# Correcting for Non-Markovian Asymptotic Effects using Markovian Representation

## TL;DR

This paper presents methods to adjust Markov models for non-Markovian effects like fixed delays and Weibull or lognormal transition times, enabling accurate steady-state and hazard rate calculations in complex systems.

## Contribution

It introduces novel procedures for incorporating non-Markovian transition distributions into Markov models for steady-state and hazard rate analysis.

## Key findings

- Effective adjustment methods for non-Markovian transition times
- Demonstrated accuracy on multiple example systems
- Enhanced Markov modeling for complex transition behaviors

## Abstract

Asymptotic properties of Markov Processes, such as steady state probabilities or hazard rate for absorbing states can be efficiently calculated by means of linear algebra even for large-scale problems. This paper discusses the methods for adjusting parameters of the Markov models to account for non-constant transition rates. In particular, transitions with fixed delays are considered along with the transitions that follow Weibull and lognormal distributions. Procedures for both steady-state solutions in the absence of an absorbing state, and for hazard rates to an absorbing state are provided and demonstrated on several examples.