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# Thermodynamic Limit and Propagation of Chaos in Polling Networks

Abstract : {${\P\n,¸N\geq 1 }$ is a sequence of standard polling networks, consisting of $N$ nodes attended by $V\n$ mobile servers. When a server arrives at a node $i$, he serves one of the waiting customers, if any, and then moves to node $j$ with probability $p_{ij}\n$. Customers arrive according to a Poisson process. Service requirements and switch-over times between nodes are independent exponentially distributed random variables. The behavior of $\P\n$ is analyzed in {\em thermodynamic limit}, i.e when both $N$ and $V\n$ tend to infinity, with \$U\egaldef\lim_{N\rightarrow\infty}V\n/N,\ 0
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https://hal.inria.fr/inria-00073291
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Submitted on : Wednesday, May 24, 2006 - 12:26:56 PM
Last modification on : Friday, February 4, 2022 - 3:10:29 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:25:20 PM

### Identifiers

• HAL Id : inria-00073291, version 1

### Citation

Franck Delcoigne, Guy Fayolle. Thermodynamic Limit and Propagation of Chaos in Polling Networks. [Research Report] RR-3398, INRIA. 1998. ⟨inria-00073291⟩

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