An interpolation approximation for the GI/G/1 queue based on multipoint Padé approximation |
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Authors: | Girish Muckai K Hu Jian-Qiang |
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Institution: | (1) Telesis Technologies Laboratory, 5000 Executive Parkway, Suite 333, San Ramon, CA 94583, USA;(2) Dept. of Manufacturing Engineering, Boston University, 15 St. Mary's Street, Boston, MA 02215, USA |
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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.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | GI/G/1 queue heavy traffic limits MacLaurin series multipoint Padé approximation |
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