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The single-server queue with independent GI/G and M/G input streams

Published online by Cambridge University Press:  01 July 2016

Teunis J. Ott
Teunis J. Ott*
Affiliation:
Bell Communications Research
*
∗Postal address: Bell Communications Research, 435 South Street, Morristown, NJ 07960-1961, USA.
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Abstract

This paper studies the single-server queueing system with two independent input streams: a GI/G and an M/G stream. A new proof is given of an old result which shows how this system can be transformed into an equivalent ‘single input stream’ GI/G/1 queue, and methods to study that equivalent system numerically are given. As part of the numerical analysis, algorithms are given to compute the moments and the distribution function of busy periods in the M/G/1 queue, and of other related busy periods. Special attention is given to the single-server queue with independent D/G and M/G input streams.

This work is to be used in the modeling of real-time computer systems, which can often be described as a single-server queueing system with independent D/G and M/G input streams, see for example Ott (1984b).

Keywords

MULTIPLE INPUT STREAMSNUMERICAL METHODSBUSY PERIODPHASE-TYPE METHODSWIENER–HOPFALMOST PHASE TYPEGENERALIZED PHASE TYPEPOLLACZEK–KHINCHINESTOCHASTIC DECOMPOSITION
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 1 , March 1987 , pp. 266 - 286
Copyright
Copyright © Applied Probability Trust 1987 

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