Zero-automatic networks

We continue the study of zero-automatic queues first introduced in [3]. These queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The simple M/M/1 queue and Gelenbe’s G-queue with positive and negative customers are the two simplest 0-automatic queues. All 0-automatic queues are quasi-reversible [3]. In this paper, we introduce and study networks of 0-automatic queues. We consider two types of networks, with either a Jackson-like or a Kelly-like routing mechanism. In both cases, and under the stability condition, we prove that the stationary distribution of the buffer content has a “product-form” and can be explicitly determined. Keywords Queueing theory, Jackson network, Kelly network, quasireversibility, product form.

• Type: Conference
• Year: 2006
• Where: VALUETOOLS
• Authors: Thu-Ha Dao-Thi, Jean Mairesse
• Keywords: 0-automatic Queues, Hardware, Simplest 0-automatic Queues, VALUETOOLS 2006, Zero-automatic Queues