Performance evaluation in stochastic process algebra dtsdPBC

We consider discrete time stochastic and deterministic Petri box calculus (dtsdPBC), recently proposed by I.V. Tarasyuk. dtsdPBC is a discrete time extension with stochastically and deterministically timed multiactions of the well-known Petri box calculus (PBC), presented by E. Best, R. Devillers, J.G. Hall and M. Koutny. In dtsdPBC, stochastic multiactions have (conditional) probabilities of execution at the next time moment while deterministic multiactions have non-negative integers associated that specify fixed (including zero) delays. dtsdPBC features a step operational semantics via labeled probabilistic transition systems. In order to evaluate performance in dtsdPBC, the underlying semi-Markov chains (SMCs) are investigated, which are extracted from the transition systems corresponding to the process expressions of the calculus. It is demonstrated that the performance analysis in dtsdPBC is alternatively possible by exploring the corresponding discrete time Markov chains (DTMCs) and their reductions (RDTMCs), obtained by eliminating the states with zero residence time (vanishing states). The method based on DTMCs permits to avoid building the embedded DTMC (EDTMC) and weighting the probability masses in the states by their average sojourn times. The method based on RDTMCs simplifies performance analysis of large systems due to eliminating the non-stop transit (vanishing) states where only instantaneous activities are executed, resulting in a smaller model that can easier be solved directly.