Uncertainty quantification in finite queues with dependent breakdowns

Abstract

This paper proposes a new framework within which one can incorporate uncertainty in input parameters tocompute performance measures of queueing models with dependent breakdowns. The proposed methodology allows us tocharacterize statistically the performance measures of the studied queueing models. The developed approach is suited forqueueing models in which the stationary distribution of the associated Markov chain describing their state can be numericallyassessed, so then one can encompass randomness after the numerical evaluation. Specifically, an efficient implementationof computational algorithm is investigated to analyze the M/G/1/N queueing model with dependent breakdowns. Variousquantities of interest characterizing the uncertain performance measures of the M/G/1/N queueing model with dependentbreakdowns are obtained; especially we are interested in computing the mean, the variance, the skewness and the kurtosisof the underlying performance. In addition, we show how to use the Markov’s inequality to estimate the risk incurredby ignoring parameter uncertainty in computing performance measures of queueing models with dependent breakdowns.Several numerical examples are presented to illustrate the potential of the proposed approach.