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. 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, semi-Markov chain, performance evaluation, stochastic equivalence, reduction.