Annals of Operations Research

, Volume 247, Issue 1, pp 211–227 | Cite as

A functional approximation for retrial queues with two way communication

Article

Abstract

In this paper we consider retrial queues with two way communication and finite orbit. We will develop a functional approximation of the stationary performances of this queue where the parameter of interest is the outgoing rate. Specifically, we will apply the Taylor series expansion method to propagate parametric uncertainty to performance measures. We provide an analysis of the \(\hbox {M}_{1},\, \hbox {M}_{2}/\hbox {G}_{1},\, \hbox {G}_{2}/1\) retrial queue with two way communication and finite orbit. The sensitivity analysis is carried out by considering several numerical examples. More specifically, this paper proposes a numerical approach based on Taylor series expansion with a statistical aspect for analyzing the stationary performances of the considered queueing model, where we assume that the outgoing rate is not assessed in a perfect manner. Additionally, approximate expressions of the probability density functions, the expectation and the variance of the performance measures are obtained and compared to the corresponding Monte Carlo simulations results.

Keywords

Retrial queues Numerical approximation Taylor series expansion Parametric uncertainty Monte Carlo simulation 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BejaiaBejaiaAlgeria
  2. 2.Research Unit LaMOSUniversity of BejaiaBejaiaAlgeria

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