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Zero-automatic queues and product form

Part of: Computer system organization Special processes

Published online by Cambridge University Press:  01 July 2016

Thu-Ha Dao-Thi  and
Jean Mairesse
Thu-Ha Dao-Thi*
Affiliation:
LIAFA
Jean Mairesse*
Affiliation:
LIAFA
*
∗ Postal address: LIAFA, CNRS-Université Paris 7, case 7014, 2 place Jussieu, 75251 Paris Cedex 05, France.
∗ Postal address: LIAFA, CNRS-Université Paris 7, case 7014, 2 place Jussieu, 75251 Paris Cedex 05, France.
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Abstract

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We introduce and study a new model: zero-automatic queues. Roughly, zero-automatic queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The salient result is that all stable zero-automatic queues have a product form stationary distribution and a Poisson output process. When considering the two simplest and extremal cases of zero-automatic queues, we recover the simple M/M/1 queue and Gelenbe's G-queue with positive and negative customers.

Keywords

Queueing theoryM/M/1 queueG-queuequasi-reversibilityproduct formquasi-birth-and-death process

MSC classification

Primary: 60K25: Queueing theory 68M20: Performance evaluation; queueing; scheduling
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 2 , June 2007 , pp. 429 - 461
Copyright
Copyright © Applied Probability Trust 2007 

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