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Journal Articles Markov Processes And Related Fields Year : 1996

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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Dates and versions

hal-00717735 , version 1 (13-07-2012)

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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, 1996, 2 (2), pp.317-348. ⟨hal-00717735⟩

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