Computation and applications of limits of certain non-stationary Markov chains

TL;DR

This paper introduces a method for computing limits of specific non-stationary Markov chains, validated mathematically, with applications in healthcare cycle prediction and large system maintenance, aiming to advance understanding and teaching of these chains.

Contribution

It presents a novel computational method for non-stationary Markov chains, validated mathematically, with practical applications in healthcare and system maintenance.

Findings

Validated the computation method mathematically

Applied the method to healthcare cycle prediction

Demonstrated usefulness in large system maintenance

Abstract

This article describes a method for computing limits of a class of non-stationary Markov chains motivated by healthcare sojourn-time cycles. A mathematical validation of the computation method is also given. Applications are described that include predicting cycles in healthcare and very large system maintenance. An objective of this article is to hopefully foster some investigation and teaching of practical non-stationary Markov chains.