Zero-automatic networks

Thu-Ha  DAO-THI; Jean  MAIRESSE

1st International ICST Conference on Performance Evaluation Methodologies and Tools

Research Article

Zero-automatic networks

Cite: BibTeX Plain Text

@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

Thu-Ha DAO-THI¹^,*, Jean MAIRESSE¹^,*

1: LIAFA, University Paris 7, France

*Contact email: daothi@liafa.jussieu.fr, mairesse@liafa.jussieu.fr

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.

Keywords: Queueing theory Jackson network Kelly network quasireversibility product form.

Published: 2012-04-06
Publisher: ACM

: http://dx.doi.org/10.1145/1190095.1190098