of EMPA (Extended Markovian Process Algebra), introduced together with the collection of its four semantics and the notion of equivalence that are required in order to implement the approach. Finally, the case study of the alternating bit protocol is presented to illustrate the adequacy of the approach. 1
Distributed State Reconstruction for Discrete Event Systems
, 2000
"... We consider a discrete event dynamic system (DEDS) obtained by the parallel composition of several subsystems. Each subsystem can be seen as a standard stochastic DEDS. The composed system is provided with true concurrency semantics that emphasize concurrent behaviors of the subsystems. For these ..."
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Cited by 22 (9 self)
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We consider a discrete event dynamic system (DEDS) obtained by the parallel composition of several subsystems. Each subsystem can be seen as a standard stochastic DEDS. The composed system is provided with true concurrency semantics that emphasize concurrent behaviors of the subsystems. For these semantics, a trajectory appears as a partial order of events. For simplicity, we focus on the case of a global system composed of only two subsystems. We assume that firings in each subsystem are collected by a local sensor, which yields a sequence of transition labels (or events). The objective is to recover the most likely global trajectory of the system from the two (asynchronous) sequences of observations. This is an almost standard hidden state estimation problem, amenable to the clasical Viterbi algorithm. We propose a solution in which this global trajectory is built recursively by two asynchronously cooperating "players, " each one being in charge of one subsystem. These two players run local Viterbi algorithms based on local states of the subsystems, plus some coordination information. This supervising architecture is particularly suited to large modular systems and is currently being applied to the distributed monitoring (and fault diagnosis) of telecommunication networks.
Structural Techniques and Performance Bounds of Stochastic Petri Net Models
 Advances in Petri Nets 1992, volume 609 of Lecture Notes in Computer Science
, 1992
"... In this paper we overview some recent results obtained by the authors and collaborators on the performance bounds analysis of some stochastic Petri net systems. The mathematical model can be seen either as a result of the addition of a particular random timing interpretation to an "autonomou ..."
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Cited by 21 (10 self)
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In this paper we overview some recent results obtained by the authors and collaborators on the performance bounds analysis of some stochastic Petri net systems. The mathematical model can be seen either as a result of the addition of a particular random timing interpretation to an "autonomous" Petri net or as a generalization of classical queueing networks with the addendum of a general synchronization primitive. It constitutes an adequate tool for both the validation of logical properties and the evaluation of performance measures of concurrent and distributed systems. Qualitative and quantitative understandings of Petri net models are stressed here making special emphasis on structural techniques for the analysis of logical and performance properties. Important aspects from the performance point of view, such as relative throughput of stations (transitions), and number of servers present at them, are related to Petri net concepts like P or Tsemiflows or liveness bounds...
Welldefined stochastic Petri nets, in
 Proceedings of the 4th International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems, MASCOTS ’96, IEEE Computer Society
, 1996
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An Efficient WellSpecified Check
, 1999
"... A longstanding problem with generalized stochastic Petri nets and extensions is that of what to do when more than one zerotimed event is scheduled to occur at the same time. If the order is left unspecified, it could lead to ambiguity that affects reward variables. Stochastic activity nets (SANs) [ ..."
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Cited by 16 (4 self)
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A longstanding problem with generalized stochastic Petri nets and extensions is that of what to do when more than one zerotimed event is scheduled to occur at the same time. If the order is left unspecified, it could lead to ambiguity that affects reward variables. Stochastic activity nets (SANs) [6, 7] have used the wellspecified condition to avoid this problem. However, the existing algorithm to perform the wellspecified check is computationally complex, proportional to the number of paths through unstable markings. We provide some theoretical results that allow us to make use of a much more efficient algorithm, with complexity proportional to the number of arcs between unstable markings.
Concurrent Execution Of Timed Petri Nets
 Proceedings of the 1994 Winter Simulation Conference
, 1994
"... The dynamics of discrete event systems can be effectively described and analyized using the timed Petri net formalism. The aim of this paper is to comprehensively present the achievements attained in accelerating Petri net executions by using parallel or distributed multiprocessing environments. The ..."
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Cited by 15 (7 self)
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The dynamics of discrete event systems can be effectively described and analyized using the timed Petri net formalism. The aim of this paper is to comprehensively present the achievements attained in accelerating Petri net executions by using parallel or distributed multiprocessing environments. The basic problem is to generate concurrent Petri net executions insuring correctness in the sense that the partial ordering of transition firings produced is consistent with the total event ordering that would be produced by a (hypothetical) sequential execution. Two lines of thought have been followed: in parallel simulations transition firings evolve as governed by a SIMD iteration mechanism. Distributed simulations aim at a proper synchronization of firings in spatially different net parts to avoid timing inconsistencies and alterations of the execution behavior. In both cases, structural properties of the underlying Petri net can be efficiently used to simplify and/or accelerate concurrent...