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Stationary queue-length and waiting-time distributions in single-server feedback queues

Published online by Cambridge University Press:  01 July 2016

Ralph L. Disney ,
Dieter König  and
Volker schmidt
Ralph L. Disney*
Affiliation:
Virginia Polytechnic Institute and State University
Dieter König*
Affiliation:
Mining Academy, Freiberg
Volker schmidt*
Affiliation:
Virginia Polytechnic Institute and State University
*
∗Postal address: Department of Industrial Engineering and Operations Research, Virginia Polytechnic and State University, Blacksburg, VA 24061, U.S.A.
∗∗ Postal address: Sektion Mathematik, Bergakademie Freiberg, DDR-9200 Freiberg (Sachs), GDR.
∗∗ Postal address: Sektion Mathematik, Bergakademie Freiberg, DDR-9200 Freiberg (Sachs), GDR.
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Abstract

For M/GI/1/∞ queues with instantaneous Bernoulli feedback time- and customer-stationary characteristics of the number of customers in the system and of the waiting time are investigated. Customer-stationary characteristics are thereby obtained describing the behaviour of the queueing processes, for example, at arrival epochs, at feedback epochs, and at times at which an arbitrary (arriving or fed-back) customer enters the waiting room. The method used to obtain these characteristics consists of simple relationships between them and the time-stationary distribution of the number of customers in the system at an arbitrary point in time. The latter is obtained from the wellknown Pollaczek–Khinchine formula for M/GI/1/∞ queues without feedback.

Keywords

POISSON ARRIVALSTIME- AND CUSTOMER-STATIONARY CHARACTERISTICS
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 2 , June 1984 , pp. 437 - 446
Copyright
Copyright © Applied Probability Trust 1984 

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References

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