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Asymptotic stationarity of queueing processes

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Władysław Szczotka
Władysław Szczotka*
Affiliation:
University of Wroclaw
*
∗Postal address: Mathematical Institute of Wroclaw University, Pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland.
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Abstract

We show that if an input process ζ to a queue is asymptotic stationary in some sense, satisfies a condition AB and some other natural conditions, then the output processes (w, ζ) and (w, q,ζ) are asymptotic stationary in the same sense. Here, w and q are the waiting time and queue length processes, respectively.

Keywords

QUEUEING SYSTEMWAITING TIME PROCESSQUEUE LENGTH PROCESSASYMPTOTIC STATIONARITYWEAK CONVERGENCECONVERGENCE IN TOTAL VARIATIONERGODICITY

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 4 , December 1997 , pp. 1041 - 1048
Copyright
Copyright © Applied Probability Trust 1997 

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References

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