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Relationships and decomposition in the delayed bernoulli feedback queueing system

Published online by Cambridge University Press:  14 July 2016

D. König  and
M. Miyazawa
D. König*
Affiliation:
Bergakademie Freiberg
M. Miyazawa*
Affiliation:
Science University of Tokyo
*
∗ Postal address: Sektion Mathematik, Bergakademie Freiberg, DDR-9200 Freiberg (Sachs), GDR.
∗∗ Postal address: Department of Information Sciences, Science University of Tokyo, Noda City, Chiba 278, Japan.
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Abstract

For the delayed Bernoulli feedback queue with first come–first served discipline under weak assumptions a relationship for the generating functions of the joint queue-length distribution at various points in time is given. A decomposition for the generating function of the stationary total queue length distribution has been proven. The Laplace-Stieltjes transform of the stationary joint workload distribution function is represented by its marginal distributions. The arrival process is Poisson, renewal or arbitrary stationary, respectively. The service times can form an i.i.d. sequence at each queue. Different kinds of product form of the generating function of the joint queue-length distribution are discussed.

Keywords

DELAYED BERNOULLI FEEDBACK QUEUESTEADY STATE DISTRIBUTIONBASIC EQUATIONQUEUE LENGTHWORK LOADDECOMPOSITIONAPPROXIMATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 169 - 183
Copyright
Copyright © Applied Probability Trust 1988 

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