Cycle time is a key performance measure in semiconductor manufacturing. Currently, discrete event simulation and queueing theory are the most common approaches to estimating the cycle time of a fabrication facility. However, the performance of both approaches has been unsatisfactory due to many factors, including the inability to perform in an environment where informal and unwritten operational rules exist. Such rules create dependence between the arrival and service processes of a toolset, and, hence, render the classical queueing models inaccurate. We propose a Markov chain framework that attempts to approximate the cycle time of a toolset in the presence of informal operational rules, and we compare our approach with classical queueing models through a series of numerical examples.