Zero-automatic queues and product form
Thu-Ha Dao-Thi (LIAFA), Jean Mairesse (LIAFA)

TL;DR
This paper introduces 0-automatic queues, a new model with a unique buffering mechanism, demonstrating that all stable instances have a product form stationary distribution and Poisson output, unifying several queue types.
Contribution
The paper defines 0-automatic queues, proves their stability and product form stationary distribution, and connects them to classical queue models like M/M/1 and G-queues.
Findings
All stable 0-automatic queues have a product form stationary distribution.
Stable 0-automatic queues produce a Poisson output process.
Special cases recover M/M/1 and Gelenbe's G-queue models.
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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Taxonomy
TopicsAdvanced Queuing Theory Analysis
