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The derivation of invariance relations in complex queueing systems with stationary inputs

Published online by Cambridge University Press:  01 July 2016

Masakiyo Miyazawa
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
*
∗ Postal address: Department of Information Sciences. Faculty of Science and Technology, Science University of Tokyo, Noda City, Chiba 278, Japan.
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Abstract

We discuss a method of obtaining invariance relations in complex systems by using the theory of point processes. New formulae are given for obtaining them generally, and in particular in many-stage models such as tandem and network queues. The formulae are shown to be useful by applications to a many-server queue and a tandem queue. Stochastic inequalities in a tandem queue are also discussed using the invariance relations obtained.

Keywords

MANY-SERVER QUEUETANDEM QUEUEMANY-STAGE QUEUESTEADY-STATE PROBABILITYPOINT PROCESSQUEUE LENGTHRESIDUAL SERVICE TIMESTOCHASTIC INEQUALITY

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 4 , December 1983 , pp. 874 - 885
Copyright
Copyright © Applied Probability Trust 1983 

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