Zero-automatic queues and product form
Discrete Mathematics
2007-07-25 v1
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.
Cite
@article{arxiv.0707.3449,
title = {Zero-automatic queues and product form},
author = {Thu-Ha Dao-Thi and Jean Mairesse},
journal= {arXiv preprint arXiv:0707.3449},
year = {2007}
}