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# Dobrushin's Mean-Field Approximation for a Queue With Dynamic Routing

Abstract : A queueing system is considered, with a large number $N$ of identical infinite-buffer FCFS single-servers. The system is fed by a Poisson flow of rate $\l N$, with i.i.d. service times, under the non-overload condition. Each arriving task joins a server by selecting it from an independently (and `completely randomly') chosen collection of $m\ll N$ servers, on the basis of some fixed dynamic routing policy. We discuss various properties of such a system as $N\to\infty$. In particular, a natural limiting random process describing statistical properties of the system turns out to be deterministic.
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https://hal.inria.fr/inria-00073361
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Submitted on : Wednesday, May 24, 2006 - 12:37:12 PM
Last modification on : Friday, February 4, 2022 - 3:08:11 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:52:00 PM

### Identifiers

• HAL Id : inria-00073361, version 1

### Citation

Nikita D. Vvedenskaya, Yuri M. Suhov. Dobrushin's Mean-Field Approximation for a Queue With Dynamic Routing. [Research Report] RR-3328, INRIA. 1997. ⟨inria-00073361⟩

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