A comprehensive method for solving finite-state semi-Markov processes

Semi‐Markov processes (SMPs) provide a rich framework for many real‐world problems. However, owing to difficulty in 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 underutilised by practitioners because of difficulty in 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 modelling 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.