A Geometric Approach for the Homothetic Approximation of Stochastic Petri nets

Lefebvre, Dimitri; Leclercq, Edouard; Akchioui, Nabil El; Cursis, E. Souza de; Khalij, Leila

doi:10.3182/20100830-3-de-4013.00040

Cited by 15 publications

(10 citation statements)

References 8 publications

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“…The offset error is particularly large for the stochastic asymptotic mean marking in the critical r-region A 1 . In this critical r-region, some locations are not limit reachable with contPNs in comparison with SPNs (Lefebvre et al 2010). …”

Section: Approximation Of Spns Asymptotic Mean Markings With Contpnsmentioning

confidence: 96%

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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Section: Approximation Of Spns Asymptotic Mean Markings With Contpnsmentioning

confidence: 96%

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

Lefebvre

Leclercq

2011

Discrete Event Dyn Syst

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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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“…In [12,7], piecewise constant timed continuous PNs have been proposed that are suitable to compute the SPNs steady state in non-critical regions (non-critical means that each join is driven by a different place). Finally, a homothetic approach has been developed to provide an approximation of the SPNs steady state in critical regions according to contPNs with modified parameters and partial homothetic initial markings [13,8]. The limitation of these last methods is that they are not constructive and provide only a global understanding of the SPNs and timed continuous PNs behaviors.…”

Section: Introductionmentioning

confidence: 99%