  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 - stochastic process discovery has
started to evolve. Stochastic process discovery considers frequencies of events
in the event data and allows for more comprehensive analysis. In particular,
when 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 allowing 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
can significantly simplify the what-if analysis of processes by providing
solutions without resorting to simulation.
