Stability in queueing networks via the finite decomposition property

Determination of the stability behavior of a queueing network is an important part of analyzing such systems. Gamarnik and Hasenbein (2005) have shown that if a fluid network has the finite decomposition property (FDP) and is not weakly stable, then any queueing network associated with the fluid network is not rate stable. In Gamarnik and Hasenbein's paper, the FDP was demonstrated for two station queueing networks only. In this paper, we show that the property holds for certain classes of queueing networks with any number of stations, thus allowing one to completely analyze the global stability of such queueing networks via the fluid model.