# Propagation of epistemic uncertainty in queueing models with unreliable server using chaos expansions

## TL;DR

This paper introduces a Polynomial Chaos-based numerical method to efficiently analyze how epistemic uncertainty propagates in queueing models with unreliable servers, improving upon traditional Monte Carlo approaches.

## Contribution

The paper develops a Polynomial Chaos expansion framework for sensitivity analysis and uncertainty propagation in queueing systems with server breakdowns, offering computational advantages.

## Key findings

- Polynomial Chaos outperforms Monte Carlo in efficiency.
- Reliable Sobol' indices for parameter importance.
- Accurate statistical moments of system performance.

## Abstract

In this paper, we develop a numerical approach based on Chaos expansions to analyze the sensitivity and the propagation of epistemic uncertainty through a queueing systems with breakdowns. Here, the quantity of interest is the stationary distribution of the model, which is a function of uncertain parameters. Polynomial chaos provide an efficient alternative to more traditional Monte Carlo simulations for modelling the propagation of uncertainty arising from those parameters. Furthermore, Polynomial chaos expansion affords a natural framework for computing Sobol' indices. Such indices give reliable information on the relative importance of each uncertain entry parameters. Numerical results show the benefit of using Polynomial Chaos over standard Monte-Carlo simulations, when considering statistical moments and Sobol' indices as output quantities.