Stochastic equivalence for performance analysis of concurrent systems in dtsiPBC

Abstract

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.

Discrete time stochastic and deterministic Petri box calculus

“…In [55,56,57,58,59], we presented an enhanced calculus dtsiPBC, an extension with immediate multiactions of dtsPBC. 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.…”