Performance analysis of the shared memory system in stochastic process algebra dtsdPBC
Igor V. Tarasyuk · International Journal of Parallel Emergent and Distributed Systems · 2025
Discrete time stochastic and deterministic Petri box calculus (dtsdPBC) is a parallel process algebra with stochastic and deterministic delays. To evaluate performance in dtsdPBC, semi-Markov chains (SMCs) and (reduced) discrete time Markov chains (DTMCs/RDTMCs) are analyzed. Stochastic bisimulation equivalence is used for quotienting the transition systems, SMCs and DTMCs/RDTMCs of the process expressions while preserving stationary behaviour and residence time. Our example of generalized shared memory system with maintenance demonstrates modeling, performance analysis and reduction by quotienting. The generalized system takes the probabilities and weights from the standard system's specification as variables, adjusted for performance optimization.