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Performance analysis of the discrete-time GI/Geom/1/N queue

Part of: Computer system organization Special processes

Published online by Cambridge University Press:  14 July 2016

M. L. Chaudhry  and
U. C. Gupta
M. L. Chaudhry*
Affiliation:
Royal Military College of Canada
U. C. Gupta*
Affiliation:
Indian Institute of Technology
*
∗ Postal address: Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario, K7K 5L0, Canada.
∗∗ Postal address: Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India.
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Abstract

This paper presents an analysis of the single-server discrete-time finite-buffer queue with general interarrival and geometric service time, GI/Geom/1/N. Using the supplementary variable technique, and considering the remaining interarrival time as a supplementary variable, two variations of this model, namely the late arrival system with delayed access (LAS-DA) and early arrival system (EAS), have been examined. For both cases, steady-state distributions for outside observers as well as at random and prearrival epochs have been obtained. The waiting time analysis has also been carried out. Results for the Geom/G/1/N queue with LAS-DA have been obtained from the GI/Geom/1/N queue with EAS. We also give various performance measures. An algorithm for computing state probabilities is given in an appendix.

Keywords

DISCRETE-TIMERECURSIVESTEADY-STATE PROBABILITY DISTRIBUTIONSUPPLEMENTARY VARIABLE

MSC classification

Primary: 60K25: Queueing theory
Secondary: 68M20: Performance evaluation; queueing; scheduling

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 1 , March 1996 , pp. 239 - 255
Copyright
Copyright © Applied Probability Trust 1996 

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