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Stochastic bisimulation and performance evaluation in discrete time stochastic and deterministic Petri box calculus dtsdPBC

  • Tarasyuk, Igor
Publication Date
May 14, 2020
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We propose dtsdPBC, an extension with deterministically timed multiactions of discrete time stochastic and immediate Petri box calculus (dtsiPBC), previously presented by I.V. Tarasyuk, H. Macià and V. Valero. In dtsdPBC, non-negative integers specify deterministic multiactions with fixed (including zero) time delays. The step operational semantics is constructed via labeled probabilistic transition systems. The denotational semantics is defined on the basis of a subclass of labeled discrete time stochastic Petri nets with determin-istic transitions. The consistency of both semantics is demonstrated. In order to evaluate performance, the corresponding semi-Markov chains and (reduced) discrete time Markov chains are analyzed. We define step stochastic bisimulation equivalence of expressions and explain how it can be used to reduce their transition systems and underlying semi-Markov chains, as well as to compare the stationary behaviour. We prove that the introduced equivalence guarantees coincidence of the functional and performance characteristics and therefore 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 with discrete fixed and stochastic delays is applied to the generalized shared memory system with maintenance.

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