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ON THE VARIANCES OF SYSTEM SIZE AND SOJOURN TIME IN A DISCRETE-TIME DAR(1)/D/1 QUEUE

Published online by Cambridge University Press:  21 July 2011

Daniel Wei-Chung Miao  and
Hung Chen
Daniel Wei-Chung Miao
Affiliation:
National Taiwan University of Science and Technology, Taipei, 106, Taiwan E-mail: miao@mail.ntust.edu.tw
Hung Chen
Affiliation:
National Taiwan University, Taipei, 106, Taiwan E-mail: hchen@math.ntu.edu.tw
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Abstract

We consider a discrete-time DAR(1)/D/1 queue and provide an analysis on the variances of both its system size and sojourn time. Our approach is simple, but the results are nice, as these variances are found in closed form. We first establish the relation between these variances, based on which we then use the conditioning technique to analyze the expected cross terms that come from its system recurrence relation. The closed-form results allow us to explicitly examine the effect from the batch size distribution and the autocorrelation parameter p. It is observed that as p grows toward 1, the standard deviations of the two performance measures will blow up in same asymptotic order of O(1/(1−p)) as their means. These are demonstrated through numerical examples.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 4 , October 2011 , pp. 519 - 535
Copyright
Copyright © Cambridge University Press 2011

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