# Perturbation analysis of Markov modulated fluid models

## TL;DR

This paper investigates how small changes in the parameters of Markov modulated fluid models affect their behavior, especially focusing on the matrix of first return probabilities, by developing a new analytical approach.

## Contribution

It introduces a novel method to analyze the impact of perturbations on the first return probability matrix in Markov modulated fluid models.

## Key findings

- Developed a substitute for the first return probability matrix.
- Analyzed the effect of perturbations on the matrix.
- Provided insights into the stability of fluid models under perturbations.

## Abstract

We consider perturbations of positive recurrent Markov modulated fluid models. In addition to the infinitesimal generator of the phases, we also perturb the rate matrix, and analyze the effect of those perturbations on the matrix of first return probabilities to the initial level. Our main contribution is the construction of a substitute for the matrix of first return probabilities, which enables us to analyze the effect of the perturbation under consideration.