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arXiv · 0707.3449

Zero-automatic queues and product form

Thu-Ha Dao-Thi·Jean Mairesse
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Abstract

We introduce and study a new model: 0-automatic queues. Roughly, 0-automatic queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The salient result is that all stable 0-automatic queues have a product form stationary distribution and a Poisson output process. 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.

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Thu-Ha Dao-Thi, Jean Mairesse. 2007-07-23. Zero-automatic queues and product form. https://arxiv.org/abs/0707.3449

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