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Stationary queue-length characteristics in queues with delayed feedback

Published online by Cambridge University Press:  14 July 2016

Dieter König  and
Volker Schmidt
Dieter König*
Affiliation:
Mining Academy, Freiberg
Volker Schmidt*
Affiliation:
Mining Academy, Freiberg
*
∗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

A class of two-node queueing networks with general stationary ergodic governing sequence is considered. This means that, in particular, a non-Poissonian arrival process and dependent service times, as well as a non-Bernoulli feedback mechanism are admitted. A mixing condition ensures that the limiting distributions of the number of customers in the nodes observed in continuous time as well as at certain embedded epochs can be expressed by the Palm distributions of appropriately chosen marked point processes. This gives the possibility of connecting the classical concept of embedding with a general point-process approach. Furthermore, it leads to simple proofs of relationships between the limiting distributions. An example is given to illustrate how these relationships can be used to derive explicit formulas for various stationary queueing characteristics.

Keywords

QUEUEING NETWORKSDELAYED FEEDBACKQUEUE LENGTHEMBEDDINGLIMIT DISTRIBUTIONSRELATIONSHIPSPOINT PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 394 - 407
Copyright
Copyright © Applied Probability Trust 1985 

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References

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