An efficient algorithm for aggregating PEPA models

Gilmore, Stephen; Hillston, Jane; Ribaudo, Marina

doi:10.1109/32.922715

Cited by 76 publications

(62 citation statements)

References 15 publications

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“…Compositional bisimulation minimisation has been applied to several examples yielding substantial state-space reductions. It allowed the analysis of IMCs (in fact, CTMCs) that could not be analysed without compositional minimisation [39,30,32]. With the advent of increasingly complex systems, more radical reduction techniques are needed.…”

Section: Theorem 11 For Any Finitely-branching Imc With State Space mentioning

confidence: 99%

The How and Why of Interactive Markov Chains

Hermanns

Katoen

2010

Lecture Notes in Computer Science

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Abstract. This paper reviews the model of interactive Markov chains (IMCs, for short), an extension of labelled transition systems with exponentially delayed transitions. We show that IMCs are closed under parallel composition and hiding, and show how IMCs can be compositionally aggregated prior to analysis by e.g., bisimulation minimisation or aggressive abstraction based on simulation pre-congruences. We survey some recent analysis techniques for IMCs, i.e., explaining how measures such as reachability probabilities can be obtained. Finally, we demonstrate that IMCs are a natural (and simple) semantic model for stochastic process algebras and generalised stochastic Petri nets and can be used for engineering formalisms such as AADL and dynamic fault trees.

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Section: Theorem 11 For Any Finitely-branching Imc With State Space mentioning

confidence: 99%

The How and Why of Interactive Markov Chains

Hermanns

Katoen

2010

Lecture Notes in Computer Science

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“…The relation can be used to aggregate the state space of a PEPA model, accelerating the production of numerical results and allowing larger modelling studies to be undertaken [GHR01].…”

Section: R)(p (β S)q) + (β S)((α R)p Q)mentioning

confidence: 99%

Formal Methods for Biochemical Signalling Pathways

Calder

Gilmore

Hillston

et al. 2009

Formal Methods: State of the Art and New Directions

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“…Next, the equivalence of statements (a)-(f) is deduced from the six equivalent conditions in Lemma 2.1 for the Markov chain {(Y t , X t )} t∈N to be strongly lumpable (see Appendix B). Theorem 3.1 (b)) implies that the FSS is strongly lumpable with respect to g. We refer to [7,11] for details and connections for other Stochastic Process Algebras.…”

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confidence: 99%

On the Relationships Between Lumpability and Filtering of Finite Stochastic Systems

Ledoux¹,

White²,

Brushe³

2008

J. Appl. Probab.

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The aim of this paper is to provide the conditions necessary to reduce the complexity of state filtering for finite stochastic systems (FSSs). A concept of lumpability for FSSs is introduced. This paper asserts that the unnormalised filter for a lumped FSS has linear dynamics. Two sufficient conditions for such a lumpability property to hold are discussed. It is shown that the first condition is also necessary for the lumped FSS to have a linear dynamics. Next, it is proven that the second condition allows the filter of the original FSS to be directly obtained from the filter for the lumped FSS. Finally, the paper generalises an earlier published result for the approximation of a general FSS by a lumpable one.

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An efficient algorithm for aggregating PEPA models

Cited by 76 publications

References 15 publications

The How and Why of Interactive Markov Chains

The How and Why of Interactive Markov Chains

Formal Methods for Biochemical Signalling Pathways

On the Relationships Between Lumpability and Filtering of Finite Stochastic Systems

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