Approximation of MTS stochastic Petri nets steady state by means of continuous Petri nets: a numerical approach

Lefebvre, Dimitri; Leclercq, Edouard; Khalij, Leila; Cursi, Eduardo Souza de; Akchioui, Nabil El

doi:10.3182/20090916-3-es-3003.00012

Cited by 11 publications

(7 citation statements)

References 6 publications

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“…. , q) leads to contPNs with steady states that do not coincide in many cases with the ones of SPNs, particularly for non-join-free PNs used in many applications [25,12,13,7,8]. The stationary approximations provided by continuous models can be considered as ''acceptable'' only if all transitions remain enabled with degree at least 1 in the long run and the marking vector does not leave the region of initial marking [26].…”

Section: Problem Formulationmentioning

confidence: 98%

Approximation of the asymptotic mean marking of SPNs with contPNs

Lefebvre

2012

Nonlinear Analysis: Hybrid Systems

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Section: Problem Formulationmentioning

confidence: 98%

Approximation of the asymptotic mean marking of SPNs with contPNs

Lefebvre

2012

Nonlinear Analysis: Hybrid Systems

Self Cite

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“…In this case, the matrix G(μ) is tedious to obtain and simulation with SPNs can be considered as a stochastic estimator of the steady state. With this discrete stochastic estimator, the determination of R(SPN, M I ) is no longer required, but the slow convergence of the estimator limits its use, particularly in case of rare events (Lefebvre et al 2009). …”

Section: Stochastic Petri Netsmentioning

confidence: 99%

“…Recently fluidification has been also introduced to relax integer constraints for SPNs (Vazquez et al 2008;Vazquez and Silva 2009;Lefebvre et al 2009). The aim of this paper is to discuss the estimation of the SPN asymptotic mean markings by using timed continuous Petri nets with constant firing rates and infinite server semantic (contPNs).…”

Section: Introductionmentioning

confidence: 99%

Piecewise constant timed continuous PNs for the steady state estimation of stochastic PNs

Lefebvre

Leclercq

2011

Discrete Event Dyn Syst

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Reliability analysis is often based on stochastic discrete event models like Markov models or stochastic Petri nets. For complex dynamical systems with numerous components, analytical expressions of the steady state are tedious to work out because of the combinatory explosion with discrete models. The computation of numerical approximations is also time consuming due to the slow convergence of stochastic simulations. For these reasons, fluidification can be investigated to estimate the asymptotic behaviour of stochastic processes. The contributions of this paper are to point out that timed continuous Petri nets may lead to biased estimators of the stochastic steady state and to introduce fluid Petri nets with piecewiseconstant maximal firing speeds and sufficient conditions in order to obtain unbiased estimators.

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“…Another semantics-modification approach has been introduced in Lefebvre et al (2009Lefebvre et al ( , 2010. There, in order to make the steady state of the continuous PN (m ss ) to coincide with that of the MPN (M ss ), the authors propose a modification of the firing rates λ of the transitions in the continuous model.…”

Section: This Is Obtained From a Probabilistic Relaxed View In Whichmentioning

confidence: 99%

On fluidization of discrete event models: observation and control of continuous Petri nets

Silva

Júlvez

Mahulea

et al. 2011

Discrete Event Dyn Syst

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As a preliminary overview, this work provides first a broad tutorial on the fluidization of discrete event dynamic models, an efficient technique for dealing with the classical state explosion problem. Even if named as continuous or fluid, the relaxed models obtained are frequently hybrid in a technical sense. Thus, there is plenty of room for using discrete, hybrid and continuous model techniques for logical verification, performance evaluation and control studies. Moreover, the possibilities for transferring concepts and techniques from one modeling paradigm to others are very significant, so there is much space for synergy. As a central modeling paradigm for parallel and synchronized discrete event systems, Petri nets (PNs) are then considered in much more detail. In this sense, this paper is somewhat complementary to David and Alla (2010). Our presentation of fluid views or approximations of PNs has sometimes a flavor of a survey, but also introduces some new ideas or techniques. Among the aspects that distinguish the adopted approach are: the focus on the relationships between discrete and continuous PN models, both for untimed, i.e., fully non-deterministic abstractions, and timed versions; the use of structure theory of (discrete) PNs, algebraic and graph based concepts and results; and the bridge to Automatic Control Theory. After discussing observability and controllability issues, the most technical part in this work, the paper concludes with some remarks and possible directions for future research.

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Approximation of MTS stochastic Petri nets steady state by means of continuous Petri nets: a numerical approach

Cited by 11 publications

References 6 publications

Approximation of the asymptotic mean marking of SPNs with contPNs

Approximation of the asymptotic mean marking of SPNs with contPNs

Piecewise constant timed continuous PNs for the steady state estimation of stochastic PNs

On fluidization of discrete event models: observation and control of continuous Petri nets

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