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

Igor V Tarasyuk (1)

1 A.P. Ershov Institute of Informatics Systems SB RAS

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. Macia 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 Petri net denotational semantics is defined via dtsd-boxes, a subclass of labeled discrete time stochastic Petri nets with deterministic transitions. We also define step stochastic bisimulation equivalence of the algebraic expressions, used to compare the qualitative and quantitative behaviour of the specified processes. The consistency of the operational and denotational semantics of dtsdPBC up to that equivalence is established. In order to evaluate performance in dtsdPBC, the underlying semi-Markov chains and (reduced) discrete time Markov chains of the process-algebraic expressions are analyzed. We explain how step stochastic bisimulation equivalence of the expressions can be used for quotienting their transition systems and corresponding Markov chains, as well as to compare the stationary behaviour and residence time properties. We prove that the 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. We also determine the main advantages of dtsdPBC by comparing it with other well-known or similar SPAs.

Mots clés: stochastic process algebra; stochastic Petri net; Petri box calculus; discrete time; stochastic multiaction; deterministic multiaction; transition system; operational semantics; stochastic transition; deterministic transition; dtsd-box; denotational semantics; Markov chain; performance evaluation; reduction; stochastic bisimulation; quotient; shared memory system

Domaines: Logique en informatique [cs.LO]

Igor V Tarasyuk. Stochastic bisimulation and performance evaluation in discrete time stochastic and deterministic Petri box calculus dtsdPBC. 2022. ⟨hal-02573419v3⟩