Article

Zero-automatic networks

Authors:

Thu-Ha Dao-Thi,

Jean MairesseAuthors Info & Claims

valuetools '06: Proceedings of the 1st international conference on Performance evaluation methodolgies and tools

Pages 3 - es

https://doi.org/10.1145/1190095.1190098

Published: 11 October 2006 Publication History

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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T.-H. Dao-Thi and J. Mairesse. Zero-automatic queues. Formal Techniques for Computer Systems and Business Processes LNCS 3670, p. 64--78, Springer, 2005. A long version is available at http://www.liafa.jussieu.fr/~mairesse/Article/0queue.ps.gz

Digital Library

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Cited By

Dao-Thi TMairesse J(2018)Zero-Automatic NetworksDiscrete Event Dynamic Systems10.1007/s10626-008-0048-118:4(499-536)Online publication date: 24-Dec-2018
https://dl.acm.org/doi/10.1007/s10626-008-0048-1
Liu CQiu J(2017)Performance Study of 802.11w for Preventing DoS Attacks on Wireless Local Area NetworksWireless Personal Communications: An International Journal10.1007/s11277-016-3812-995:2(1031-1053)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1007/s11277-016-3812-9
Do T(2011)Bibliography on G-networks, negative customers and applicationsMathematical and Computer Modelling: An International Journal10.1016/j.mcm.2010.08.00653:1-2(205-212)Online publication date: 1-Jan-2011
https://dl.acm.org/doi/10.1016/j.mcm.2010.08.006

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cover image ACM Other conferences

valuetools '06: Proceedings of the 1st international conference on Performance evaluation methodolgies and tools

October 2006

638 pages

ISBN:1595935045

DOI:10.1145/1190095

General Chairs:
Luciano Lenzini
University of Pisa, Italy
,
Rene Cruz
UCSD, US

Copyright © 2006 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 11 October 2006

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Cited By

Dao-Thi TMairesse J(2018)Zero-Automatic NetworksDiscrete Event Dynamic Systems10.1007/s10626-008-0048-118:4(499-536)Online publication date: 24-Dec-2018
https://dl.acm.org/doi/10.1007/s10626-008-0048-1
Liu CQiu J(2017)Performance Study of 802.11w for Preventing DoS Attacks on Wireless Local Area NetworksWireless Personal Communications: An International Journal10.1007/s11277-016-3812-995:2(1031-1053)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1007/s11277-016-3812-9
Do T(2011)Bibliography on G-networks, negative customers and applicationsMathematical and Computer Modelling: An International Journal10.1016/j.mcm.2010.08.00653:1-2(205-212)Online publication date: 1-Jan-2011
https://dl.acm.org/doi/10.1016/j.mcm.2010.08.006

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