Sensitivity Analysis and Simulation of a Multiserver Queueing System with Mixed Service Time Distribution

Abstract

The motivation of mixing distributions in communication/queueing systems modeling is that some input data (e.g., service time in queueing models) may follow several distinct distributions in a single input flow. In this paper, we study the sensitivity of performance measures on proximity of the service time distributions of a multiserver system model with two-component Pareto mixture distribution of service times. The theoretical results are illustrated by numerical simulation of the M/G/c systems while using the perfect sampling approach.

On Comparison of Multiserver Systems with Multicomponent Mixture Distributions

“…Theorem 4. If the parameters of (k + n)-component Exponential-Pareto mixture distribution (12) satisfy the following conditions…”

“…To illustrate, assume that a random variable X has hyperexponential distribution (15) and a random variable Z has two-component Pareto mixture (17). Then it has been shown in [12] that…”

“…It is easy to check that assumptions (13) are satisfied and it is seen that the distributions are ordered in failure rate as in accordance with inequalities(14). Now we consider three two-component mixtures which are particular cases of(12). Suppose that X has the hyperexponential distribution (k = 2, n = 0 in (12)),…”