NDLI: Zero-Automatic Networks

Content Provider	Springer Nature Link
Author	Dao Thi, Thu Ha Mairesse, Jean
Copyright Year	2008
Abstract	We continue the study of zero-automatic queues first introduced in Dao-Thi and Mairesse (Adv Appl Probab 39(2):429–461, 2007). 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 stable 0-automatic queues have an explicit “multiplicative” stationary distribution and a Poisson departure process (Dao-Thi and Mairesse, Adv Appl Probab 39(2):429–461, 2007). 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 contents has a “product-form” and can be explicitly determined. Furthermore, the departure process out of the network is Poisson.
Starting Page	499
Ending Page	536
Page Count	38
File Format	PDF
ISSN	09246703
Journal	Discrete Event Dynamic Systems
Volume Number	18
Issue Number	4
e-ISSN	15737594
Language	English
Publisher	Springer US
Publisher Date	2008-09-16
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Queueing theory Jackson network Kelly network Product form Zero-automatic Manufacturing, Machines, Tools Electronic and Computer Engineering Convex and Discrete Geometry Operations Research/Decision Theory Systems Theory, Control
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering Modeling and Simulation

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