  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. Maci\`a, 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.
