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A conservation property for general GI/G/1 queues with an application to tandem queues

Published online by Cambridge University Press:  01 July 2016

E. Nummelin
E. Nummelin*
Affiliation:
Helsinki University of Technology
*
∗Postal address: Institute of Mathematics, Helsinki University of Technology, 02150 Espoo 15, Finland.
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Abstract

We show that, if the input process of a general GI/G/1 queue is a positive recurrent Markov renewal process then the output process, too, is a positive recurrent Markov renewal process (the conservation property). As an application we consider a general tandem queue and prove a total variation limit theorem for the associated waiting and service times.

Keywords

QUEUEINPUT PROCESSOUTPUT PROCESSMARKOV RENEWAL PROCESSMARKOV CHAINHARRIS RECURRENT
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 3 , September 1979 , pp. 660 - 672
Copyright
Copyright © Applied Probability Trust 1979 

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