Geodesic
Stochastic equivalence for performance analysis of concurrent systems in dtsiPBC
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1743-1812

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We propose an extension with immediate multiactions of discrete time stochastic Petri Box Calculus (dtsPBC), presented by I.V. Tarasyuk. The resulting algebra dtsiPBC is a discrete time analogue of stochastic Petri Box Calculus (sPBC) with immediate multiactions, designed by H. Macìa, V. Valero et al. within a continuous time domain. The step operational semantics is constructed via labeled probabilistic transition systems. The denotational semantics is based on labeled discrete time stochastic Petri nets with immediate transitions. To evaluate performance, the corresponding semi-Markov chains are analyzed. We define step stochastic bisimulation equivalence of expressions that is applied to reduce their transition systems and underlying semi-Markov chains while preserving the functionality and performance characteristics. We explain how this equivalence can be used to simplify performance analysis of the algebraic processes. In a case study, a method of modeling, performance evaluation and behaviour reduction for concurrent systems is outlined and applied to the shared memory system.
Keywords: stochastic process algebra, Petri box calculus, discrete time, immediate multiaction, operational and denotational semantics, performance evaluation, stochastic equivalence, reduction.
Mots-clés : semi-Markov chain 
@article{SEMR_2018_15_a119,
     author = {I. V. Tarasyuk and H. Maci\`a and V. Valero},
     title = {Stochastic equivalence for performance analysis of concurrent systems in {dtsiPBC}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1743--1812},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a119/}
}
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I. V. Tarasyuk; H. Macià; V. Valero. Stochastic equivalence for performance analysis of concurrent systems in dtsiPBC. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1743-1812. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a119/