Uncertainty quantification and global sensitivity analysis of an M/G/1 retrial queue with Bernoulli schedule

In this paper, we are interested in studying uncertainty quantification and global sensitivity analysis in retrial queueing models. Specifically, we investigate the M/G/1 retrial queue with priority customers, Bernoulli schedule and general retrial times. We develop a new methodology for integrating epistemic uncertainties into the computation of performance measures of retrial queueing models, where these measures are considered as functions of the input random parameters and approximated with polynomial chaos expansions. In order to perform global sensitivity analysis, we use Sobol' indices which allow us to make an importance ranking of parameters. In addition, we characterise statistically several performance measures, given that distribution of the model parameter expressing the uncertainty about the exact parameter value is known. Furthermore, we use the Markov inequality to assess the risk induced by working with uncertain performance measures instead of that evaluated at fixed parameters. Several numerical results are provided and compared to Monte Carlo simulations ones.