# Dynamic Routing in the Mean-Field Approximation

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1 HIPERCOM - High performance communication Inria Paris-Rocquencourt, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR

Abstract : A queuing system is considered, with stations $1$, $2$, where station $i$ contains a collection $S i$ of infinite-buffer FCFS single servers. The number of servers in each $S i$ is $N$, and we assume that $N$ is large formally, $N\to\infty$. The system is fed by a Poisson flow of rate $2\l N$, with i.i.d. exponential service times of mean one. Upon arrival, a customer chooses two servers according to the following rule. He performs two independent trials, each time choosing station $1$ with probability $p 1$ and $2$ with probability $p 2=1-p 1$ and then choosing a server at random from the corresponding collection $S i$. He then selects the server with a shortest queue from the two, breaking ties at random if necessary. We assume that $p 1\geq p 2\geq 0$; the main result is that a the inequalities \$\lambda

Autor: Philippe Jacquet - Yuri Suhov Nikita Vvedenskaya -

Fuente: https://hal.archives-ouvertes.fr/

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