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VALUETOOLS
2006
ACM

Zero-automatic networks

10 years 28 days ago
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.
Thu-Ha Dao-Thi, Jean Mairesse
Added 14 Jun 2010
Updated 14 Jun 2010
Type Conference
Year 2006
Where VALUETOOLS
Authors Thu-Ha Dao-Thi, Jean Mairesse
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