Zero-automatic queues and product form

Details Zero-automatic queues and product form Zero-automatic queues and product form

2007-07-23

arxiv.org/abs/0707.3449v1

Advances in Applied Probability 39, 2 (2007) 429-461

Computer Science

Discrete Mathematics

Scientific paper

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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