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.

翻译：过程挖掘是数据分析中一门成熟的学科，专注于从信息系统的事件日志中发现过程模型。近年来，过程挖掘的一个新兴子领域——随机过程发现——开始发展。随机过程发现考虑了事件数据中事件的频率，并允许进行更全面的分析。特别地，当事件日志中包含活动持续时间时，可以对所发现的随机模型的性能特征进行分析，例如，可以估计整体过程的执行时间。现有的性能分析技术通常从事件数据中发现随机过程模型，然后通过模拟这些模型来评估其执行时间。这些方法依赖于经验性方法。本文提出了用于性能分析的分析技术，允许在事件时间分布由半马尔可夫过程建模的情况下，推导出整体过程执行时间的统计特征。所提出的方法能够在不依赖模拟的情况下提供解决方案，从而显著简化过程的假设分析。