# On the Rates of Convergence of Erlang's Model

Abstract : The convergence to equilibrium of the renormalized M/M/$N/N$ queue is analyzed. Some upper bounds on the distance to equilibrium are given and we prove the cutoff property for two regimes of this queue. We use simple probabilistic methods, such as coupling technics and martingales, to derive our results.
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https://hal.inria.fr/inria-00073321
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 12:32:11 PM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM
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### Identifiers

• HAL Id : inria-00073321, version 1

### Citation

Christine Fricker, Philippe Robert, Danielle Tibi. On the Rates of Convergence of Erlang's Model. [Research Report] RR-3368, INRIA. 1998. ⟨inria-00073321⟩

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