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Exponential upper bounds via martingales for multiplexers with Markovian arrivals

Published online by Cambridge University Press:  14 July 2016

E. Buffet*
Affiliation:
Dublin City University
N. G. Duffield*
Affiliation:
Dublin City University
*
Postal address: School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland.
Postal address: School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland.

Abstract

We obtain explicit upper bounds in closed form for the queue length in a slotted time FCFS queue in which the service requirement is a sum of independent Markov processes on the state space {0, 1}, with integral service rate. The bound is of the form [queue length for any where c < 1 and y > 1 are given explicitly in terms of the parameters of the model. The model can be viewed as an approximation for the burst-level component of the queue in an ATM multiplexer. We obtain heavy traffic bounds for the mean queue length and show that for typical parameters this far exceeds the mean queue length for independent arrivals at the same load. We compare our results on the mean queue length with an analytic expression for the case of unit service rate, and compare our results on the full distribution with computer simulations.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

The authors are also affiliated to the School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Ireland.

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