Performance preserving equivalences for dtsPBC

For a discrete time stochastic extension dtsPBC of finite Petri box calculus (PBC) enriched with iteration, we define a number of stochastic equivalences. They allow one to identify processes with similar behaviour which are differentiated by the too discriminate semantic equivalence of the calculus. We investigate which is the weakest equivalence that guarantees a coincidence of performance indices for stochastic systems and can be used to simplify their performance evaluation.