A Comprehensive Method for Solving Finite-State Semi-Markov Processes

TL;DR

This paper presents practical computational methods for implementing semi-Markov processes, enabling their use in real-world applications like hospital patient movement modeling, bridging the gap between theory and practice.

Contribution

It introduces accessible computational techniques for SMPs, making their complex theory usable in practical, real-world scenarios.

Findings

Demonstrated methods with a hospital patient movement case study

Enabled practical application of SMPs without extensive mathematical expertise

Improved usability of SMP models for practitioners

Abstract

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.