IJPAM: Volume 30, No. 4 (2006)

ERGODICITY CONDITIONS IN
A SIMPLE BEST EFFORT QUEUEING NETWORKS

Abdeldjebbar Kandouci$^1$, Abdelmadjid Ezzine$^2$, Toufik Guendouzi$^3$
$^{1,2,3}$Laboratory of Mathematics
Djilali Liabes University
P.O. Box 89, Sidi Bel Abbes, 22000, ALGERIA
$^1$e-mail: kandouci1974@yahoo.fr
$^2$e-mail: abdelmadjide@yahoo.fr
$^3$e-mail: tguendouzi@laposte.net


Abstract.In this article, we are interested in a network of the type ``best effort" where the band-width available is distributed in the equitable way between the users, by considering a policy known as ``min" which is in fact an approximation of the traditional policy of ``Equite Max-Min". A simple example of such a model is a star distribution system which we give necessary and sufficient conditions of ergodicity by using Lyapunov functions.

Received: June 1, 2006

AMS Subject Classification: 90B05

Key Words and Phrases: Lyapunov functions, queueing networks, ergodicity

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 4