# Asymptotics and Scalings for Large Closed Product-Form Networks via the Central Limit Theorem

Abstract : We consider a closed product-form network with $n$ queues and $m$ clients. We are interested in its asymptotic behaviour when $m$ and $n$ become simultaneously large. Our method relies on Berry-Esseen type approximations of the Central Limit Theorem. This leads to simple and natural conditions applicable to general networks, whereas the purely analytical methods used previously imposed restrictions on the queues. In particular, we show that the «optimal» dependence of $m$ w.r.t. $n$ is not necessarily linear. An application of these results to a transportation network is presented. We show how some queues can act as bottlenecks, limiting thus the efficiency of the whole system.This report contains and extends the results obtained in~\cite{FayLas:1}.
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Cited literature [11 references]

https://hal.inria.fr/inria-00073938
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Submitted on : Wednesday, May 24, 2006 - 2:07:44 PM
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• HAL Id : inria-00073938, version 1

### Citation

Guy Fayolle, Jean-Marc Lasgouttes. Asymptotics and Scalings for Large Closed Product-Form Networks via the Central Limit Theorem. [Research Report] RR-2754, INRIA. 1995. ⟨inria-00073938⟩

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