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arXiv · 1207.3237

Asymptotics and scalings for large product-form networks via the Central Limit Theorem

Guy Fayolle·Jean-Marc Lasgouttes
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Abstract

The asymptotic behaviour of a closed BCMP network, with $n$ queues and $m_n$ clients, is analyzed when $n$ and $m_n$ become simultaneously large. Our method relies on Berry-Esseen type approximations coming in the Central Limit Theorem. We construct critical sequences $m^0_n$, which are necessary and sufficient to distinguish between saturated and non-saturated regimes for the network. Several applications of these results are presented. It is shown that some queues can act as bottlenecks, limiting thus the global efficiency of the system.

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Guy Fayolle, Jean-Marc Lasgouttes. 2012-07-13. Asymptotics and scalings for large product-form networks via the Central Limit Theorem. https://arxiv.org/abs/1207.3237

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