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

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 modeling 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.

Keywords:

• Chaos expansions
• Epistemic uncertainty
• Orthogonal polynomial
• Sobol’ indices
• Unreliable queueing model

AMS 2010 subject classifications:

• 90B22
• 60K25
• 65C05
• 65C50

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable remarks and constructive comments that contributed to improve the final version of the paper.