Abdeldjebbar   Kandouci
Abdelmadjid   Ezzine
Benamar   Chouaf

A New Criterion of Stability for Stochastic Networks With Two Stations and Two Heterogeneous Servers

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 62, 3 - 19 (2007)

MSC: 60K25 Queueing theory
  90B22 Queues and service
  60J10 Makov chains with discrete parameter

Abstract:   We introduce and study a new notion of stability of a stochastic fluid model in terms of random stopping times (partially building on ideas used by Stolyar \cite{kan-stoly} in his deterministic setting). It may be viewed as an analog of the original criterion for random $T$'s (which may differ for different $\varphi$'s). In particular, it is shown that our notion of stability is equivalent to $L_{p}$-stability for some $p > 1 .$ We consider an example of a polling system with tow stations and two servers in which the corresponding fluid model may be unstable in the sense as it was written in (\cite{kan-stoly}) but stable from the generalised viewpoint that we adopt.

Keywords:   stability, queueing networks, polling systems
 

karin.martin@uni-rostock.de
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