Discrete Time Stochastic Petri Box Calculus with Immediate Multiactions dtsiPBC

Tarasyuk, Igor V.; Macií, Hermenegilda; Valero, Valentín

doi:10.1016/j.entcs.2013.07.015

Cited by 6 publications

(7 citation statements)

References 15 publications

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“…Concerning differences from our previous papers about dtsiPBC Tarasyuk et al (2013Tarasyuk et al ( , 2015, the present text is much more detailed and many new important results have been added. In particular, immediate multiactions now have positive real-valued weights (instead of previously used positive integer weights), all the used notions (such as numbering, functions collecting executable activities, probability functions) are formally defined and completely explained with examples; the operational and denotational semantics are given in full detail (the inaction, action rules, LDTSPNs and dtsi-boxes are extensively described and discussed); compact illustrative examples (of standard and alternative solution methods) are presented; keeping properties of original Markov chains (irreducibility, positive recurrence and aperiodicity) in their embedded and state-aggregated versions is studied.…”

Section: Our Contributionsmentioning

confidence: 67%

“…The main advantage of dtsPBC is that concurrency is treated like in PBC having step semantics, whereas in sPBC parallelism is simulated by interleaving, obliging one to collect the information on causal independence of activities before constructing the semantics. In Tarasyuk et al (2013Tarasyuk et al ( , 2015, we presented the extension dtsiPBC of the latter calculus with immediate multiactions. Immediate multiactions increase the specification capability: they can model logical conditions, probabilistic branching, instantaneous probabilistic choices and activities whose durations are negligible in comparison with those of others.…”

Section: Stochastic Extensions Of Petri Box Calculusmentioning

confidence: 99%

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Stochastic equivalence for performance analysis of concurrent systems in dtsiPBC

Tarasyuk¹,

Macià²,

Valero³

2018

Sib. Elektron. Mat. Izv.

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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. Macià, 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.

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Section: Our Contributionsmentioning

confidence: 67%

Section: Stochastic Extensions Of Petri Box Calculusmentioning

confidence: 99%

Stochastic equivalence for performance analysis of concurrent systems in dtsiPBC

Tarasyuk¹,

Macià²,

Valero³

2018

Sib. Elektron. Mat. Izv.

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“…The performance evaluation in dtsPBC with iteration is accomplished using the underlying discrete time Markov chains (DTMCs) of the algebraic processes. Tarasyuk et al (2010) defined dtsiPBC by extending dtsPBC through the addition of immediate multiactions. The performance analysis in dtsiPBC is based on the underlying semi-Markov chains (SMCs) and (reduced) DTMCs.…”

Section: Time Extensions Of Petri Box Calculusmentioning

confidence: 99%

Equivalence relations for modular performance evaluation in dtsPBC

Tarasyuk

2013

Math. Struct. Comp. Sci.

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We define a number of stochastic equivalences in the dtsPBC framework, which is a discrete time stochastic extension of finite Petri box calculus (PBC) enriched with iteration. These equivalences allow the identification of stochastic processes that have similar behaviour but are differentiated by the semantics of the calculus. We explain how the equivalences we propose can be used to reduce transition systems of expressions, and demonstrate how to apply the equivalences to compare the stationary behaviour. The equivalences guarantee a coincidence of performance indices for stochastic systems, and can be used for performance analysis simplification. We use a case study to outline a method of modelling, performance evaluation and behaviour preserving reduction of concurrent computing systems, and apply it to the dining philosophers system.

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“…We also develop an alternative, more optimal, solution method based on the corresponding DTMC. This paper is an extended and modified version of our previous paper [15], which was published in the proceedings of an international conference on practi cal applications of stochastic modeling, enriched with detailed description of syntax and semantics of algebra dtsiPBC, as well as with formal definitions and use of some additional important concepts (for example, numbering of expressions, numbering function, etc.). It also includes a new alternative method for perfor mance evaluation and supplementary illustrative examples.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we describe performance evaluation methods for computing systems in the final version of the algebra discrete time stochastic and immediate PBC (dtsiPBC) introduced in [14]. dtsiPBC is an extension of dtsPBC with iteration by immediate mul tiactions having zero time delay.…”

Section: Introductionmentioning

confidence: 99%

Performance analysis of concurrent systems in algebra dtsiPBC

Tarasyuk

Macià²,

Valero

2014

Program Comput Soft

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Petri box calculus PBC is a well known algebra of concurrent processes with a Petri net semantics. In the paper, an extension of PBC with discrete stochastic time and immediate multiactions, which is referred to as discrete time stochastic and immediate PBC (dtsiPBC), is considered. Performance analysis methods for concurrent and distributed systems with random time delays are investigated in the framework of the new stochastic process algebra. It is demonstrated that the performance evaluation is possible not only via the underlying semi Markov chains of the dtsiPBC expressions but also with the use of the underlying discrete time Markov chains, and the latter analysis technique is more optimal.

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Discrete Time Stochastic Petri Box Calculus with Immediate Multiactions dtsiPBC

Cited by 6 publications

References 15 publications

Stochastic equivalence for performance analysis of concurrent systems in dtsiPBC

Stochastic equivalence for performance analysis of concurrent systems in dtsiPBC

Equivalence relations for modular performance evaluation in dtsPBC

Performance analysis of concurrent systems in algebra dtsiPBC

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