A conservation property for general GI/G/1 queues with an application to tandem queues
- 1 March 1979
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 11 (03) , 660-672
- https://doi.org/10.1017/s0001867800032869
Abstract
We show that, if the input process of a generalGI/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
This publication has 11 references indexed in Scilit:
- Networks of queues and the method of stagesAdvances in Applied Probability, 1976
- Queueing output processesAdvances in Applied Probability, 1976
- Networks of queuesAdvances in Applied Probability, 1976
- Renewal Theory for Functionals of a Markov Chain with General State SpaceThe Annals of Probability, 1974
- On the use of a fundamental identity in the theory of semi-Markov queuesAdvances in Applied Probability, 1972
- Markov additive processes. IProbability Theory and Related Fields, 1972
- Two servers in series, studied in terms of a Markov renewal branching processAdvances in Applied Probability, 1970
- The departure process from the GI/G/1 QueueJournal of Applied Probability, 1969
- On semi-Markov processes on arbitrary spacesMathematical Proceedings of the Cambridge Philosophical Society, 1969
- The Correlation Structure of the Output Process of Some Single Server Queueing SystemsThe Annals of Mathematical Statistics, 1968