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An analysis of a modified M/G/1 queue using a martingale technique

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Matthew Roughan
Matthew Roughan*
Affiliation:
CSSIP, Adelaide
*
∗ Postal address: Cooperative Research Centre for Sensor Signal and Information Processing, SPRI Building, Technology Park, The Levels, Adelaide, South Australia 5095, Australia.
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Abstract

We consider a variation of the M/G/1 queue in which, when the system contains more than k customers, it switches from its initial general service distribution to a different general service distribution until the server is cleared, whereupon it switches back to the original service distribution. Using a technique due to Baccelli and Makowski we define a martingale with respect to an embedded process and from this arrive at a relationship between the process and a modified Markov renewal process. Using this an analysis of the stationary behaviour of the queue is possible.

Keywords

M/G/1 QUEUETHRESHOLDMARTINGALESDOOB'S OPTIONAL SAMPLING THEOREMQUEUEING THEORY

MSC classification

Primary: 60G42: Martingales with discrete parameter
Secondary: 60G55: Point processes

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 1 , March 1996 , pp. 224 - 238
Copyright
Copyright © Applied Probability Trust 1996 

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References

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