  Semi-Markov processes (SMPs) provide a rich framework for many real-world
problems. However, due to difficulty implementing practical solutions they are
rarely used with their full capability. The theory of SMPs is quite mature but
was mainly developed at a time when computational resources were not widely
available. With the exception of some of the simplest cases, solutions to SMPs
are inherently numerical, and SMPs have been underutilized by practitioners
because of difficulty implementing the theory in applications. This paper
demonstrates the theory and computational methods needed to implement SMP
models in practical settings. Methods are illustrated with an application
modeling the movement of coronary patients in a hospital. Our aim is to allow
practitioners to use richer SMP models without being burdened with the rigorous
mathematical theory.
