Equivalence relations for modular performance evaluation in dtsPBC

Abstract

We define a number of stochastic equivalences in the dtsPBC framework, which is a discrete time stochastic extension of finite Petri box calculus (PBC) enriched with iteration. These equivalences allow the identification of stochastic processes that have similar behaviour but are differentiated by the semantics of the calculus. We explain how the equivalences we propose can be used to reduce transition systems of expressions, and demonstrate how to apply the equivalences to compare the stationary behaviour. The equivalences guarantee a coincidence of performance indices for stochastic systems, and can be used for performance analysis simplification. We use a case study to outline a method of modelling, performance evaluation and behaviour preserving reduction of concurrent computing systems, and apply it to the dining philosophers system.