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# Asymptotic Behavior of a Multiplexer Fed by a Long-Range Dependent Process

Abstract : In this paper we study the asymptotic behavior of the tail of the stationary backlog distribution in a single server queue with constant service capacity c, fed by the so-called «$M/G/\infty$ input process» or «Cox input process». Asymptotic lower bounds are obtained for any distribution $G$ and asymptotic upper bounds are derived when $G$ is a subexponential distribution. We find the bounds to be tight in some instances, e.g., $G$ corresponding to either the Pareto or lognormal distribution and $c-\rho<1$, where $\rho$ is the arrival rate to the buffer.
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https://hal.inria.fr/inria-00073459
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Submitted on : Wednesday, May 24, 2006 - 12:51:45 PM
Last modification on : Friday, February 4, 2022 - 3:16:08 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:47:15 PM

### Identifiers

• HAL Id : inria-00073459, version 1

### Citation

Zhen Liu, Philippe Nain, Don Towsley, Zhi-Li Zhang. Asymptotic Behavior of a Multiplexer Fed by a Long-Range Dependent Process. RR-3230, INRIA. 1997. ⟨inria-00073459⟩

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