  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.
