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Capturing stochastic behaviors in business and work processes is essential toquantitatively understand how nondeterminism is resolved when taking decisionswithin the process. This is of special interest in process mining, where eventdata tracking the actual execution of the process are related to processmodels, and can then provide insights on frequencies and probabilities.Variants of stochastic Petri nets provide a natural formal basis for this.However, when capturing processes, such nets need to be labelled with (possiblyduplicated) activities, and equipped with silent transitions that modelinternal, non-logged steps related to the orchestration of the process. At thesame time, they have to be analyzed in a finite-trace semantics, matching thefact that each process execution consists of finitely many steps. These twoaspects impede the direct application of existing techniques for stochasticPetri nets, calling for a novel characterization that incorporates labels andsilent transitions in a finite-trace semantics. In this article, we providesuch a characterization starting from generalized stochastic Petri nets andobtaining the framework of labelled stochastic processes (LSPs). On top of thisframework, we introduce different key analysis tasks on the traces of LSPs andtheir probabilities. We show that all such analysis tasks can be solvedanalytically, in particular reducing them to a single method that combinesautomata-based techniques to single out the behaviors of interest within a LSP,with techniques based on absorbing Markov chains to reason on theirprobabilities. Finally, we demonstrate the significance of how our approach inthe context of stochastic conformance checking, illustrating practicalfeasibility through a proof-of-concept implementation and its application todifferent datasets.

Enjoy the Silence: Analysis of Stochastic Petri Nets with Silent Transitions