Supplementary variable approach applied to the transient analysis of age-MRSPNs

Telek, Miklós; Horváth, Ádám

doi:10.1109/ipds.1998.707708

Cited by 17 publications

(15 citation statements)

References 15 publications

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“…As no disabling happens by the firing of t 1 , the last step in computing the density associated with class Σ 1 is to consider the enabling of t 3 applying (10). This leads to f 1 (a, Next we consider the firing of transition t 2 leaving class Σ 1 leading to the new class Σ 3 with marking p 3 p 4 .…”

Section: Discussionmentioning

confidence: 99%

“…Analysis methods for this class of models have been finely developed relying on Markov renewal theory [4,5] and on the method of supplementary variables [9,6,10].…”

Section: Underlying Stochastic Processmentioning

confidence: 99%

“…In principle, the analysis of a model with multiple concurrent generally distributed timers can be formulated through the theory of supplementary variables [9,6,10], extending the logical state (the marking) with the vector of ages of generally distributed enabled transitions. However, this results in a set of integro-differential equations whose practical solution is limited to one or two concurrently enabled non-exponential distributions, thus falling again within the limits of the enabling restriction [11].…”

Section: Introductionmentioning

confidence: 99%

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Transient analysis of non-Markovian models using stochastic state classes

Horváth

Paolieri

Ridi

et al. 2012

Performance Evaluation

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a b s t r a c tThe method of stochastic state classes approaches the analysis of Generalised Semi Markov Processes (GSMPs) through the symbolic derivation of probability density functions over supports described by Difference Bounds Matrix (DBM) zones. This makes steady state analysis viable, provided that at least one regeneration point is visited by every cyclic behaviour of the model.We extend the approach providing a way to derive transient probabilities. To this end, stochastic state classes are extended with a supplementary timer that enables the symbolic derivation of the distribution of time at which a class can be entered. The approach is amenable to efficient implementation when model timings are given by expolynomial distributions, and it can be applied to perform transient analysis of GSMPs within any given time bound. In the special case of models underlying a Markov Regenerative Process (MRGP), the method can also be applied to the symbolic derivation of local and global kernels, which in turn provide transient probabilities through numerical integration of generalised renewal equations. Since much of the complexity of this analysis is due to the local kernel, we propose a selective derivation of its entries depending on the specific transient measure targeted by the analysis.

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Section: Discussionmentioning

confidence: 99%

“…Analysis methods for this class of models have been finely developed relying on Markov renewal theory [4,5] and on the method of supplementary variables [9,6,10].…”

Section: Underlying Stochastic Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Transient analysis of non-Markovian models using stochastic state classes

Horváth

Paolieri

Ridi

et al. 2012

Performance Evaluation

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“…In this way, the class of models that are amenable to steady state analysis through aggregated classes becomes a proper extension of the class of models that can be managed through Markov Renewal Theory [2], [3], through the method of Supplementary (Single) Variable [1], [6] or through the theory of stochastic state classes [8], [9], [7].…”

Section: Remark 42mentioning

confidence: 99%

“…In the theory of supplementary variables [1], [6], the logical state is supplemented by the vector of ages of the enabled general transitions, and its evolution is described through a set of integro-differential state equations. Even if formulated for any number of concurrent generally distributed transitions, practical tractability requires that two generally distributed transitions are not enabled simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Aggregated Stochastic State Classes in Quantitative Evaluation of non-Markovian Stochastic Petri Nets

Horváth

Vicario

2009

2009 Sixth International Conference on the Quantitative Evaluation of Systems

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Abstract-The method of stochastic state classes provides a new approach for the analysis of non-Markovian stochastic Petri Nets, which relies on the stochastic expansion of the graph of nondeterministic state classes based on Difference Bounds Matrix (DBM) which is usually employed in qualitative verification. In so doing, the method is able to manage multiple concurrent nonexponential (GEN) transitions and largely extends the class of models that are amenable to quantitative evaluation. However, its application requires that every cycle in the graph of nondeterministic state classes visits at least a regeneration point where all GEN transitions are newly enabled. In particular, this rules out models whose non-deterministic class graph includes cycles within a Continuous Time Markov Chain (CTMC) subordinated to the activity period of one or more GEN transitions.In this paper, we propose an extension that overcomes this limitation by aggregating together classes that are reached through firings that do not change the enabling status of GEN transitions. This enlarges the class of models that can be analysed through the method of stochastic state classes and makes it become a proper extension of the class of models that satisfies the so called enabling restriction.Index Terms-non-Markovian stochastic Petri nets, stochastic time Petri nets, steady state analysis, stochastic state classes.

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Non-Markovian Analysis

German

2001

Lecture Notes in Computer Science

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Supplementary variable approach applied to the transient analysis of age-MRSPNs

Cited by 17 publications

References 15 publications

Transient analysis of non-Markovian models using stochastic state classes

Transient analysis of non-Markovian models using stochastic state classes

Aggregated Stochastic State Classes in Quantitative Evaluation of non-Markovian Stochastic Petri Nets

Non-Markovian Analysis

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