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Busy periods in time-dependent M/G/1 queues

Published online by Cambridge University Press:  01 July 2016

Stig. I. Rosenlund
Stig. I. Rosenlund*
Affiliation:
University of Göteborg
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Abstract

A single-server queue with batch arrivals in a non-homogeneous Poisson process and with balking is studied with respect to the busy period, using supplementary variables. A system of integral equations is obtained on the base of which the transforms are expressed in series. For the homogeneous case, assuming finite waiting room, the solutions are obtained via Cramer's rule. This gives asymptotic expressions for the expectations for large arrival intensity. An efficiency measure giving the long run loss probability is given. For a special case contour integral representations are given as solutions.

Keywords

BUSY PERIODBALKINGBATCH ARRIVALSTIME-DEPENDENT ARRIVAL INTENSITYLINEAR EQUATIONS IN TRANSFORMSFINITE WAITING ROOMDETERMINANT CALCULUS
Type
Research Article
Information
Advances in Applied Probability , Volume 8 , Issue 1 , March 1976 , pp. 195 - 208
Copyright
Copyright © Applied Probability Trust 1976 

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References

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