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Imbedded and non-imbedded stationary characteristics of queueing systems with varying service rate and point processes

Published online by Cambridge University Press:  14 July 2016

D. König  and
V. Schmidt
D. König*
Affiliation:
Bergakademie Freiberg
V. Schmidt*
Affiliation:
Bergakademie Freiberg
*
∗Postal address: Sektion Mathematik, Bergakademie Freiberg, 92 Freiberg (Sachs), DDR.
∗Postal address: Sektion Mathematik, Bergakademie Freiberg, 92 Freiberg (Sachs), DDR.
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Abstract

In this paper a unified approach is used for proving relationships between customer-stationary and time-stationary characteristics of service systems with varying service rate and point processes. This approach is based on an intensity conservation principle for general stationary continuous-time processes with imbedded stationary marked point processes. It enables us to work under weaker independence assumptions than usual in queueing theory.

Keywords

STATIONARY QUEUESVARYING SERVICE RATEPOINT PROCESSESINTENSITY CONSERVATION PRINCIPLECUSTOMER- AND TIME-STATIONARY PROBABILITIESQUEUE LENGTHWAITING TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 753 - 767
Copyright
Copyright © Applied Probability Trust 1980 

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