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Les files et les reseaux zero-automatiques

Abstract : We introduce and study a new model: Zero-automatic queues. First, we consider the service discipline First In First Out. Roughly, 0-automatic queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. When considering the two simplest and extremal cases of 0-automatic queues, we recover the simple M/M/1 queue, and Gelenbe's G-queue with positive and negative customers.
The salient result is that all stable 0-automatic queues have a product form stationary distribution and a Poisson departure process. This is a crucial point to build a network of 0-automatic queues with product form stationary distribution.
We consider two types of networks, with either a Jackson-like or a Kelly-like routing mechanism. In both cases, and under the stationary condition, we prove that the stationary distribution has a product form and can be explicitly determined. Furthermore, the departure process out of the network is Poisson.
At last, consider the 0-automatic queues with the service discipline Last In First Out. Some nice properties of the FIFO 0-automatic queues still hold for the LIFO queue, but not all of them. We obtain interesting results by comparing the stability region of the same 0-automatic queue under the two disciplines FIFO and LIFO.
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https://tel.archives-ouvertes.fr/tel-00195119
Contributor : Thu Ha Dao Thi <>
Submitted on : Thursday, November 6, 2008 - 10:20:02 PM
Last modification on : Friday, March 27, 2020 - 3:45:00 AM
Long-term archiving on: : Wednesday, September 22, 2010 - 10:41:19 AM

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  • HAL Id : tel-00195119, version 2

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Thu Ha Dao Thi. Les files et les reseaux zero-automatiques. Réseaux et télécommunications [cs.NI]. Université Paris-Diderot - Paris VII, 2007. Français. ⟨tel-00195119v2⟩

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