An interpolation approximation for the GI/G/1 queue based on multipoint Padé approximation

An interpolation approximation for the GI/G/1 queue based on multipoint Padé approximation

0.00 Avg rating0 Votes
Article ID: iaor20002513
Country: United States
Volume: 26
Issue: 3/4
Start Page Number: 269
End Page Number: 284
Publication Date: Nov 1997
Journal: Queueing Systems
Authors: ,
Keywords: GI/G/1 queues
Abstract:

The performance evaluation of many complex manufacturing, communication and computer systems has been made possible by modeling them as queueing systems. Many approximations used in queueing theory have been drawn from the behavior of queues in light and heavy traffic conditions. In this paper, we propose a new approximation technique, which combines the light and heavy traffic characteristics. This interpolation approximation is based on the theory of multipoint Padé approximation which is applied at two points: light and heavy traffic. We show how this can be applied for estimating the waiting time moments of the GI/G/1 queue. The light traffic derivatives of any order can be evaluated using the MacLaurin series analysis procedure. The heavy traffic limits of the GI/G/1 queue are well known in the literature. Our technique generalizes the previously developed interpolation approximations and can be used to approximate any order of the waiting time moments. Through numerical examples, we show that the moments of the steady state waiting time can be estimated with extremely high accuracy under all ranges of traffic intensities using low orders of the approximant. We also present a framework for the development of simple analytical approximation formulas.

Reviews

Required fields are marked *. Your email address will not be published.