On Comparison of Multiserver Systems with Multicomponent Mixture Distributions

Abstract

In this paper, we introduce and study the relations between parameters of the m-component mixture distributions which imply the stochastic and failure rate comparisons. Then we apply the failure rate and stochastic ordering techniques to construct the upper and lower bounds for the steady-state performance indexes in a multiserver queueing system with multicomponent exponential-Pareto mixture service time distribution. The uniform distance between multicomponent mixture distribution and its parent distribution is discussed. The obtained theoretical results are then illustrated by a few numerical examples based on the regenerative simulation multiserver queueing systems with mixture service time distributions.