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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 methodrelies on Berry-Esseen type approximations coming in the Central Limit Theorem.We construct critical sequences $m^0_n$, which are necessary and sufficient todistinguish between saturated and non-saturated regimes for the network.Several applications of these results are presented. It is shown that somequeues can act as bottlenecks, limiting thus the global efficiency of thesystem.

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