Zero-Automatic Queues

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 0-automatic queues are quasi-reversible. 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.

• Type: Conference
• Year: 2005
• Where: EPEW
• Authors: Thu-Ha Dao-Thi, Jean Mairesse
• Keywords: 0-automatic Queues, EPEW 2005, Simple M/m/1 Queue, Special Buffering Mechanism