Discrete time stochastic and deterministic Petri box calculus

Abstract: We propose an extension with deterministically timed multiactions of discrete time stochastic and immediate Petri box calculus (dtsiPBC), previously presented by I.V. Tarasyuk, H. Maci`a and V. Valero. In dtsdPBC, non-negative integers specify 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 deterministic 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.