Product-form and stochastic Petri nets: a structural approach

Haddad, Serge; Moreaux, Patrice; Sereno, Matteo; Silva, M.

doi:10.1016/j.peva.2004.08.004

Cited by 18 publications

(43 citation statements)

References 21 publications

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“…Our analysis method relies on a decomposition of a class of Petri nets into special structures, called building blocks (BBs). In general, the conditions for a SPN to belong to this class are not only structural (as with the product-form class studied in [26], for example) but also rate-dependent. In [31,8], a class of SPN models with rate-dependent product-form conditions was studied, yielding a result based on a rank-theorem, in which the rank of a matrix whose entries depend on the whole net structure and the rates must be investigated.…”

Section: Resultsmentioning

confidence: 99%

“…In the paper we show how this follows from RCAT's rate equations. Rate dependent product-form conditions are very important in stochastic Petri nets, as initially shown in [8] and, more recently, in [26,35,3]. We add to this topic by giving a compositional interpretation of such conditions in terms of our building block basic structures.…”

Section: Motivating Examplementioning

confidence: 93%

“…Moreover, when such a composition forms a closed SPN, then the product-form belongs to the class of ordinary product-form SPNs of [31,8,26]. We now show that Theorem 1 and Proposition 1 not only generalise the product-form result in a uniform way from closed nets to open ones (with, in general, rate-dependent conditions), but also allows one to derive product-form solutions for more complex models that are closely related to G-networks and their variants.…”

Section: Product-forms For Ordinary Spns With Signalsmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of stochastic Petri nets with signals

Marin¹,

Balsamo²,

Harrison³

2012

Performance Evaluation

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Section: Resultsmentioning

confidence: 99%

Section: Motivating Examplementioning

confidence: 93%

Section: Product-forms For Ordinary Spns With Signalsmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of stochastic Petri nets with signals

Marin¹,

Balsamo²,

Harrison³

2012

Performance Evaluation

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“…A reaction network may also be modeled as a stochastic Petri net [2,9,17,23,25] . For such networks, the transient distribution P(X (t ) = n), n ∈ S, is of interest.…”

Section: Reaction Network and Product Form In The Literaturementioning

confidence: 99%

Transient detailed balance and product form for reaction networks

Boer

Boucherie

2017

Stochastic Models

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This paper explores the boundary of the set of reaction networks that have an exact transient (truncated) multidimensional Poisson or product-form distribution for the number of particles of different types. Motivated by the birth-death process, we introduce the notions of transient detailed balance and delay functions, and use these notions to obtain the novel transient product-form distribution in a coagulation-fragmentation process for polymers with a tree-like structure from that of the pure coagulation process.

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“…In this paper, we use GSPN [16,17] as the intermediate representation of WS-CDL. The definition of GSPN is given below.…”

Section: Gspnmentioning

confidence: 99%

A model‐driven approach to predicting dependability of WS‐CDL based service composition

Xia

Dai

et al. 2011

Concurrency and Computation

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SUMMARYWeb Service Choreography Description Language (WS-CDL) is a mainstream standard for the description of peer-to-peer collaborations for the participants of service composition. To predict the dependability of composite service processes specified in WS-CDL allows service designers and user to decided whether the process meets the nonfunction requirements of trustworthiness, and to choose the process with better dependability to those with identical function. Unfortunately, very limited research attention is paid to dependability of WS-CDL. In this paper, we propose a model-driven approach for dependability prediction of composite service built on WS-CDL. The main innovation of this research includes a complete translation from WS-CDL to generalized stochastic Petri nets (GSPN) and a dependability (using processnormal-completion-probability as the metric of dependability of service composition) calculation algorithm based on GSPN. We also validate the accuracy of the approach in the experimental study by showing 95% confidence intervals obtained from experimental dependability results that cover the corresponding theoretical prediction values.

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Product-form and stochastic Petri nets: a structural approach

Cited by 18 publications

References 21 publications

Analysis of stochastic Petri nets with signals

Analysis of stochastic Petri nets with signals

Transient detailed balance and product form for reaction networks

A model‐driven approach to predicting dependability of WS‐CDL based service composition

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