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

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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https://hal.inria.fr/hal-00717735
Contributor : Jean-Marc Lasgouttes <>
Submitted on : Friday, July 13, 2012 - 2:58:45 PM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM
Long-term archiving on: : Sunday, October 14, 2012 - 3:05:15 AM

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  • HAL Id : hal-00717735, version 1
  • ARXIV : 1207.3237

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Guy Fayolle, Jean-Marc Lasgouttes. Asymptotics and scalings for large product-form networks via the Central Limit Theorem. Markov Processes and Related Fields, Polymath, 1996, 2 (2), pp.317-348. ⟨hal-00717735⟩

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