Performance Analysis: Discovering Semi-Markov Models From Event Logs

Process mining is a well-established discipline of data analysis focused on the discovery of process models from information systems' event logs. Recently, an emerging subarea of process mining, known as stochastic process discovery, has started to evolve. Stochastic process discovery considers frequencies of events in the event data and allows for a more comprehensive analysis. In particular, when the durations of activities are presented in the event log, performance characteristics of the discovered stochastic models can be analyzed, e.g., the overall process execution time can be estimated. Existing performance analysis techniques usually discover stochastic process models from event data, and then simulate these models to evaluate their execution times. These methods rely on empirical approaches. This paper proposes analytical techniques for performance analysis that allow for the derivation of statistical characteristics of the overall processes' execution times in the presence of arbitrary time distributions of events modeled by semi-Markov processes. The proposed methods include express analysis, focused on the mean execution time estimation, and full analysis techniques that build probability density functions (PDFs) of process execution times in both continuous and discrete forms. These methods are implemented and tested on real-world event data, demonstrating their potential for what-if analysis by providing solutions without resorting to simulation. Specifically, we demonstrated that the discrete approach is more time-efficient for small duration support sizes compared to the simulation technique. Furthermore, we showed that the continuous approach, with PDFs represented as Mixtures of Gaussian Models (GMMs), facilitates the discovery of more compact and interpretable models.