Asymptotics and scalings for large product-form networks via the Central   Limit Theorem
  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. 
Guy Fayolle (INRIA Rocquencourt), Jean-Marc Lasgouttes (INRIA   Rocquencourt)
math.PR