Research Article
Zero-automatic networks
@INPROCEEDINGS{10.1145/1190095.1190098, author={Thu-Ha DAO-THI and Jean MAIRESSE}, title={Zero-automatic networks}, proceedings={1st International ICST Conference on Performance Evaluation Methodologies and Tools}, publisher={ACM}, proceedings_a={VALUETOOLS}, year={2012}, month={4}, keywords={Queueing theory Jackson network Kelly network quasireversibility product form.}, doi={10.1145/1190095.1190098} }- Thu-Ha DAO-THI
Jean MAIRESSE
Year: 2012
Zero-automatic networks
VALUETOOLS
ACM
DOI: 10.1145/1190095.1190098
Abstract
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.
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